text:
Alko ( Oy Alko Ab) is a stock corporation under Finnish law in government property that has in Finland on an exclusive license for the retail sale of alcoholic beverages with an alcohol content of more than 4.7 percent. Only alcoholic beverages with less than 4.7 percent can be purchased in regular grocery stores. So there is beer in categories I to less than 2.8 percent and III (medium ( keskiolut ) ) with 3.7 to 4.7 percent.
In the years 1919-1932 there was a total ban on alcohol in Finland ( kieltolaki ), which, however, was undermined by private schnapps. The first alcohol - branch (then Alkoholiliike Oy Ab) was then opened also for a referendum in December 1931 on April 5, 1932 by 10 clock in Helsinki. At that time, customers still had to ask for products and know what they wanted to buy, since the bottles were not presented with the label to the customer on the shelves behind the seller.
Alko presented for the Winter War in the years 1939-1940 a total of 450,000 forth Molotov cocktails that were used against Russian tanks.
In 1995, when Finland joined the European Union, Finland has pledged to dissolve monopolies in production and import. Subsequently, the company was divided into three areas: alcohol ( Sales), Primalco (production ) and Havistra ( bulk purchase ), which all belong to the Altia Group. In 1998, Alko completely solved by Altia and is since then as an independent legal entity, although alcohol remains the main customer of Altia.
May Finns since January 1, 2004, other EU countries, 110 liters of beer, 90 liters of wine, 10 liters of spirits 20 liters and introduce other alcoholic beverages without taxes. Previously, only one liter of spirits and five liters of wine were allowed. Since the alcohol import from Sweden and Norway hardly worth because of the prevailing high prices, most alcohol from Tallinn is introduced, since the Estonian and Finnish language are relatively similar and there are several ferries that the route Helsinki - cope Tallinn in 90 minutes.
There are now 341 Alko shops and 127 order points in places where there is no alcohol outlets. A reorder point is often found in small supermarkets or shops in the country, where you can order products from the Alko range and pick up the next day.
Because of a ban on advertising for high-percentage alcohol drinks also makes the negative effects of alcohol in his advertising attention.
In many Nordic countries, there are similar alcohol monopolies, as in Sweden, Systembolaget, in Norway the Vinmonopolet in Iceland and the Faroe Islands, the Vínbúð the Rúsdrekkasøla Landsins. In Denmark, however, alcohol is freely available.
Types of business entity Osakeyhtiö Alcohol by volume Kamppi Prohibitionism Finnish prohibition referendum, 1931


text:
\section{INTRODUCTION}

Today, 30 years after the pioneering work by Larson (1981), observations and
simulations of the interstellar medium (ISM) are revealing its turbulent
nature with higher and higher fidelity (see, e.g., Elmegreen \& Scalo 2004;
McKee \& Ostriker 2007; Romeo et al.\ 2010).  A fundamental aspect of ISM
turbulence is the existence of scaling relations between the mass column
density ($\Sigma$), the 1D velocity dispersion ($\sigma$), and the size of
the region over which such quantities are measured ($\ell$):
\begin{equation}
\Sigma\propto\ell^{a},\;\;\;
\sigma\propto\ell^{b}.
\end{equation}
The values of $a$ and $b$, and the range of scales spanned by $\ell$ depend
on which ISM component we consider.  In this paper we focus on cold
interstellar gas, which is highly supersonic and hence strongly compressible,
and which is known to play an important role in the gravitational instability
of galactic discs (e.g., Lin \& Shu 1966; Jog \& Solomon 1984a,\,b; Bertin \&
Romeo 1988, and references therein).

In the molecular gas, $\mathrm{H}_{2}$, the scaling exponents are $a\approx0$
and $b\approx\frac{1}{2}$, and Eq.\ (1) holds up to scales of a few 100 pc.
In fact, both Galactic and extragalactic giant molecular clouds (GMCs) are
fairly well described by Larson's scaling laws, $\Sigma=constant$ and
$\sigma\propto\ell^{1/2}$, although the uncertainties are still large (e.g.,
Larson 1981; Solomon et al.\ 1987; Bolatto et al.\ 2008; Heyer et al.\ 2009;
Hughes et al.\ 2010; Kauffmann et al.\ 2010; Lombardi et al.\ 2010;
S\'{a}nchez et al.\ 2010; Azimlu \& Fich 2011; Ballesteros-Paredes et
al.\ 2011; Field et al.\ 2011; Kritsuk \& Norman 2011; Roman-Duval et
al.\ 2011; Beaumont et al.\ 2012).  Besides, Larson-type scaling relations
have now been observed, for the first time, in the dense star-forming clumps
of a high-redshift galaxy (Swinbank et al.\ 2011).

