text:
\section{Introduction}
In the course of its evolution, the tidal interaction of a planet with the protoplanetary disc in which
it formed is known to cause a significant change of the planet orbital elements.  In particular, low-mass planets
can experience dramatic changes of their distance from the central star under
the process of Type I migration (Ward 1997; Tanaka et al. 2002). Type II migration concerns more massive planets that are
able to strongly modify the underlying disc structure by creating a gap around their orbit
(Lin \& Papaloizou 1986). In that case,
a planet undergoing Type II migration is locked to the disc viscous evolution and migrates inward on a timescale
corresponding to the disc viscous timescale, provided that the characteristic disc mass is still larger than the planet mass (Nelson et al. 2000).\\
The gravitational torque exerted by the disc on the planet and causing Type I migration  consists of two components. The differential
Lindblad torque results from the angular momentum exchange between the planet and the spiral density waves it
  generates inside the disc.  For sufficiently low-mass planets, the Lindblad torque is well described by
a linear analysis, which shows that the specific value of this torque scales linearly with disc mass and planet mass and as the inverse square of the disc aspect ratio (Tanaka et al. 2002). Although its sign depends on the  density and temperature gradients inside the  disc, the differential Lindblad
torque is generally negative for typical disc models and is therefore responsible for inward migration.\\
The corotation torque is due to the torque exerted by the material located in the coorbital region of the planet. A linear
analysis reveals that the corotation torque consists of a barotropic part  which scales with the vortensity (i.e.
the ratio between the vertical component of the vorticity and the disc surface density) gradient
 (Goldreich \& Tremaine 1979) plus an entropy-related part which scales with the entropy gradient (Baruteau \& Masset 2008; Paardekooper \& Papaloizou 2008).
A negative vortensity (resp. entropy) gradient gives
rise to a positive vortensity (resp. entropy) related corotation torque.
The consequence is that for midly
positive surface density gradients or negative entropy gradients, a positive  corotation torque can eventually counteract the effect of a
negative differential Lindblad torque,  which may stall or even reverse migration (Masset et al. 2006; Paardekooper \& Papaloizou 2009).
 In isothermal discs, the corotation torque is a non-linear process generally referred as the horsehoe drag and whose amplitude
is controlled by advection-diffusion of vortensity inside the horsehoe region. In non-isothermal discs, singular production
of vortensity also arises due to the entropy discontinuity on downstream separatrices (Masset \& Casoli 2009;
Paardekooper et al. 2010) and in that case, the amplitude of the
corotation torque is therefore powered by advection-diffusion-production of vortensity inside the horseshoe region.\\
In the absence of any diffusion processes inside the disc, vortensity and entropy gradients
 across the horseshoe region tend to flatten through phase mixing, which causes the two components of the
horseshoe drag to  saturate.
Consequently, desaturating the horseshoe drag requires that some amount of viscous and thermal diffusions are operating inside the
horseshoe region. In that case, the amplitude of the horseshoe drag depends on the ratio between the diffusion timescales and the horseshoe
libration timescale and its optimal value, also referred as the fully unsaturated horseshoe drag,
is obtained when the diffusion timescales are approximately equal to half the horseshoe libration time
 (see e.g. Baruteau \& Masset 2012 for a recent review).
In the limit where the diffusion timescales become shorter than the U-turn timescale, the corotation torque decreases and approaches the value
predicted by linear theory. Therefore, the corotation torque can be considered as a linear combination of the fully unsaturated
horseshoe drag and the linear corotation torque with coefficients depending on the ratio between the diffusion timescales and
the horseshoe libration timescale. Corotation torque
formulae as a function of viscosity and thermal diffusivity were recently proposed by Paardekooper et al. (2011) and
Masset \& Casoli (2010). \\
So far, most of the studies aimed at studying the process of saturation of the corotation torque focused on laminar disc models with prescribed values of kinematic viscosity and thermal diffusivity. However, it is likely that both angular momentum and heat transport in protoplanetary discs occur because of turbulence probably due to the magneto-rotational instability (MRI, Balbus \& Hawley 1991) and it is not
clear how the disc turbulence really impacts the corotation torque. In the case of isothermal discs, Uribe et al. (2011)
performed 3D MHD simulations of planet migration in stratified discs that suggested the torques coming from
the corotation region can remain unsaturated due to viscous stresses in the disc. Baruteau et al. (2011) recently
confirmed the existence of an unsaturated corotation torque and demonstrated that a horseshoe dynamics is indeed at work in turbulent discs
with a weak toroidal magnetic field. Using 2D hydrodynamical simulations in which disc turbulence is modelled through stochastic
forcing, Baruteau \& Lin (2010) showed that in isothermal discs, the running time-averaged torque experienced by a
protoplanet is in good agreement with that obtained from a laminar disc model with a similar vortensity diffusion coefficient, and  in which the total torque consists of  the Lindblad torque plus the  barotropic part of the corotation torque. \\
In this paper we adopt a similar strategy as in Baruteau \& Lin (2010) but focus on non-isothermal discs in which the horseshoe
drag has an additional contribution due to the presence of an entropy gradient across the horseshoe region. The aim
is to investigate whether the entropy-related horseshoe drag remains unsaturated in presence of turbulence and whether the running
 time-averaged torques in turbulent runs are in good agrement with a laminar viscous disc model with appropriate values for the vortensity and
entropy diffusion coefficients. \\
In the context of planetary population synthesis models aimed at reproducing
the  mass-semi-major axis diagram of exoplanets, it is of crucial importance to investigate whether in turbulent disc
 models the entropy-related corotation torque behaves as in laminar viscous discs since it may be responsible for significantly
slowing down or reversing Type I migration in the latter case. \\
The paper is organized as follows. In Sect. 2, we give the basic equations and notations we use in this work and describe
the numerical set-up in Sect. 3. In Sect. 4, we present the properties of turbulence in our simulations. In particular,
we evaluate the vortensity and entropy diffusion coefficients as well as the turbulent Prandtl number. In Sect. 5, we estimate the effects of
turbulence on the entropy-related corotation torque and compare with the torque formulae of Paardekooper et al. (2011) and
with laminar calculations as well. We
finally discuss our results and draw our conclusions in Sect.6.

\section{Physical model}
\subsection{Basic equations}
We adopt a 2D adiabatic disc model for which all the physical
quantities are vertically averaged. We work in a frame rotating
with angular velocity $\Omega_{p}$,
and adopt cylindrical polar coordinates $(R,\phi)$ with the origin
located at the position of the central star. The continuity, equation of motion and
energy equation respectively read:
\begin{equation}
\frac{\partial{\Sigma}}{\partial t}+\nabla\cdot(\Sigma \vec{v})=0,
\end{equation}
\begin{equation}
\frac{\partial{\vec{v}}}{\partial t}+(\vec{v}.\nabla)\vec{v}=-\frac{\nabla p}{\Sigma}
-\nabla \Phi,
\label{eq:vel}
\end{equation}
and,
\begin{equation}
\frac{\partial{S}}{\partial t}+(\vec{v}\cdot\nabla) S=0
\end{equation}
where $\Sigma$ is the disc surface density, $\vec{v}$ the velocity, $P$ the pressure and
$S$ the entropy which is defined as:
\begin{equation}
S=\frac{p}{\Sigma^{\gamma_{ad}}},
\end{equation}
where $\gamma_{ad}$ is the adiabatic index. Here we use an ideal gas equation of state
$p=\Sigma R_g T/\mu $ where $R_g$ is the gas constant, T the temperature and $\mu$
the mean molecular weight. \\
In Eq. \ref{eq:vel}, $\Phi$ is the gravitational potential and reads:
\begin{equation}
\Phi=-\frac{GM_\star}{R}-\frac{1}{2}\Omega_{p}^2 R^2+\Phi_{ind}+\Phi_{turb}
\end{equation}
where $M_\star$ is the mass of the central star and  $\Phi_{ind}$ is an indirect term which accounts from the fact that the frame centered
on the star is non-inertial (e.g. Nelson et al. 2000). Effects resulting from turbulence
are modelled by applying the external turbulent potential $\Phi_{turb}$ of Laughlin et al. (2004) (see Sect. 3). Previous
studies (e.g. Baruteau \& Lin 2010; Pierens et al. 2011) have shown that the perturbations induced by this
stochastic forcing term  have similar  statistical properties to those resulting from 3D MHD simulations. In
isothermal discs, it is well known that fluctuations arising from turbulence generate transport of angular momentum through Reynolds and Maxwell stresses (e.g. Papaloizou \& Nelson 2003). For non-isothermal discs, additional turbulent energy transport is expected as a consequence of
entropy perturbations.

\subsection{Averaged quantities and turbulent  diffusion coefficients}

To estimate the rate of angular momentum and energy transport resulting from turbulence, we adopt a common procedure and
  make use of averaged quantities. The mass-weighted azimuthal average of the quantity $Q(r,\phi,t)$ is given by:
\begin{equation}
\bar Q(R,t)=\frac{\int \Sigma(R,\phi,t) Q(R,\phi,t) d\phi}{\int \Sigma(R,\phi,t) d\phi}
\end{equation}
where the integral is performed over $2\pi$ in azimuth. Setting $v_R=\bar v_R +\delta v_R$ and
$v_\phi=\bar v_\phi +\delta v_\phi$, where $\delta v_R$ and $\delta v_\phi$ are the radial and azimuthal velocity
fluctuations respectively, and averaging the azimuthal component of the equation
of motion (Eq. \ref{eq:vel}) gives the following equation for the conservation of the specific angular momentum
$j=Rv_\phi$ (e.g. Fromang \& Nelson 2006):
\begin{equation}
\frac{\partial}{\partial t} (\Sigma \bar j)+\frac{1}{R} \frac{\partial}{\partial R} (R \Sigma \bar v_R \bar j)=
-\frac{1}{R}\frac{\partial}{\partial R} (R^2 \Sigma \overline{\delta v_R \delta v_\phi})
\end{equation}
The previous equation can be re-written as (Balbus \& Papaloizou 1999):
\begin{equation}
\frac{\partial}{\partial t} (\Sigma \bar j)+\frac{1}{R} \frac{\partial}{\partial R} (R \Sigma \bar v_R \bar j)=
-\frac{1}{R}\frac{\partial}{\partial R} (\Sigma R^2\alpha_R \overline{P}/\overline{\Sigma})
\end{equation}
where  $\alpha_R$ is the  Reynolds stress parameter  which is defined as:
\begin{equation}
\alpha_R=\frac{\bar \Sigma \overline{\delta v_R \delta v_\phi}}{\bar P}
\label{eq:alpha}
\end{equation}

Adopting a similar averaging procedure for the energy equation leads to the following relation for the conservation of entropy:

\begin{equation}
\frac{\partial}{\partial t} (\Sigma \bar S)+\frac{1}{R}\frac{\partial}{\partial R}(R\Sigma \bar v_R \bar S)=
-\frac{1}{R}\frac{\partial}{\partial R}(R\Sigma \overline{\delta v_R\delta S})
\end{equation}
which can be recast as:
\begin{equation}
\frac{\partial}{\partial t} (\Sigma \bar S)+\frac{1}{R}\frac{\partial}{\partial R}(R\Sigma \bar v_R \bar S)=
\frac{1}{R}\frac{\partial}{\partial R}(\kappa R\Sigma \frac{\partial \bar S}{\partial R})
\end{equation}
where $\kappa$ is  the diffusion coefficient associated with the entropy and is given by:
\begin{equation}
\kappa=-\frac{\overline{\delta v_R\delta S}}{\partial \bar S/\partial R}
\label{eq:kappa}
\end{equation}

 Here, we  note that the previous equation was derived assuming an adiabatic disc model. This neglects
turbulent heating, which is modelled in our simulations by artificial viscous heating at shocks arising from
 the turbulence (see Sect. \ref{sec:num}).  Turbulent heating remains small, however, for the turbulence amplitudes
considered in this study. To estimate the effective thermal diffusion  coefficient in
the simulations, we therefore simply neglect the turbulent heating term and make use of Eq. \ref{eq:kappa}.