In the atomic gas, H\,\textsc{i}, the scaling exponents are instead
$a\sim\frac{1}{3}$ and $b\sim\frac{1}{3}$, and Eq.\ (1) seems to hold up to
scales of a few kpc.  A Kolmogorov scaling for both $\sigma$ and $\Sigma$ is
suggested by the observed power spectra of H\,\textsc{i} intensity
fluctuations, and is also consistent with other measurements (e.g., Lazarian
\& Pogosyan 2000; Elmegreen et al.\ 2001; Begum et al.\ 2006; Kim et
al.\ 2007; Dutta et al.\ 2008; Roy et al.\ 2008; Dutta et al.\ 2009a,\,b;
Block et al.\ 2010; Bournaud et al.\ 2010; Dutta et al.\ 2010; Dutta 2011;
Combes et al.\ 2012; Zhang et al.\ 2012).  Note, however, that the
uncertainties are larger than in the $\mathrm{H}_{2}$ case.  For example,
high-resolution simulations of supersonic turbulence suggest a Burgers
scaling for both $\sigma$ and $\Sigma$, i.e.\ $a\sim\frac{1}{2}$ and
$b\sim\frac{1}{2}$ (e.g., Fleck 1996; Kowal \& Lazarian 2007; Kowal et
al.\ 2007; Kritsuk et al.\ 2007; Schmidt et al.\ 2008; Price \& Federrath
2010).  Other recent simulation surveys suggest that the scaling exponent $a$
is significantly affected by turbulence forcing (Federrath et al.\ 2009,
2010) and self-gravity (Collins et al.\ 2012).

In spite of such a burst of interest in ISM turbulence, and in spite of the
dynamical importance of cold interstellar gas, there have been very few
theoretical works aimed at evaluating the effect of turbulence on disc
instability.  In fact, traditional stability analyses do not take into
account the scale-dependence of $\sigma$ (or $\Sigma$), but identify $\sigma$
with the typical 1D velocity dispersion observed at galactic scales.  The
first theoretical work devoted to the gravitational instability of turbulent
gas discs was made by Elmegreen (1996), who assumed Larson-type scaling
relations [see Eq.\ (1)] and investigated the case $a=-1$ and
$b=\frac{1}{2}$.  He found that the disc is always stable at large scales and
unstable at small scales.  Romeo et al.\ (2010) also assumed Larson-type
scaling relations, but explored the whole range of values for $a$ and $b$.
They showed that turbulence has an important effect on the gravitational
instability of the disc: it excites a rich variety of stability regimes,
several of which have no classical counterpart.  See in particular the
`\emph{stability map of turbulence}' (fig.\ 1 of Romeo et al.\ 2010), which
illustrates such stability regimes and populates them with observations,
simulations and models of interstellar turbulence.

In the gravitational instability of galactic discs, there is an important
interplay between stars and cold interstellar gas (e.g., Agertz et al.\ 2009;
Elmegreen 2011; Forbes et al.\ 2011; Cacciato et al.\ 2012).  The
gravitational coupling between these two components does not alter the form
of the local stability criterion, $Q_{\mathrm{eff}}\geq1$, but makes the
effective $Q$ parameter different from both the stellar and the gaseous
Toomre (1964) parameters (Bertin \& Romeo 1988; Romeo 1992, 1994; Elmegreen
1995; Jog 1996; Rafikov 2001; Shen \& Lou 2003; Elmegreen 2011; Romeo \&
Wiegert 2011).  The gravitational coupling between stars and gas also changes
the least stable wavelength (Jog 1996), among other diagnostics.

What is the effect of ISM turbulence in this more realistic context?  The
first published attempt to answer this question was made by Shadmehri \&
Khajenabi (2012).  They considered two-component discs of stars and turbulent
gas, chose $a$ and $b$ so as to sample five of the seven stability regimes
found by Romeo et al.\ (2010), and studied the dispersion relation
numerically.  Their study suggests that turbulence has a significant effect
on disc instability even when stars are taken into account.  The goal of our
paper is to answer the question above in detail, extending previous work
along two directions:
\begin{enumerate}
\item We perform a rigorous stability analysis of two-com\-ponent turbulent
  discs, motivated by observations of ISM turbulence in nearby galaxies.  In
  particular, we consider two complementary cases: H\,\textsc{i} plus
  $\mathrm{H}_{2}$, and gas plus stars.  In the first case, we examine the
  dispersion relation analytically, and illustrate how the gravitational
  coupling between H\,\textsc{i} and $\mathrm{H}_{2}$ modifies the main
  stability regimes of gas turbulence, which were originally derived
  neglecting such a coupling (Romeo et al.\ 2010).  In the second case, we
  show that there are four stability regimes of galactic interest, similar to
  those analysed above, but in only one of them do stars play a
  non-negligible role.  We then focus on such a regime, and illustrate how
  gas turbulence affects the onset of gravitational instability in the disc,
  i.e.\ the local stability threshold and the corresponding characteristic
  wavelength.
\item We apply this analysis to a large sample of star-form\-ing spirals from
  The H\,\textsc{i} Nearby Galaxy Survey (THINGS), previously analysed by
  Leroy et al.\ (2008) and Romeo \& Wiegert (2011), and illustrate how ISM
  turbulence affects a full set of stability diagnostics: the condition for
  star-gas decoupling, the effective $Q$ parameter, and the least stable
  wavelength.
\end{enumerate}