\section{Numerical set-up}
\label{sec:num}
 Simulations were performed with the FARGO and GENESIS numerical codes which solve the
 equations for the disc on a polar grid.
These codes employ an advection scheme based on the monotonic transport algorithm
(Van Leer 1977) and include the FARGO algorithm (Masset 2000) to avoid time step limitation
due to the Keplerian orbital velocity at the inner edge of the grid. The energy equation
that is implemented in both codes reads:
\begin{equation}
\frac{\partial e}{\partial t}+\nabla \cdot (e{\bf v})=-(\gamma_{ad}-1)e{\nabla \cdot {\bf v}}+Q^+_{bulk}
\end{equation}
where $e$ is the thermal energy density and $Q^+_{bulk}$ is the heating source term by artificial
viscosity and provided by shocks arising from turbulent fluctuations. This term is handled by
 adopting a standard von Neumann-Richtmyer artificial bulk viscosity (see Stone \& Norman 1992) with
$C_2=1.4$, where $C_2$ represents the number of zones over which artificial viscosity will
spread a shock.  Here, no cooling term is included as an additional source term, which means that reaching a thermal equilibrium
for the disc is not possible and that the temperature profile may be progressively altered by turbulent heating, especially in the case of strong turbulent fluctuations. However, from the results of simulations presented in Sect. \ref{sec:withplanet}, we anticipate
that using a cooling term is not necessary since for most of the turbulence amplitudes considered in this
study, turbulence heating has little impact on the temperature profile over the runtime covered by the
calculations. In fact,
not considering such a term enables to investigate effects resulting from turbulent diffusion only without continuously
changing the temperature profile close to the planet. We further note that the results presented in Sect. \ref{sec:withplanet} may depend strongly on the expression employed for the cooling term. \\

The computational units  that we adopt are such that the unit of mass is the
central mass $M_*$, the unit of distance is the initial orbital radius
$R_p$  of
the  planet and the unit of time is $\Omega_p^{-1}=(GM_*/R_p^3)^{-1/2}$.
In the simulations presented here, we use $N_R=512$ radial grid cells
uniformly distributed between $R_{in}=0.4$ and $R_{out}=1.8$, and
$N_{\phi}=1200$ azimuthal grid cells. Wave-killing zones are employed
 for $R<0.5$ and $R>1.58$ to avoid wave reflections at the disc edges (de Val-Borro et al. 2006).\\

The initial disc surface density profile is $\Sigma=\Sigma_p\times(R/R_p)^{-\sigma}$ with
$\Sigma_p=5\times 10^{-4}$ and $\sigma=1.5$ by default. For such a disc surface density profile,
the initial vortensity-related part of the corotation torque cancels out so that the corotation torque consists only of its
entropy-related part. The initial disc aspect ratio is $h=h_p\times(R/R_p)^f$ with $h_p=0.03$ and where
$f$ is the disc flaring index which is set to $f=0.3$ in this work. This corresponds to an initial temperature
profile decreasing as $R^{-\beta}$ with $\beta=1-2f=0.4$. For an adiabatic index $\gamma=5/3$ which
corresponds to the value adopted here, the
initial entropy profile therefore varies as $R^{-\xi}$ with $\xi=\beta-(\gamma-1)\sigma=-0.59$.  As will be justified
in Sect. \ref{sec:withplanet}, such a positive gradient for the initial
entropy profile is chosen to minimize the maximum convergence time of the turbulent runs, since both the entropy-related corotation torque and the differential Lindblad torque are negative in that case.

In the simulations presented here, turbulence is modelled by applying at each time-step a turbulent
potential $\Phi_{turb}$ to the disc (Laughlin et al.
2004, Baruteau \& Lin 2010) and corresponding to the superposition of $50$
wave-like modes. This reads as:

\begin{equation}
\Phi_{turb}(R,\phi,t)=\gamma R^2 \Omega^2\sum_{k=1}^{50}\Lambda_k(R,\phi,t),
\label{eq:phi}
\end{equation}

with

\begin{equation}
\Lambda_k=\xi_k e^{-\frac{(R-R_k)^2}{\sigma_k^2}}
\cos(m_k\phi-\phi_k-\Omega_k\tilde{t_k})
\sin(\pi \tilde{t_k}/\Delta t_k).
\label{eq:lambda}
\end{equation}

In Eq. \ref{eq:lambda}, $\xi_k$ is a dimensionless constant  parameter randomly
  sampled with a Gaussian distribution of unit width.
$R_k$ and $\phi_k$ are, respectively, the radial and
azimuthal initial coordinates of the mode with wavenumber $m_k$,
 $\sigma_k=\pi R_k /4m_k$ is the radial extent of that mode, and
$\Omega_k$ denotes the Keplerian angular velocity at $R=R_k$.
 Both $R_k$ and $\phi_k$ are randomly  sampled with a uniform
distribution, whereas $m_k$ is randomly sampled  with a logarithmic
distribution between $m_k=1$ and $m_k=96$.
Each mode of wavenumber $m_k$ starts at time $t=t_{0,k}$ and
 terminates when $\tilde{t_k}=t-t_{0,k} > \Delta t_k $,
where $\Delta t_k=0.2\pi R_k /m_k c_s$ denotes the lifetime of mode with wavenumber $m_k$, $c_s$ being the sound speed.  Such a value for
$\Delta t_k$ yields  an autocorrelation timescale $\tau_c\sim 0.5 T_{orb}$,
where $T_{orb}$ is the orbital period at $R=1$ (Baruteau \& Lin 2010, and see Sect. \ref{sec:kappa}).\\
Following Ogihara et al. (2007),
 we set $\Lambda_k=0$ if $m_k > 6$  to save computing time.
 As noticed by Baruteau \& Lin (2010), such an assumption is supported by the fact that
a turbulent mode with wavenumber $m$ has an amplitude decreasing as $\exp(-m^2)$ and a lifetime
$\propto 1/m$, so that the contribution to the turbulent potential of a high wavenumber turbulent mode
 is relatively weak.
  \\
In Eq. \ref{eq:phi}, $\gamma$ denotes the value of the turbulent
forcing parameter, which controls the amplitude of the stochastic density perturbations.
In the simulations presented here, we used values for $\gamma$ ranging from $10^{-5}$ to
$2\times 10^{-4}$.  Given that $\gamma$ is related to the dimensionless $\alpha$
viscosity of Shakura \& Sunyaev (1973)  by the relation
$\alpha\sim 120(\gamma/h_p)^2$ (see Sect. \ref{sec:kappa}), the latter values for $\gamma$
correspond to $\alpha$ ranging from $\sim 10^{-5}$ to $\sim 5 \times 10^{-3}$.  \\
In the following, we first estimate how both the viscous and thermal
diffusion coefficients induced by turbulence depend on the amplitude of the turbulent
potential $\gamma$. We then present the results of calculations of a low-mass planet embedded
 in a non-isothermal disc subject to stochastic forcing. We consider different values for
$\gamma$ and study how the running time-averaged torque deduced from our simulations compare with
laminar runs and with the analytical formulae of Paardekooper et al. (2011) for the torque due to Lindblad resonances
and horseshoe drag in the presence of viscous and thermal diffusion.

\section{Turbulence properties}

\subsection{Estimation of the turbulent thermal diffusivity}
\label{sec:kappa}

\begin{figure}
\centering
\includegraphics[width=0.95\columnwidth]{alpha_g8em5.eps}
\includegraphics[width=0.95\columnwidth]{kappa_g8em5.eps}
\caption{{\it Upper panel:} Reynolds stress parameter $\alpha(R)$ as a function of radius for $\gamma=8\times10^{-5}$
and time-averaged over $700$ $T_{orb}$. {\it Lower panel:} same but for the entropy diffusion coefficient $\kappa(R)$ defined by Eq. \ref{eq:kappa}.}
\label{fig:kvsr}
\end{figure}
In non-isothermal discs, the main effect of the applied turbulent potential is to generate velocity and temperature
fluctuations responsible for  both entropy and angular momentum transport. In a previous
study dedicated to isothermal discs, Baruteau \& Lin (2010) showed that for the adopted turbulent potential,
the resulting Reynolds stress parameter scales as $\gamma^2$.
Here, in order to investigate the dependence of the entropy diffusion coefficient on the amplitude of
turbulence $\gamma$, we performed a series of simulations in the non-rotating frame of a non-isothermal disc with turbulence
driven by stochastic forcing,
varying the value for $\gamma$ from $\gamma=2\times 10^{-5}$ to $\gamma=2\times 10^{-4}$ and using the disc
model described in Sect. \ref{sec:num}. From the results of these simulations, the Reynolds stress parameter
$\alpha_R(R,t)$ and the entropy diffusion coefficient $\kappa (R,t)$  are computed using Eqs. \ref{eq:alpha} and
\ref{eq:kappa} respectively.  To examine how these two quantities vary with radius,  a time
average over $700$ $T_{orb}$ is performed. For $\gamma=8\times 10^{-5}$, Fig. \ref{fig:kvsr} displays the
time-averaged coefficients $\alpha_R(R)$
and $\kappa(R)$ as a function of radius. Clearly, both quantities appear to be
approximately uniform with radius, except in the vicinity of the wave-killing zones.  \\

We now consider an additional space average of $\alpha_R(R)$ and $\kappa(R)$ in the range $0.9\le R \le 1.1$ and
 in the following, we simply denote
by $\alpha_R$ and $\kappa$  the resulting numbers.  In  simulations with an embedded planet presented in Sect.
\ref{sec:withplanet}, the planet is on a fixed circular orbit located at $R_p=1$. Given that the corotation torque
experienced by the planet depends on the viscous and thermal diffusion timescales across the horseshoe region whose
half-width is a fraction of the disc scale height $H$ for the planet masses we consider,  the range over which the space average
is performed therefore corresponds to the disc region which contributes the most to the torque exerted on the planet. The upper  panel of Fig. \ref{fig:akvsg} represents
$\alpha_R$ as a function of $\gamma$. As expected,  $\alpha_R$ appears to scale as $\gamma^2$
and is found to be well approximated by:
\begin{equation}
\alpha_R \; \approx 30 \left(\frac{\gamma}{h_p}\right)^2,
\label{eq:fitalpha}
\end{equation}
which is in  excellent agreement with the relation derived by Baruteau \& Lin (2010).
A slight discrepancy arises because we average with radius in the range $0.9 \le R \le 1.1$ whereas
the space average is performed over the  disc region located outside the wave-killing zones  in Baruteau \& Lin (2010).
 While in laminar discs vortensity diffusion is controlled by the kinematic viscosity, this is not necessary the
case in turbulent discs
where the vortensity's diffusion coefficient $D$  can differ from the turbulent viscosity
$\nu_R=\alpha_R c_s H$  associated with the turbulent diffusion of angular momentum. For
instance, Baruteau \& Lin (2010)
have shown that in isothermal discs, the ratio $S_c=\nu_R/D$ usually referred as the Schmidt number is
$S_c\sim 0.25$. Although not shown here, we have checked that this value also holds in non-isothermal discs and in the following,
we will make use of the dimensionless vortensity's diffusion coefficient that we define as
$\alpha_D=S_c^{-1}\alpha_R\sim 4 \alpha_R$. Given that in MHD calculations, the  total viscous stress parameter
corresponding to the dimensionless $\alpha$ viscosity of Shakura \& Sunyaev (1973) is
$\sim 4 \alpha_R$ (Fromang \& Nelson 2009),  this suggests that our value for $\alpha_D$ is close to that
corresponding to the standard $\alpha$ viscous stress parameter. Using Eq. \ref{eq:fitalpha}, the dimensionless
viscosity of Shakura \& Sunyaev (1973) can consequently be well approximated  by:
\begin{equation}
\alpha \; \approx 120 \left(\frac{\gamma}{h_p}\right)^2,
\label{eq:fitalphav}
\end{equation}

\begin{figure}
\centering
\includegraphics[width=0.95\columnwidth]{alpha.eps}
\includegraphics[width=0.95\columnwidth]{kappa.eps}
\caption{{\it Upper panel:} Averaged Reynolds stress parameter $\alpha$ as a function of turbulence amplitude $\gamma$.
{\it Lower panel:} Averaged entropy diffusion coefficient $\kappa$ as a function  of turbulence amplitude $\gamma$.}
\label{fig:akvsg}
\end{figure}

We plot the entropy diffusion coefficient $\kappa$ as a function of $\gamma$ in the lower panel of Fig.
\ref{fig:akvsg}.
Again, $\kappa$ is found to increase as $\gamma^2$, which is in agreement with the expectation that both $\delta v_r$ and
$\delta S$ scale with $\gamma$. The best-fitting solution is found to be:
\begin{equation}
\kappa \; \approx 125 \; \gamma^2 R_p^2\Omega_p,
\label{eq:fitkappa}
\end{equation}
\begin{figure}
\centering
\includegraphics[width=0.49\columnwidth]{gauss_g6em5.eps}
\includegraphics[width=0.49\columnwidth]{gauss_g1em4.eps}
\caption{Perturbed entropy profile at $t=4.5T_{orb}$  averaged over six different realizations  with $\gamma=6\times 10^{-5}$
({\it left panel}) and
$\gamma=10^{-4}$ ({\it right panel}) and in which a $10 \%$ negative perturbation is applied to the
background entropy profile at $R_d=1$. The solid line corresponds to the analytical fit given by
Eq. \ref{eq:gaussfit} with $\kappa$  given by Eq. \ref{eq:fitkappa}.}
\label{fig:gaussian}
\end{figure}

\begin{figure}
\centering
\includegraphics[width=0.95\columnwidth]{dprofile.eps}
\includegraphics[width=0.95\columnwidth]{sprofile.eps}
\caption{{\it Upper panel:} Surface density profile at $t=700 \; T_{orb}$ for the different values of $\gamma$ we
considered. {\it Lower panel:} Same but for the entropy profile.}
\label{fig:profiles}
\end{figure}

To check the consistency of the previous estimation, we followed the approach of Baruteau \& Lin (2010) and
performed a series of runs varying the value for $\gamma$
and in which a $10 \%$ negative perturbation with a $\delta$-function profile is applied to the initial entropy profile at
$R_d\sim 1$. This is achieved by applying a positive perturbation to the density profile together with
a negative temperature perturbation with same amplitude, in such a way that the initial pressure perturbation is zero.
The evolution of the perturbed entropy profile is then compared with  the function:
\begin{equation}
\delta S(R,t)=\frac{\delta S_0\Delta R}{\sqrt{4\pi \kappa t}} \exp\left(\frac{-(R-R_d)^2}{4\kappa t}\right),
\label{eq:gaussfit}
\end{equation}
where $\delta S_0$ is the initial entropy perturbation at $R=R_d$, $\Delta R$ is the radial resolution of the grid
and $\kappa$ is the estimation of the entropy diffusion coefficient given by  Eq. \ref{eq:fitkappa}.
The results of this set of simulations are presented in Fig. \ref{fig:gaussian} where we plot
for $\gamma=6\times 10^{-5}$ and $\gamma=10^{-4}$
both the perturbed entropy profile averaged over six different realizations at $t=4.5$ $T_{orb}$ and the fitting formula given
by Eq. \ref{eq:gaussfit}. Clearly, the
perturbed entropy profile closely matches the expected one, which indicates that
Eq. \ref{eq:fitkappa} provides a fairly good estimation of the effective entropy diffusion coefficient.\\
It is worthwhile to notice that this model can suffer from the time evolution of the entropy profile due to artificial viscous heating at shocks. This is illustrated in Fig. \ref{fig:profiles} which shows the surface density and entropy profiles
at $t=700\; T_{orb}$ for the different values of $\gamma$ we considered. Although the surface density profile
remains almost constant, we see
that the entropy profile can be significantly altered in turbulent runs with high values of $\gamma$.
 This is due not only to turbulent diffusion which makes the
entropy profile steeper but also to  turbulent heating  which tends
to increase the local value for the entropy. Looking at Fig. \ref{fig:profiles}, we see that effects resulting from turbulent
heating are more pronounced near the radial boundaries.
However, we are
confident that this process does not strongly affect our estimations of $\alpha$ and $\kappa$ since these are determined
using space averages in the range $0.9<R<1.1$, which corresponds to disc regions where the entropy profile is only
slightly modified over the runtime of the simulations. To check this, we computed these two quantities
using normalizations by the initial pressure or entropy profiles
and found good agreement with the estimations given by Eqs. \ref{eq:fitalphav} and \ref{eq:fitkappa} for which
normalizations by time averaged profiles were considered.

\subsection{Determination of the turbulent Prandtl number}

In this section, we investigate how the turbulent Prandtl number $P_r$ depends on the amplitude of the turbulent
forcing $\gamma$. The turbulent Prandtl number is commonly defined as:

\begin{equation}
P_r=\frac{\nu_R}{\kappa}=\frac{\alpha_Rc_s H}{\kappa}
\label{eq:prandtl}
\end{equation}

Since both $\alpha_R$ and $\kappa$ scale with $\gamma^2$, we expect $P_r$ to not depend on the value
for $\gamma$. This is confirmed by inspecting Fig. \ref{fig:prandtl} where $P_r$ is displayed  as
as a function of $\gamma$ and which reveals that the turbulent Prandtl number is $P_r\sim 0.3$ on average.
Such a  value
is close  to that derived by Ruediger et al. (1988) who estimate that a value $P_r\sim 0.1$ is necessary to explain the outburst behaviour of  cataclysmic variables. In the case of shear-driven hydrodynamic turbulence, it is also of interest to mention that Lathrop et al. (1992) measured a turbulent Prandtl number $P_r\sim 0.176$
in experiments of Couette-Taylor flows at Reynolds numbers well beyond the onset of chaos.

\begin{figure}
\centering
\includegraphics[width=0.95\columnwidth]{prandtl.eps}
\caption{Estimated turbulent Prandtl number as a function of turbulence amplitude $\gamma$.}
\label{fig:prandtl}
\end{figure}

\subsection{Turbulent transport of entropy in a radiative protoplanetary disc}

As mentioned above, no cooling source term is included in the energy equation that is
employed in this work. However, in a more realistic disc model in which turbulent effects and
radiative processes are both included, we expect a thermal equilibrium state to be reached
when radiative cooling compensates turbulent heating. For such a radiative turbulent disc,  diffusion of entropy is due
not only to turbulent transport  as it is the case for the idealized disc considered here  but also to radiative diffusion. For an active laminar disc
model with turbulent heating balanced by radiative losses, the  thermal diffusion
coefficient $\kappa_{rad}$ associated with radiative transport can be expressed as (Paardekooper et al. 2011):
\begin{equation}
\kappa_{rad}=9\gamma_{ad}(\gamma_{ad}-1)\nu\left(1+\frac{2\sqrt{3}}{3\tau}+\frac{2}{3\tau^2}\right)
\label{eq:kappar}
\end{equation}
where $\tau$ is the optical depth and $\nu=\alpha c_s H$ the kinematic viscosity. Noting that
$\nu=S_c^{-1}P_r \; \kappa$ from the results of the previous section and using Eq. \ref{eq:kappar},
we obtain the following expression for the ratio between the thermal diffusion coefficient
associated with radiative effects and that associated with the turbulent transport of entropy:
\begin{equation}
\frac{\kappa_{rad}}{\kappa}=9S_c^{-1}P_r\gamma_{ad}(\gamma_{ad}-1)\left(1+\frac{2\sqrt{3}}{3\tau}+\frac{2}{3\tau^2}\right)
\label{eq:ratio}
\end{equation}
Previous equation shows than in optically thick inner regions of protoplanetary discs, turbulent and radiative diffusion
coefficients will tend to be of the same order of amplitude whereas in optically thin outer regions, radiative transport
will be much more efficient than turbulent transport for diffusing entropy.

\section{Effects of turbulence on the entropy-related corotation torque}
\label{sec:withplanet}

In this section, we evaluate the  effect of turbulence on the entropy-related corotation torque.
To investigate this issue, we performed simulations of a low-mass planet on a
circular orbit at $R_p=1$ and $\phi_p=\pi$ and embedded in a non-isothermal
disc subject to stochastic forcing. We used values for the amplitude of the turbulent potential
ranging from $\gamma=10^{-5}$ to
$\gamma=2\times 10^{-4}$. The disc model is the same as described in Sect. \ref{sec:num}
with  power-law indexes for
the initial surface density, temperature and entropy profiles of $\sigma=1.5$, $\beta=0.4$ and $\xi=-0.59$
respectively and an aspect ratio at the planet position of $h_p=0.03$.
We considered planets with mass ratio
$q=5\times 10^{-6}$ and $q=10^{-5}$ which corresponds to planets with masses of $1.6$ $M_\oplus$ and
$3.2$ $M_\oplus$ if the central star has a solar mass.  For $q=5\times 10^{-6}$ and for a
softening parameter $b=0.4h_p$ which is the value set in this work, the half-width of the
horseshoe region is  $x_s\sim 1.1/{\gamma_{ad}}^{1/4} R_p \sqrt{q/h_p}\sim 0.013$  (Paardekooper et al. 2010) which means
that the horseshoe region is resolved by about 12 grid cells in the radial direction.
Also, we note that in calculating the torque experienced by the
planet, we include the disc material located inside the Hill sphere of the planet.

\subsection{Total torque exerted on the planet}

As shown by Baruteau \& Lin (2010)  in the case of isothermal discs, turbulence can unsaturate the  vortensity-related part of the  corotation torque
in the same way as an alpha viscosity does in a laminar disc.
In the following, we make the  assumption that thermal diffusion resulting from turbulence can also unsaturate
the entropy-related part of the corotation torque and assume that this effect can be modelled
by an entropy diffusion coefficient. This will be checked in the next section. \\
In the presence of turbulence, the torque exerted on a low-mass planet embedded in a turbulent disc can be considered as the
sum of the differential Lindblad torque $\Gamma_L$, the corotation torque $\Gamma_{c}$ and the turbulent
torque $\Gamma_{turb}$. In the adiabatic limit and for a smoothing parameter $b=0.4h_p$,
the Lindblad torque is given by (Paardekooper et al. 2010):
\begin{equation}
\Gamma_L=(-2.5-1.7\beta+0.1\sigma)\frac{\Gamma_0}{\gamma_{ad}}
\label{eq:gammal}
\end{equation}
where $\Gamma_0$ is given by:
\begin{equation}
\Gamma_0=\left(\frac{q}{h_p}\right)^2\Sigma_pR_p^4\Omega_p^2
\end{equation}
In the previous equation, the subscript "p"
indicates that quantities are evaluated at the orbital position of the planet $R_p$. \\
 Provided the surface density profile is not strongly
affected by turbulence, we expect the barotropic part of the corotation torque to cancel for our disc model  in which
$\sigma=1.5$, since the latter scales
with the vortensity gradient. In that case, the corotation torque consists only
 of its entropy-related part $\Gamma_{c,e}$ and the total torque $\Gamma$ exerted on the planet simplifies into:
\begin{equation}
\Gamma=\Gamma_L+\Gamma_{c,e}+\Gamma_{turb}
\end{equation}
 For diffusion timescales across the horseshoe region shorter than the horseshoe libration period
$\tau_{lib}=8\pi R_p/3\Omega_px_s$ but longer than the horseshoe U-turn timescale
$\tau_{U-turn}\sim h_p \tau_{lib}$ (Baruteau \& Masset 2008),
the entropy-related horseshoe drag is close to its fully unsaturated value given (Paardekooper et al. 2010):
\begin{equation}
\Gamma_{hs,e}=\frac{\Gamma_0}{\gamma_{ad}}\left(\frac{7.9\xi}{\gamma_{ad}}\right)
\label{eq:gammahse}
\end{equation}
while for diffusion timescales smaller than the U-turn timescale, $\Gamma_{c,e}$  decreases toward the entropy-related part of the linear
corotation torque $\Gamma_{c,lin,e}$ with:
\begin{equation}
\Gamma_{c,lin,e}=\frac{\Gamma_0}{\gamma_{ad}}\left(2.2-\frac{1.4}{\gamma_{ad}}\right)\xi
\label{eq:gammacline}
\end{equation}
A model of the entropy-related corotation torque including its dependence on the diffusion timescale can be obtained
by writing $\Gamma_{c,e}$ as a linear combination of $\Gamma_{hs,e}$ and $\Gamma_{c,lin,e}$. Paardekooper et al. (2011)
have shown that $\Gamma_{c,e}$ can be indeed well approximated by:
\begin{eqnarray}
\Gamma_{c,e} = & F(p_\nu)F(p_\chi)\sqrt{G(p_\nu)G(p_\chi)}\Gamma_{hs,e}\\+
\label{eq:gammace}
&\sqrt{(1-K(p_\nu))(1-K(p_\chi)}\Gamma_{c,lin,e}\nonumber
\end{eqnarray}
where $p_\nu$ is the saturation parameter related to viscosity and is given by:
\begin{equation}
p_\nu=\frac{2}{3}\sqrt{\frac{R_p^2\Omega_p x_s^3}{2\pi \nu}}
\end{equation}
and $p_\chi$ is the saturation parameter related to thermal diffusion with:
\begin{equation}
p\chi=\frac{2}{3}\sqrt{\frac{R_p^2\Omega_p x_s^3}{2\pi \kappa}}
\end{equation}
where $\nu=\alpha c_s H$ with $\alpha$ given by Eq. \ref{eq:fitalphav} and where $\kappa$ is related to the amplitude of
turbulence by Eq. \ref{eq:fitkappa}.
In  Eq. $28$, the function $F(p)$ of the parameter $p$ is defined by:
\begin{equation}
F_p=\frac{1}{1+(p/1.3)^2}
\end{equation}
while the functions $G(p)$ and $K(p)$ are given by:
\begin{equation}
G(p)=
\begin{cases}
\frac{16}{25}\left(\frac{45\pi}{8}\right)^{3/4}p^{3/2}, & \text{if}\; p < \sqrt{8/(45\pi)} \\
1-\frac{9}{25}\left(\frac{8}{45\pi}\right)^{4/3}p^{-8/3}, & \text{if}\; p\ge \sqrt{8/(45\pi)}
\end{cases}
\end{equation}

and:
\begin{equation}
K(p)
\begin{cases}
\frac{16}{25}\left(\frac{45\pi}{28}\right)^{3/4}p^{3/2}, & \text{if}\; p < \sqrt{28/(45\pi)} \\
1-\frac{9}{25}\left(\frac{28}{45\pi}\right)^{4/3}p^{-8/3}, & \text{if}\; p\ge \sqrt{28/(45\pi)}

\end{cases}
\end{equation}
Regarding the turbulent torque $\Gamma_{turb}$; its amplitude is given by (Nelson 2005;
Baruteau \& Lin 2010):
\begin{equation}
|\Gamma_{turb}|=\sigma_{turb}\left(\frac{t}{\tau_c}\right)^{-1/2}
\label{eq:gammaturb}
\end{equation}

where $\sigma_{turb}\sim 2.4\times 10^2 \Sigma_p q \gamma R_p^4 \Omega_p^2$ (Baruteau \& Lin 2010)
is the mean deviation of the turbulent torque distribution and
$\tau_c\sim 0.5\; T_{orb}$ is the correlation time of the turbulence. Using the previous
equation leads to an estimation of  the convergence time $t_{conv}$ of the simulations
over which  $|\Gamma_{turb}|$ is a
small fraction
$f$ of $|\Gamma_L+\Gamma_{c,e}|$.  Using Eq. \ref{eq:gammaturb}, the convergence time is given by:
\begin{equation}
t_{conv}\sim \tau_c f^{-2}\left(\frac{\sigma_{turb}}{\Gamma_L+\Gamma_{c,e}}\right)^2
\end{equation}
Previous
equation shows that the maximum convergent time of the turbulent runs is reduced in the case where both the entropy-related corotation  torque and
the differential Lindblad torque have the same sign. In order to minimize $t_{conv}$ and given that the differential Lindblad torque is negative,
we employed a positive initial entropy gradient so that the entropy-related corotation torque is negative as well.
Using the expression for $\Gamma_L$ given by Eq. \ref{eq:gammal} and taking the fully unsaturated value  for the
entropy-related corotation torque given by Eq. \ref{eq:gammahse}, we estimate the  convergence time
to be approximately  given by:
\begin{equation}
t_{conv}\sim 0.2\left(\frac{\gamma}{q}\right)^2T_{orb},
\label{eq:tconv}
\end{equation}
 where we assumed $f=0.1$. For $q=5\times 10^{-6}$ and $\gamma=10^{-4}$, this gives $t_{conv}\sim 100\; T_{orb}$
 Over timescales typical to those covered by our simulations
($\sim 1500$ $T_{orb}$ ) and
provided that there is no significant coupling between the Lindlad torque and the turbulent torque, we therefore
expect the steady-state torque experienced by the planet to be approximately given by:
\begin{equation}
\Gamma\sim \Gamma_L+\Gamma_{c,e}
\label{eq:totaltorque}
\end{equation}
where $\Gamma_L$ and $\Gamma_{c,e}$ are respectively given by Eqs. \ref{eq:gammal} and \ref{eq:gammace}. We emphasize that the previous
equation is valid in the case where the effect of turbulent thermal diffusion on the desaturation of
the entropy-related corotation torque is similar to that corresponding to a laminar entropy diffusion coefficient. The aim of the
following section is to check this assumption.

\subsection{Time evolution of the running time-averaged torque}
\begin{figure*}
\centering
\includegraphics[width=0.49\textwidth]{torque_q5em6.eps}
\includegraphics[width=0.49\textwidth]{torque_q1em5.eps}
\caption{{\it Left panel:} Time evolution of the running time-averaged specific torque for the different values of $\gamma$ we considered and for $q=5\times 10^{-6}$. {\it Right panel:} same but for $q=10^{-5}$.}
\label{fig:torque}
\end{figure*}

For $q=5\times 10^{-6}$, the time evolution of the running time-averaged torque over $1500$ orbits for turbulent
runs with $\gamma$ in the range $10^{-5}-2\times 10^{-4}$ is displayed in the left panel of
Fig. \ref{fig:torque}.  From Eq. \ref{eq:tconv}, we expect that the running time-averaged torques have
converged over this timescale  except for the run with $\gamma=2\times 10^{-4}$ in which the temperature
profile is found to be continuously altered by turbulence (see Sect. \ref{sec:analytics}). Also shown is the result of an inviscid simulation with $\gamma=0$ in which the torque
saturates toward the differential Lindblad torque $\Gamma_L$ . In that case, $\Gamma_L$ is found to slowly increase
by $\sim 2\%$ between $1000$ and $1500$ orbits due to the continuous formation of a gap around the planet. We note
that such a  process was also observed in the isothermal turbulent simulations of Baruteau \& Lin (2010).\\
In turbulent runs, the running time-averaged torque typically reaches a quasi-stationary value after $\sim 200$ orbits for moderate
values of $\gamma$, which is relatively consistent with the estimation of the convergence time given by
Eq. \ref{eq:tconv}. Up to $\gamma=10^{-4}$, we see that this stationary value decreases as $\gamma$ increases whereas for
higher values of $\gamma$,  it tends to increase with $\gamma$. As the differential Lindblad torque
should not be significantly altered by turbulence (Baruteau \& Lin 2010, Baruteau et al. 2011) and since the
barotropic part of the corotation torque is expected to cancel for the chosen surface density profile ($\sigma=1.5$),
this seems to suggest that turbulence  does unsaturate the entropy-related corotation torque. In that case, we indeed expect
that as $\gamma$ increases, the torque experienced by the planet decreases from the differential Lindblad torque down
to value close to that corresponding to the  sum of the differential Lindblad torque plus the unsaturated entropy-related horseshoe drag.
Such a value is reached when the thermal diffusion
timescale across the horseshoe region $\tau_d=x_s^2/\kappa$ is approximately equal to half the libration timescale $\tau_{lib}=8\pi R_p/(3\Omega_p x_s)$. Using Eq. \ref{eq:fitkappa}, we estimate the unsaturated entropy-related horseshoe drag
to be obtained for:
\begin{equation}
\gamma\sim 0.07\left(\frac{q}{h_p}\right)^{3/4}
\label{eq:gammacr}
\end{equation}
Using Eq. \ref{eq:fitalphav}, this corresponds to:
\begin{equation}
\alpha \sim  0.6q^{3/2}h_p^{-7/2}
\end{equation}

For $q=5\times 10^{-6}$, this gives  $\gamma\sim 1.1\times 10^{-4}$ ($\alpha\sim 1.6\times 10^{-3}$) which is close to the value observed in the
simulations. For higher values of $\gamma$, the diffusion timescale across the horseshoe region can approach
the U-turn timescale $\tau_{U-turn}\sim h_p \tau_{lib}$ (Baruteau \& Masset 2008) and the amplitude of the entropy-related
corotation torque starts to decrease toward a value corresponding to that predicted by the linear theory.\\
The results for $q=10^{-5}$ are shown in the right panel of Fig. \ref{fig:torque} which presents the time evolution of the
running time-averaged torque for $\gamma \le 2\times 10^{-4}$. For $\gamma=0$, it appears that the torque  oscillates
around a value corresponding to the differential Lindblad torque.  As discussed in Baruteau \& Lin (2010), these
oscillations are due to the formation of vortices flowing along the edge of the gap created by the planet
(Li et al. 2005). However, the running time-averaged torque does converge toward the
differential Lindblad torque but compared with the case $q=5\times 10^{-6}$,  the torque saturates much more
slowly.
For $\gamma \ne 0$, we estimate using Eq. \ref{eq:gammacr} that the value
of $\gamma$ from which the entropy-related horseshoe drag starts to decrease toward its linear value is $\gamma\sim 1.8\times 10^{-4}$.
This is in decent agreement with the results of the simulations for $q=10^{-5}$ which show, in the limit of
$\gamma \le 2\times 10^{-4}$, a  tendency for the torque amplitude to increase with $\gamma$. Again, this enlightens the process of desaturation of the entropy-related corotation torque
by turbulence.

\subsection{Comparison with laminar viscous disc models}
\label{sec:analytics}
\begin{figure*}
\centering
\includegraphics[width=0.49\textwidth]{rta_q5em6b.eps}
\includegraphics[width=0.49\textwidth]{rta_q1em5b.eps}
\caption{ Running time-averaged specific torque (stars) in turbulent runs as a function of the turbulence amplitude $\gamma$ (top axis) and as a
function of the effective entropy diffusion coefficient $\kappa$ (bottom axis) computed using Eq. \ref{eq:fitkappa}. Diamonds
 correspond to the results of laminar simulations with values for the viscous and thermal diffusion coefficients equal
to those effective in turbulent runs. The initial surface density and entropy profiles in laminar runs correspond to
the profiles in turbulent runs time averaged over $1500$ $T_{orb}$. The solid line depicts the analytic estimation of Paardekooper et al. (2011)
expected for the torque as a function of the thermal diffusivity $\kappa$, for a kinematic viscosity $\nu=S_c^{-1}P_r \kappa=
1.2\kappa$ and using the initial surface density and entropy profiles in turbulent runs. The upper and lower dashed lines
depict the values of the differential Lindblad torque and the fully unsaturated torque respectively.}
\label{fig:rta}
\end{figure*}

In this section, we compare the values for the running time-averaged torques deduced from the turbulent runs with the torque
formulae for non-isothermal Type I migration  derived by Paardekooper et al. (2011)  and with laminar
simulations with constant values for the kinematic viscosity and thermal diffusivity. In Fig. \ref{fig:rta} are
plotted, for $q=5\times 10^{-6}$ (left panel) and $q=10^{-5}$ (right panel), the running time-averaged torques computed at $t=1500$ $T_{orb}$ as a function of
the estimated entropy turbulent diffusion coefficient $\kappa$. The top axis gives the corresponding value for the  $\gamma$ parameter which is related to $\kappa$
by the relationship given in Eq. \ref{eq:fitkappa}. The solid line in Fig. \ref{fig:rta} depicts the approximation for
the total torque given  by Eq. \ref{eq:totaltorque} where we remind  the reader that $\Gamma_L$ is the Lindblad torque and $\Gamma_{c,e}$ the
entropy-related corotation torque given by Eq. \ref{eq:gammace}. In this latter relation, we computed the saturation
parameter related to viscosity $p_\nu$ by setting $\nu=S_c^{-1} P_r\kappa\sim 1.2 \kappa$. Moreover, we used the results from
the run  with
$\gamma=0$ and in which the corotation torque is expected to saturate to determine $\Gamma_L$. From this simulation we measure $\Gamma_L\sim 1.54\Gamma_0$
for $q=5\times 10^{-6}$ and $\Gamma_L \sim 1.34 \Gamma_0$ for $q=10^{-5}$ which differs from the estimation for the Lindblad torque given in Eq. \ref{eq:gammal} by $\sim 15 \%$ and
$\sim 25 \%$ respectively. We interpret this
slight discrepancy as being due to a change of the temperature profile in the vicinity of the planet.
This is exemplified in Fig. \ref{fig:tinviscid} which displays for the two values of $q$ we considered the temperature profile in the case where $\gamma=0$.
It reveals that the temperature tends to increase at distances
$\pm 2H$ from the planet, corresponding to a local increase of the disc aspect ratio and resulting consequently in a decrease of the
Lindblad torque. \\
For the run with $\gamma=0$, the fully unsaturated horseshoe drag was evaluated to be $\Gamma_{hs,e}\sim 1.82 \Gamma_0$ for $q=5\times 10^{-6}$ and $\Gamma_{hs,e}=1.92\Gamma_0$ for $q=10^{-5}$ which are values close to the estimation given by Eq. \ref{eq:gammahse} which predicts $\Gamma_{hs,e}\sim 1.7 \Gamma_0$. Regarding the linear corotation torque, it can be  crudely estimated
by  subtracting the differential Lindblad torque from the total torque at $t\sim 2$ $T_{orb}$ ( that is,
$t\sim 0.5\tau_{U-turn}$; Baruteau \& Masset 2008;  Paardekooper \& Papaloizou 2008; Casoli \& Masset 2010) and this
gives $\Gamma_{c,lin,e}\sim 0.71 \Gamma_0$ for $q=5\times 10^{-6}$ and $\Gamma_{c,lin,e}\sim 0.86\Gamma_0$ for $q=10^{-5}$
while using Eq. \ref{eq:gammacline} leads to $\Gamma_{c,lin,e}\sim 0.46 \Gamma_0$.\\
For modest values of $\gamma$, we see that good agreement is obtained between the results of the turbulent runs
and the analytic formulae of
Paardekooper et al. (2011). The basic reason for the differences at higher values of $\gamma$ possibly arises
from the evolution of the disc temperature profile. This is illustrated in Fig. \ref{fig:tprofile} which shows for
$q=5\times 10^{-6}$ the entropy and surface density profiles time-averaged over $1500$ $T_{orb}$. We note that in Fig.
\ref{fig:tprofile} the entropy profile corresponding to $\gamma=2\times 10^{-4}$ was offset by a factor of $2$ for clarity. Although the density remains
almost unchanged, the entropy profile can be significantly affected in the vicinity of the planet for $\gamma \ge 10^{-4}$ and this should in principle affect the value for the total torque.
For $\gamma=10^{-4}$, we find that with respect to an inviscid run, the entropy gradient is  increased by $\sim 20 \%$ at the location of the planet, which should increase the amplitude of the (negative) entropy-related corotation torque by the same amount. The corresponding change
on the slope of the temperature profile is estimated to lead to a $\sim 13 \%$ decrease in the amplitude of the (negative) differential Lindblad torque. Interestingly, such changes in the values for the corotation and the differential Lindblad torques
are found to almost cancel each other which suggests that in that case the modification of the
temperature by turbulence has little impact on the total torque experienced by the planet.
In the calculation with $\gamma=2\times 10^{-4}$, the  surface density at $R=1$ in only slightly reduced by $\sim 3\%$
with respect to the initial profile  but the temperature is found to be higher by a
factor of $\sim 2$, with the consequence that the torque exerted on the planet is weaker by the same factor compared to a
laminar run. Moreover, we quantify the corotation torque and the differential Lindblad torque
to be altered by $\sim 57 \%$  and $\sim 65 \%$ respectively due to the modification of the temperature slope at the
position of the planet. From these values, we estimate that for the run with $\gamma=2\times 10^{-4}$
and $q=5\times10^{-6}$, the
specific torque exerted on the planet would be $\sim 10^{-5}$ in the absence of modification of the temperature
profile by turbulence, which is somewhat larger than the value predicted by Eq. \ref{eq:totaltorque}. We note
that differences between the time-averaged turbulent torques and the analytical estimations may be also related to
uncertainties in Eqs. \ref{eq:fitalphav} and \ref{eq:fitkappa} which relate the value of $\gamma$ to those of $\alpha$ and
$\kappa$. \\
\begin{figure}
\centering
\includegraphics[width=0.95\columnwidth]{inviscid.eps}
\caption{Temperature profile at $t=1000$ $T_{orb}$ for $q=5\times 10^{-6}$ black line and $q=10^{-5}$ (red line).  The
dashed line corresponds to the initial temperature profile.}
\label{fig:tinviscid}
\end{figure}
\begin{figure}
\centering
\includegraphics[width=0.95\columnwidth]{entropy_q5em6.eps}
\includegraphics[width=0.95\columnwidth]{density_q5em6.eps}
\caption{{\it Upper panel:} Entropy profile in turbulent runs with $q=5\times 10^{-6}$ and time averaged over $1500$ $T_{orb}$.
 For $\gamma=2\times 10^{-4}$, the entropy profile was offset by a factor of $2$ for clarity.  The dashed line
corresponds to the initial entropy profile. {\it Lower panel:} Same but for the surface density profile.}
\label{fig:tprofile}
\end{figure}

\begin{figure*}
\centering
\includegraphics[width=0.325\textwidth]{2d_ent_lam.eps}
\includegraphics[width=0.325\textwidth]{2d_ent_turb_int.eps}
\includegraphics[width=0.325\textwidth]{2d_ent_turb.eps}
\caption{{\it Left panel:} Snapshot of the disc perturbed entropy at $t=800\;T_{orb}$ for a laminar run with
$q=5\times 10^{-6}$ and with constant thermal and viscous diffusion coefficents with values $\kappa=4.5\times 10^{-7}$ and $\nu=5.4\times 10^{-7}$ respectively. Streamlines are overplotted as black lines. {\it Middle panel:} same but for a turbulent
run with $\gamma=6\times 10^{-5}$. {\it Right panel:}  Contour plot of the perturbed entropy for the same turbulent
run but time-averaged
 between $750$ and $850$ orbits and over $6$ different realizations. Averaged streamlines are overplotted as black lines. }
\label{fig:2dplot}
\end{figure*}

We now turn to the question of how the torque dependence upon turbulence strength in turbulent simulations
compares with the torque dependence upon kinematic viscosity and thermal diffusivity in laminar runs. To investigate
this issue, we have performed an additional suite of laminar simulations in which we vary the value for
the thermal diffusivity while  the kinematic viscosity is set to $\nu= S_c^{-1}P_r\kappa\sim 1.2 \kappa$. The values for the thermal
diffusivity are chosen in such a way as to correspond to the effective values for thermal diffusivity in
turbulent runs and estimated using Eq. \ref{eq:fitkappa}. In order to take into account the alteration of the
temperature profile at high levels of turbulence, the inital surface
density and temperature profiles in these laminar simulations consist of the surface density and temperature profiles
in turbulent runs time-averaged over $1500$ orbits. The laminar torques typically reach a quasi-stationary value by $500$
 $T_{orb}$ and they are directly compared to the running time-averaged turbulent torques at $t=1500$ $T_{orb}$ in Fig. \ref{fig:rta}.
 Again, for the two values of $q$ we consider, relatively good agreement is obtained between the laminar and turbulent runs, even for high values of the thermal diffusivity for which the temperature profile can be strongly modified in turbulent runs. One can notice
however a tendency for the turbulent torques amplitudes to be slightly smaller than the laminar torques, which would
suggest that for similar values of the thermal and viscous diffusion coefficients, the corotation torque is slightly more saturated in turbulents discs than in laminar viscous disc models.  We note that such a trend was not observed in previous studies
of  the vorticity-related corotation torque in turbulent discs (Baruteau \& Lin 2010; Baruteau et al. 2011) which suggested
that the turbulent torque experienced by a protoplanet embedded in a isothermal turbulent disc is in decent agreement with its counterpart in a laminar
viscous disc model.  This discrepancy may arise because in non-isothermal discs, the
entropy-related corotation torque is associated with singular production of vortensity on downstream separatrices and
we may expect that compared with a turbulent disc, such a process is slightly more efficient in a laminar viscous disc model.
The fair agreement between turbulent and laminar torques reveals not only that the total torque experienced by a protoplanet
 can be decomposed into a laminar torque plus a stochastic torque, which was already suggested by Baruteau \& Lin (2010)
 in the case of isothermal disc models, but also that the entropy-related horseshoe drag takes similar values in
 turbulent and laminar disc models. This suggests that the structure of the horseshoe region
in turbulent discs should be similar  in time average to that in laminar disc models, which can be confirmed by
comparing  contour plots of the perturbed entropy for a turbulent run to those
corresponding to a laminar
calculation with similar values for the viscous and thermal diffusion coefficients. In Fig.
\ref{fig:2dplot} we present the perturbed entropy field  for a laminar
simulation (left panel) with $\kappa=4.5\times 10^{-7}$ and $\nu=5.4\times 10^{-7}$ and for a turbulent
run (middle panel) with $\gamma=6\times 10^{-5}$ (which correspond to effective values $\nu\sim 5.4\times 10^{-7}$ and $\kappa \sim 4.5\times 10^{-7}$) at $t=800\;T_{orb}$.
Overplotted are a few streamlines which are indicated with black lines and which were computed using the same initial
coordinates in the $R-\phi$ plane for the laminar and the turbulent runs.
 The right panel displays, for the turbulent run, the corresponding entropy field
and  streamlines averaged between $750$ and $850$ orbits (using field outputs produced every planet orbit) and over $6$ different realizations. Interestingly, one can see that
the averaged streamlines in the turbulent run have very similar shape to the streamlines in the laminar
simulation, which is in agreement with the results of Baruteau \& Lin (2010) in the case of isothermal discs. Here,
since the initial entropy
gradient is positive, dynamics in the horseshoe region yields a positive entropy perturbation at the  inward downstream
separatrix ($\phi>\phi_p$; $R<R_p$) whereas a negative entropy perturbation is created at the  outward downstream separatrix ($\phi<\phi_p$; $R>R_p$).
It is clear that these entropy perturbations for the turbulent run are very similar to those corresponding to
the laminar calculation, which
confirms  that the thermal diffusion coefficients are indeed close to each other in both
cases.

\section{Discussion and conclusion}
In this paper, we have presented the results of 2D hydrodynamical simulations which study the interaction
of an embedded low-mass planet with a turbulent
non-isothermal disc.
The aim is to investigate the role of turbulence on Type I migration in non-isothermal discs, with
particular emphasis on the process of desaturation of the entropy-related corotation torque
by turbulence. \\
We employ the turbulence model of Laughlin et al. (2004) in which a turbulent potential
corresponding to the superposition of multiple wave-like modes is applied to the disc. This
turbulence potential  had been shown previously to reproduce the main statistical properties of MHD turbulence
  in isothermal discs (Baruteau \& Lin 2010) . In non-isothermal discs,
turbulent density and entropy fluctuations generate transport of momentum and heat inside the
disc and we show that both the associated viscous and thermal diffusion coefficients scale as $\gamma^2$,
where $\gamma$ refers to the amplitude of the turbulent forcing. This results in a turbulent
Prandtl number $P_r=\alpha_R c_s H/\kappa$ where $\alpha_R$ is the Reynolds stress parameter  which is almost constant with $\gamma$ and we estimate
 for the first time that $P_r \sim 0.3$ in non-isothermal turbulent discs.  We caution, however, that such a value for the turbulent Prandtl number should be checked against 3D
MHD, non-isothermal simulations in which turbulence is generated by the MRI. \\
By investigating the evolution of the running time-averaged torque experienced by a protoplanet for
different values of $\gamma$, we show that turbulence can unsaturate the entropy-related corotation
torque.  For similar values for the viscous and thermal diffusion coefficients, we find that the formulae of Paardekooper
et al. (2011) for non-isothermal Type I migration in laminar disc models reproduce quite satisfactorily the time-averaged torques
deduced from our turbulent runs,  provided that the typical amplitude of turbulent fluctuations is not too large
so that turbulent transport of heat and momentum do not significantly modify the background density and
temperature profiles. For high values
of $\gamma$  corresponding to  values for the dimensionless $\alpha$ viscosity of Shakura \& Sunyaev (1973) $\alpha \gtrsim 10^{-3}$, we indeed observe discrepancies between the analytical estimate and the results of simulations which, to
a large extent, are related to the alteration of the temperature profile by turbulence.
We find also that the amplitudes of the running time-averaged
turbulent torques  are slightly smaller than the torques amplitudes deduced from laminar simulations with initial density and temperature
profiles corresponding to the time averaged profiles resulting from turbulent runs. This suggests
that the entropy-related horseshoe drag in presence of turbulence is slightly more saturated compared
to an equivalent laminar disc model with similar vortensity and entropy diffusion coefficients. \\
Although these results were obtained from a disc model in which the initial entropy gradient is
 positive, similar conclusions  should be drawn in the case of a negative initial entropy gradient.
 Since in that case
the amplitude of the total torque is only a small fraction of the typical amplitude of the stochastic torque,
turbulent runs would require a much longer convergence time than the simulations presented here.
For a negative initial entropy gradient, the
entropy-related corotation torque is positive and can eventually counteract the effect of the (negative)
differential Lindblad torque, depending on the local temperature gradient and provided that the viscous and thermal
diffusion coefficients are large enough to keep the entropy-related corotation torque from saturating. \\
The positive results obtained in this paper bring further support for the entropy-related corotation torque as a possible solution for the discrepancy between the mass-semi-major axis diagram of observed exoplanets, and that inferred from theories of planetary formation and evolution (e.g., Ida \& Lin 2008, Mordasini et al. 2009, Howard et al. 2010, Hellary \& Nelson 2012).\\
The simulations we have presented have neglected radiative processes and we will present in a future paper
simulations  with radiative transfert treated in the flux-limited approximation. We will also investigate the effects of turbulence on the dynamics of
multiple protoplanets located in the vicinity of an opacity transition where an entropy jump can act as a planet trap
and promotes embryo growth (Horn et al. 2012).
\section*{Acknowledgments}
Simulations were performed using HPC resources from GENCI-cines (c2012046733). Cl\'ement Baruteau is
supported by a Herchel-Smith Postdoctoral Fellowship of the University of Cambridge.

redpajama_set_name: RedPajamaArXiv


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A leaked slide from accessory-maker PDP puts a solid date on the arrival of Nintendo's next-gen game console, possibly coming ahead of Black Friday for a holiday push.
It's been known for some time that Nintendo is preparing its next-generation Wii U for a big holiday push and now a reported leak from a third-party accessory maker may have identified Nov. 18 as the day the new game console hits shelves.
That date was listed in a presentation delivered at a GameStop management conference in Texas by accessory-maker PDP, Kotaku reported Monday, citing an anonymous attendee whose account appeared to be backed up by a poster on the NeoGAF message board.
"A rep for PDP was showing the company's fall line-up at the conference and wrapped their presentation by saying the peripherals would be available just ahead of the Wii U's November 18 release date," Kotaku cited its source as saying.
UPDATE: A PDP executive has unequivocally denied that the company leaked the Wii U release date, saying it was an impossibility. The full story is here.
After the Kotaku post went live, a PDP spokesperson sought to downplay the company's possible knowledge of Nintendo's Wii U plans.
"[A]t this time we can't confirm Nintendo's dates and we don't know exactly what was heard, but we simply do not know that this point. We are launching accessories, but the date for the accessories doesn't mean a confirmation on the hardware. If you seek confirmation on the date that is something that is going to need to go specifically though Nintendo, but we can't confirm or deny dates on any of their hardware," PDP community manager Candace Hinton told Kotaku.
But Kotaku's Stephen Totilo reckoned the Nov. 18 date, a Sunday, had the ring of truth to it, given Nintendo's history of product releases on that specific day in that specific month. The Wii and the GameCube were also launched on Sundays in November, he noted. Nov. 18, meanwhile, is the last Sunday before Black Friday this year, another strong sign pointing towards the veracity of the PDP leak.
Nintendo is releasing its new console a full year before rivals Microsoft and Sony unleash their own successors to the Xbox 360 and PlayStation 3. Nintendo previewed some upcoming Wii U titles at the E3 gaming expo in Los Angeles earlier this year (video below).


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Migrating Windows XP to VirtualBox | It's "pwned" idiots not "pawned"
I needed to migrate a Windows XP box because it has a special piece of software…what special piece of software you ask? A real museum piece! Lotus 1-2-3 with a special quote form I didn't have time to migrate into something more contemporary.
1 – Make an image of the current physical box with clonezilla. It will bust it up into different size files, the default is 2000 megabytes (2 gig chunks). I'd make it much larger, if you have an 80 gig drive make it 85000 (85 gig just to be safe). I didn't happen to do that but I think it's an arbitrary thing ultimately since when you read the image back into the disk clonezilla automatically does it's thing regardless of chunk size.
2 – Create a new XP virtual machine in VirtualBox (can't hold your hand on this one…it would take too long to tell you how to do that so I assume you're not a total derp and you can manage this step).
3 – Select the new XP image > settings > storage > select the CD drive (Empty) > Click the drop down to the far right of "Optical Drive" and select your clonezilla ISO (I assume you have this in a folder on the new machine running VirtualBox).
4 – Boot the machine and image your saved image back to the virtual drive. Once done shut the machine down.
Virtual Box boots up and it's just a black screen. For this you need to be quick on the draw and hit F8 repeatedly to bring up the safe mode prompt. Then boot into safe mode, you should see either more black screen OR files flying accross the screen.
I found that in c:\windows\inf\ <– that folder on my imaged machine was EMPTY! Copy the data from your old physical box into your new one. I had to rename the INF folder to INF.kill > make a new INF folder then dump my files in there. You might also want to delete any "oem" inf files, in Linux you can do a: "ls | grep oem" to see the files with oem in their names then "rm -f oem*.inf" to delete all the INF files, note there are "PNF" files still left. I left those…not sure what they're for!
Once you do that…more problems but we can fix them.
Good one! It says: \SystemRoot\System32\Config\DEFAULT or its log or alternate. It is corrupt, absent, or not writable.
You can also go to your old physical box > boot up a Linux Live disk > migrate to that folder and copy your current "default" file onto removable media (USB disk) > then sneaker net it over to your other box > overwrite the default in the c:\windows\….config folder.
Reboot! Try safe mode just to be safe.
Success (at least for me). You then login and you get errors about: "The file or directory c:\windows\system is corrupt and unreadable. Please run the Chkdsk utility.".
** Fair warning again – this totally HOSED me when it booted up because when it booted up it didn't want to run the registration wizard so I re-did the migration knowing what to check (see above notes so far) and it went perfectly the second time…I think the original image back was borked since the INF folder was empty and the registry file was bad.
Windows will go through a litany of file systems checks and repair the error. Windows should now come up normally.
After that's all done > install your guest additions > make sure your drivers area good and things work. If it mostly works I'd call it a success!
Now reboot and let it boot up normally.


Browse by Topic AS/400 Business Intelligence Career Development Channel Cloud Computing Compliance Consumerization Content Management CRM Data Management Database DataCenter Desktop Management Development Email Administration Hardware IT Strategy Linux Lotus Domino Chris says: June 17, 2012 at 8:07 am I deleted the file but it didn't work.. I Google searched and found various options, mainly: -Locate and then click the following registry key: HKEY_Local_Machine\Software\Microsoft\Windows\CurrentVersion\Explorer\User Shell Folders-In the right pane of Registry Editor, double-click Common Administrative Tools.-In the Value Erasing stuff seems weird 10 pointsBadges: report Next View All Replies ADD YOUR REPLY There was an error processing your information.
NOTE: In the instructions below "[USERNAME]" should be replaced with your username, which may be different than the name you login to Windows with. I've been at this for days, just about given up...Again, many thanks for your solution and your help.Cheers mate. You can download a prog from microsoft which will fix my pics file it is Microsoft Fixit 50356.msi hope this helps a few people. 35 pointsBadges: report Evandunn Mar 20, 2010 If you reside outside of the United States, you consent to having your personal data transferred to and processed in the United States.
I don't have a clue how you knew the solution but I'm a happy camper. Can anyone please help me.. by Grif Thomas Forum moderator / June 21, 2005 1:24 AM PDT In reply to: Similar problem in XP - any ideas? ...removing the "Recent" key per my first instructions. in my application there is no registry like: HKEY_CURRENT_USER\ Software\ Microsoft\ Windows\ CurrentVersion\ Explorer\ Shell Folders..
Site Version: 2.13.0 I am facing same problem & i tried installation through CMD it got installed but i ma unable to open my report Juan Manuel Palomino Wolff Thank you very helfun [email protected] It won't hurt anything and usually fixes the problem similar to yours..In addition, there is a brand new Windows Installer 3.1 V2 and it's possible that it will help the issue. Flag Permalink This was helpful (0) Collapse - Thank you!
If you can't start the computer into "normal" windows, try installing, updating, and running the scans AFTER the computer is started into Safe Mode.. I'm not sure whichservice pack I'm running, but I do have automaticupdate "on" if that helps. Press ENTER after each command.regsvr32 wuapi.dllregsvr32 wuaueng.dllregsvr32 wuaueng1.dllregsvr32 wucltui.dllregsvr32 wups.dllregsvr32 wups2.dllregsvr32 wuweb.dllAttempt to run Windows Update Hope this helps and let us know how it goes.Grif Flag Permalink This was helpful Thanks.
HKEY_USERS\.DEFAULT\Software\Microsoft\Windows\CurrentVersion\Explorer\Shell Folders Check: Name | Value Local Settings | C:\WINDOWS\system32\config\systemprofile\Local Settings Local AppData | C:\WINDOWS\system32\config\systemprofile\Local Settings\Application Data Note: The values for the above registry entry may vary from machine to machine, I looked at theother links to the 1606 problem that relate toother registry entries and could't apply the fixesto my problem, as there was no problem with theFavorites entry in my Operating system, brand and model number, etc.? simply….
Double-click the old key and copy/paste it's Value into the new key. - AppData = %USERPROFILE%\ Application Data - Cache = %USERPROFILE%\ Local Settings\ Temporary Internet Files - Cookies = %USERPROFILE%\ by Grif Thomas Forum moderator / December 27, 2009 8:35 AM PST In reply to: Almost the same problem except... ..You'll need to perform the registry edits mentioned and make sure Windows may require a restart. Get Access Questions & Answers ?
Could Not Access Network Location .All Users\'' Error Message When You Install a Program?http://support.microsoft.com/default.aspx?scid=kb;en-us;Q315352Or?.?Error Message When You Install Plus! But if it doesn't exist, instead of skipping that version of Office, it returns a blank string resulting in the installation being unable to find the \Startup folder and aborting.To work Send me notifications when members answer or reply to this question. Just a quick update, I finally got the problem solved!First, I tried all deleting the Recent entry again,rebooted, no help.
For some reason, that keeps getting disabled. by R. Flag Permalink This was helpful (0) Collapse - (NT) (NT) Amblawn, Glad It Helped! What can i do?
It's XP Home Edition.I will try the new install link you mentionedand let you know how I make out.Thanks,Bill Flag Permalink This was helpful (0) Collapse - Bill, To Determine Which And Have You Tried??


text:
Q: Getting all values comma separated as last option in ng-repeat I have a select in which I am using ng-repeat to generate options. I am trying to have a last option as All which should have comma separated values of all the options
<select ng-model="facilityIdForEquipment" ng-change="loadFacilityEquipments()" >
      <option value="" selected>(Please select)</option>
      <option ng-repeat="facility in Facilities" value="{{facility.value}}">{{facility.text}}</option>
      <option value="">All Facilities</option>
</select>

I want to have comma separate values of all the options values in my All Facilities options. Something like this
<option value="1809,856,3214">All Facilities</option>

I can modify the object while loading these values from js but is there any way I can do this on markup using angular?

A: You can create a function to return csv.
<option value="{{ getValues(Facilities)}}">All Facilities</option>

method
$scope.getValues(facilities){
    return facilities.map(function(f){
        return f.value;
    }).join(',');
}

redpajama_set_name: RedPajamaStackExchange


text:
Dana Corporation Acquires Delphi's Southampton, U.K., Filtration Manufacturing Operation
TOLEDO, Ohio, Dec. 15 /PRNewswire/ -- In a strategic move to strengthen
its presence in the European marketplace, Dana Corporation (NYSE: DCN) today
announced that it has acquired the filtration manufacturing operation of
Delphi Energy & Engine Management Systems U.K. Overseas Corp., located in
Southampton, U.K.  Terms of the agreement were not announced.
The Southampton operation had 1997 sales of approximately $50 million
primarily from oil, air, fuel, and panel filtration products.  The operation
employs approximately 450 people.
According to Bill Lasky, president of Dana's Filtration Products Group,
the acquisition offers Dana a European foothold with solid growth potential in
a core business.  "This acquisition will strengthen our European presence --
with both original equipment and aftermarket customers," Lasky said.
"Along with our Quinton Hazell aftermarket filter operations in the U.K.,
and our Wix Filtron filtration products operations located in Poland, this
acquisition provides Dana with an excellent European base from which to grow
this core business," Lasky said.
Delphi Energy & Engine Management Systems is a division of Delphi
Automotive Systems, with lead responsibility for the generation, conversion,
and storage of electrical energy, the flow of air and fuel into an engine, the
combustion process, and the cleaning of exhaust emissions.  Headquartered in
Flint, Mich., the division employs more than 29,000 men and women in 28 wholly
owned manufacturing plants, nine joint ventures, 10 engineering centers, and
19 sales offices in 21 countries.
One of the world's largest independent suppliers to vehicular, off-
highway, and industrial manufacturers and their related aftermarkets, Dana
Corporation produces components and systems used on more than 95 percent of
the world's 670 million motor vehicles.  Founded in 1904 and based in Toledo,
Ohio, the company operates 270 major facilities in 33 countries and employs
more than 79,000 people.  The company had pro forma sales of $11.9 billion in
1997.  Dana's Internet address is http://www.dana.com.
SOURCE Dana Corporation
Web Site: http://www.dana.com
Company News On Call: Company News On-Call:
http://www.prnewswire.com/comp/226839.html or fax, 800-758-5804,
ext. 226839

redpajama_set_name: RedPajamaCommonCrawl


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text:
From Left to Right is an album by American jazz pianist Bill Evans, released in 1971.

Reissues
 From Left to Right was reissued on CD by Verve Records on November 13, 1998 with bonus tracks.
From Left to Right was reissued on CD by Universal in 2005 with the same bonus tracks as the 1998 release.

Track listing
 "What Are You Doing the Rest of Your Life?" (Alan Bergman, Marilyn Bergman, Michel Legrand) – 4:05
 "I'm All Smiles" (Michael Leonard, Herbert Martin) – 5:42
 "Why Did I Choose You?" (Leonard, Martin) – 5:04
 "Soirée" (Earl Zindars) – 3:24
 "The Dolphin-Before" (Luíz Eça) – 3:05
 "The Dolphin-After" (Luíz Eça) – 3:06
 "Lullaby for Helene" (Earl Zindars) – 2:50
 "Like Someone in Love" (Johnny Burke, Jimmy Van Heusen) – 5:38
 "Children's Play Song" (Evans) – 4:11
Bonus tracks:
 "What Are You Doing the Rest of Your Life?" (Bergman, Bergman, Legrand) – 4:44
 "Why Did I Choose You?" (Leonard, Martin) – 4:18
 "Soirée" [alternate take] (Earl Zindars) – 3:26
 "Lullaby for Helene" (Earl Zindars) – 2:39

Personnel
Bill Evans – Steinway grand piano, Fender-Rhodes electric piano
Eddie Gómez – bass
Marty Morell – drums
Sam Brown – guitar
Michael Leonard – conductor, arranger
Unidentified brass, woodwinds and strings

References

External links
Jazz Discography entries for Bill Evans
Bill Evans Memorial Library discography

1971 albums
Bill Evans albums
MGM Records albums
Verve Records albums

redpajama_set_name: RedPajamaWikipedia


text:
Home › News › Windows 10 1511 Fall Update ISO for Enterprise now Available for Download
Windows 10 1511 Fall Update ISO for Enterprise now Available for Download
After releasing the ISOs for the Fall Update, also known as Threshold 2 or Windows 10 version 1511, Microsoft has now released the ISO of the Enterprise Edition for business customers.
Thus, you can now download the latest version of Windows 10 as an image, without having to worry about previous updates. Windows 10 comes with quite a few new features for Enterprise users, and they will be able to enjoy all of them:
Windows Update for Business
Windows Store for Business
Azure Active Directory Join
Security upgrades, such as the option to turn off the collection of telemetry data
According to recent data, Microsoft has already announced that 12 million business PCs have already been updated to Windows 10 and the company is looking to increase that number even more.
Personal users still represent Microsoft's main business, but the company is continuously interested in enterprise users, as they mean bulk users and bigger fees to be paid by them.
Even if the ISOs were already been available on MSDN since last week, most of the business users get their Windows images through the Volume Licensing Center, and such is the case this time, as well. Go ahead and follow this link to download them.
Many enterprise users are still relying on Windows 7 for their needs, and even worse, some of them stick to Windows XP. So now it's high time for Microsoft to show what exactly is Windows 10 capable in doing for them.
windows 10 builds


text:
Rhynchospora cordatachenia är en halvgräsart som beskrevs av Mark T. Strong. Rhynchospora cordatachenia ingår i släktet småag, och familjen halvgräs. Inga underarter finns listade i Catalogue of Life.

Källor

Småag
cordatachenia


It's been three weeks since I finished work and I haven't yet woken up desperately searching for purpose. It might have something to do with my days being filled with french classes my evenings being filled with moving out of the house. Next week will be marked by a break in both of those activities, so we'll see if I discover boredom then. To be honest, though, I think I'll always be busy. I was born busy.
I had hoped to put my alarm clock up for sale on ebay by now, but, alas, it is still getting a lot of action. That will probably continue to be the case for the forseeable future. My blowdryer and flat iron, on the other hand, are enjoying retirement.
I'm adjusting to a life without an income. Making my own coffee and lunches. Washing my tupperware and thermos at night. I think this is what normal people do.
I walk to my french classes away from the flow of the downtown pedestrian traffic. The abundance of furrowed brows heading to the core makes me conscious of the absence of stress from my life, and I know that I'm moving in the right direction.
I eat my lunch outside. And slowly. Even when it rains.
I've made a game out of seeing how long the $20 bill in my pocket can last. I'm learning which little indulgences that I can go without and I'm rediscovering the joy of free stuff. I'm going for coffee with someone on friday and I'm looking forward to the 'free' coffee. I might even order a mocha!
I'm looking forward to spending some time with my family before I go. Moving in with my parents next week should help facilitate this. My schedule, so far, has not. The challenge, then, will be to find ways to hang out with Erik. Oh, these days are too short.
Less than three weeks now until I leave for Singapore.


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text:
Posted inFactCheck.org
Sequencing Used to Identify Delta, Other Coronavirus Variants
by WI Guest Author August 4, 2021 December 21, 2021
SciCheck Digest
Researchers use genomic sequencing — not the clinical tests used to diagnose patients with COVID-19 — to identify and track specific variants of the novel coronavirus, SARS-CoV-2, including the highly contagious delta variant. But viral posts try to deny the existence of the variant by misleadingly claiming there is "no 'Delta Variant' test."
The delta variant of the novel coronavirus — now the dominant version of the virus in the U.S. — has presented additional challenges as the country tries to mitigate the spread of COVID-19. The highly contagious variant is responsible for a surge in outbreaks across the country, particularly in areas with low vaccination rates. Vaccines still protect against the variant, especially against serious illness and death, but may be less effective against delta compared to other forms of the virus.
Yet false and misleading claims have recently sought to not only cast doubt on the seriousness of the variant, but question its existence.
One such meme shared on Facebook more than 12,000 times misleadingly asks, "Since there is no 'Delta Variant' test, how exactly are people being diagnosed with the 'Delta Variant'?"
The same question was presented in a July 26 tweet shared by thousands that was posted by Errol Webber, a film producer and Republican who unsuccessfully ran for Congress in California last year. Similar posts have been shared hundreds of times each.
Adding to the misperception, at a White House press briefing July 30, Emerald Robinson, a reporter for the conservative outlet Newsmax, asked, of the delta variant, "How do you test, when — that it's the dominant strain in the area, when people just test whether they're COVID positive?"
White House Principal Deputy Press Secretary Karine Jean-Pierre, seemingly perplexed, said "we don't test it" and that "we listen to public health and scientists, and they tell us that it's the Delta variant."
On Twitter, Robinson — who has nearly 400,000 followers — has since misleadingly claimed that "the Biden Administration is unable to provide any proof that Delta variant is real" and later that the administration "has no idea how to test for the Delta variant."
But the various posts trying to cast doubt on the validity of the delta variant betray a lack of understanding of how variants are being identified and tracked. There is testing to identify delta and other variants, but it's more sophisticated than the routine clinical testing — often by polymerase chain reaction, or PCR, tests — used to simply determine whether someone has COVID-19.
Dr. Benjamin Pinsky, an associate professor of pathology and medicine at Stanford University, told us in a phone interview that it's worth first noting that "all the diagnostic tests are capable of detecting the delta variant — they just don't distinguish it from different lineages." In other words, the PCR tests do detect the delta variant as SARS-CoV-2.
Identifying and tracking specific variants, however, requires additional analysis.
To do that, scientists use a process called genomic sequencing. As the Centers for Disease Control and Prevention explains, sequencing is a way to decode the genes of a virus to better understand factors such as its spread and evolution.
John Everett, who helps conducts such research at Penn Medicine to understand the virus' presence in the Delaware Valley, explained it this way: "Research institutions, including Penn, study samples collected from the community by sequencing viral genomes in those samples. We identify mutations in the genomes, compared to the original Wuhan strain, where groupings of specific mutations are used to define viral variants or lineages."
"We track the relative rise and fall of different lineages which we can break apart by zip code to build a picture of how the different lineages are spreading in our area," Everett, the bioinformatics director for the University of Pennsylvania lab group behind the research, told us by email.
The group's data show how the delta variant has rapidly become the main lineage identified in most samples tested from the University of Pennsylvania Health System.
Some findings done through PCR tests can provide insights into the suspected lineage present. For example, the alpha variant — first identified in the United Kingdom in September 2020 — caused PCR failuresinvolving the virus' S gene, which codes for the surface spike protein, because of the variant's mutations.
The phenomenon of variants causing test issues is expected, Everett said, which is why PCR tests check against "multiple regions of the viral genome." That's "another reason why surveillance is important — to identify mutations in the community which may interfere with tests and adjust the tests as needed," he said.
Dr. Marie-Louise Landry, director of the Clinical Virology Laboratory at Yale New Haven Hospital, noted that the S gene issue"was only suggestive of alpha" since it was only one of the characteristic mutations of alpha. Sequencing the whole genome, she told us by email, is still needed to confirm that it was indeed the alpha variant.
Pinsky, who is also medical director of the Clinical Virology Laboratory for Stanford Health Care, said his lab runs a second, different PCR test on samples that are positive for SARS-CoV-2 to look for specific mutations that are seen in variants of concern and variants of interest prior to sequencing.
For the delta variant, Pinsky said, what's known as the L452R mutation is often a telling sign: About 94% of the samples analyzed by his lab that show that mutation are proven to be delta once sequenced, he said. Moreover, about 90% of all positive samples recently sequenced by his lab are delta, he said.
"Delta is certainly not a hoax," Pinsky said.
And while some of the viral posts online suggest patients are being "diagnosed" with the delta variant, all the experts we consulted said that patients would not be typically informed of the lineage identified — though, in areas with predominantly delta transmission, patients may be able to make inferences.
Dr. Atul Butte noted to us in an email that sequencing analyses "are NOT clinical tests."
"These sequences are used for public health tracking and epidemiology," said Butte, a University of California, San Francisco pediatrics and epidemiology professor who also directs the university's Bakar Computational Health Sciences Institute. "We wouldn't deliver any different medical care right now, based on whether one variant is present or another."
Editor's note: SciCheck's COVID-19/Vaccination Project is made possible by a grant from the Robert Wood Johnson Foundation. The foundation has no control over our editorial decisions, and the views expressed in our articles do not necessarily reflect the views of the foundation. The goal of the project is to increase exposure to accurate information about COVID-19 and vaccines, while decreasing the impact of misinformation.
Butte, Atul. Professor of pediatrics and epidemiology, University of California, San Francisco. Email to FactCheck.org. 2 Aug 2021.
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"COVID-19 Vaccine Breakthrough Case Investigation and Reporting." Centers for Disease Control and Prevention. Accessed 2 Aug 2021.
Everett, John. Bioinformatics director, Bushman Lab, University of Pennsylvania. Email to FactCheck.org. 2 Aug 2021.
Hale Spencer, Saranac. "Meme Trumpets Falsehood About Delta Variant." FactCheck.org. 9 Jul 2021.
"Karine Jean-Pierre holds White House news briefing." Rev.com. 30 Jul 2021.
Landry, Marie-Louise. Director, Clinical Virology Laboratory at Yale New Haven Hospital. Email to FactCheck.org. 3 Aug 2021.
"Penn Medicine Surveillance Sequencing of SARS-CoV-2 Variants." University of Pennsylvania. Accessed 2 Aug 2021.
Pinsky, Benjamin. Associate professor of pathology and medicine, Stanford University. Phone interview with FactCheck.org. 3 Aug 2021.
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Post Comes to Premature Conclusions About COVID-19 Omicron Variant Severity
In "FactCheck.org"
Vaccines Remain Largely Effective Against Delta Variant, Counter to Claims From Fox News Guest
Q&A on the Omicron Variant
Tagged: COVID-19, FactCheck.org


Michiana's First Night of Two Tweetups - Search Engine Marketing: PPC & SEO. Startups & Strategy in Bay Area & Beyond.
Scheduling snafus, controversies, and an uphill battle were among the events encircling last night's Northern Indiana Social events for those in Michiana. I would be less than honest if I didn't confess that my thoughts on the drive up were with them.
My thoughts were also on that drive up US 12 along the National Lakeshore. Its been too long since I had a good sundown drive along the lake, listening to good live music. It's the first time I drove that route, in that setting, in that car. But I'd a sworn the car knew every curve.
It put me in a Tweetup state of grace.
The first thing I heard when I got to the "It's Vegas, Baby," room was that the Michiana Tweetup was a success, and that a few of them made the drive over to be with us. Michelle Hillaert, Between the Buns Grill…wow. I was glad they hadn't had their taste for Tweetups spoiled.
Always good to see Lacy. Rumor had it his Indiana SBDC presentation that morning went off without a hitch. And Daver was allowed to pitch the Tweetup during the session.
Fun, friends, foods…and though Blue Chip Casino no longer carries Gumballhead, it was good to be back for the evening.
If it ain't free, it ain't for me. It's the only way to be.
…with the exception of the occasional killer milk & honey events like Social Media Club.
April 2010 NWITWeetup in pictures, through the eyes of my buddy, Tat .
What I hope the Michiana tweeps learned from the evening is that choices are plentiful. Nobody needs to get pigeonholed into any one particular event.
And they all can work together.