The rest of the paper is organized as follows.  The (in)stability of
two-component turbulent discs is analysed in Sect.\ 2, our application to
THINGS spirals is shown in Sect.\ 3, the relation between our results and
those of Shadmehri \& Khajenabi (2012) is discussed in Sect.\ 4, and the
conclusions are drawn in Sect.\ 5.

\section{(IN)STABILITY OF TWO-COMPONENT TURBULENT DISCS}

\subsection{Summary of the one-component case}

Here we summarize some of the results found by Romeo et al.\ (2010), which
are fundamental to a proper understanding of Sects 2.2--2.4.

The dispersion relation of a turbulent and realistically thick gas disc is
\begin{equation}
\omega^{2}=\kappa^{2}-2\pi G\Sigma(k)\,k+\sigma^{2}(k)\,k^{2},
\end{equation}
where $\omega$ and $k$ are the frequency and the wavenumber of the
perturbation, and $\kappa$ is the epicyclic frequency.  $\Sigma(k)$ and
$\sigma(k)$ are the mass column density and the 1D velocity dispersion
measured over a region of size $\ell=1/k$, as inferred from observations
(see, e.g., Elmegreen \& Scalo 2004; McKee \& Ostriker 2007; Romeo et
al.\ 2010):
\begin{equation}
\Sigma(k)=\Sigma_{0}\left(\frac{k}{k_{0}}\right)^{-a},\;\;\;
\sigma(k)=\sigma_{0}\left(\frac{k}{k_{0}}\right)^{-b}.
\end{equation}
If the disc has volume density $\rho$ and scale height $h$, then
$\Sigma\approx2\rho\ell$ for $\ell\la h$ and $\Sigma\approx2\rho h$ for
$\ell\ga h$.  The range $\ell\la h$ corresponds to the case of 3D turbulence
(GMCs and H\,\textsc{i} at small scales), whereas the range $\ell\ga h$
corresponds to the case of 2D turbulence (H\,\textsc{i} at large scales).
The quantity $\ell_{0}=1/k_{0}$ introduced in Eq.\ (3) is the fiducial scale
at which $\Sigma$ and $\sigma$ are observed.  This is also the scale at which
the Toomre parameter $Q$ and other stability quantities are measured, so that
$Q_{0}=\kappa\sigma_{0}/\pi G\Sigma_{0}$.

The scaling exponents $a$ and $b$ have an important effect on the shape of
the dispersion relation [Eq.\ (2)], and hence on the condition for local
gravitational instability ($\omega^{2}<0$).  As $a$ and $b$ vary, turbulence
drives the disc across seven stability regimes, three of which are densely
populated by observations, simulations and models of galactic turbulence (see
fig.\ 1 of Romeo et al.\ 2010):
\begin{itemize}
\item For $b<\frac{1}{2}\,(1+a)$ and $-2<a<1$ (hereafter \emph{Regime A}),
  the stability of the disc is controlled by $Q_{0}$: the disc is stable at
  all scales if and only if $Q_{0}\geq\overline{Q}_{0}$, where
  $\overline{Q}_{0}$ depends on $a$, $b$ and $\ell_{0}$.  This is the domain
  of H\,\textsc{i} turbulence.  Both H\,\textsc{i} observations and
  high-resolution simulations of supersonic turbulence are consistent with
  the scaling $a=b$.  In such a case, the local stability criterion
  degenerates into $Q_{0}\geq1$, as if the disc were non-turbulent and
  infinitesimally thin.
\item For $b>\frac{1}{2}\,(1+a)$ and $-2<a<1$ (hereafter \emph{Regime C}),
  the stability of the disc is no longer controlled by $Q_{0}$: the disc is
  always unstable at small scales (i.e.\ as $k\rightarrow\infty$) and stable
  at large scales (i.e.\ as $k\rightarrow0$).
\item For $b=\frac{1}{2}\,(1+a)$ and $-2<a<1$ (hereafter \emph{Regime B}),
  the disc is in a phase of transition between stability \`{a} la Toomre
  (Regime A) and instability at small scales (Regime C).  This is the domain
  of $\mathrm{H}_{2}$ turbulence.  Note, however, that even small deviations
  from Larson's scaling laws can drive the disc into Regime A or Regime C,
  and thus have a strong impact on its gravitational instability.
\end{itemize}

\begin{figure}
\centering
\includegraphics[scale=1.]{fig1.eps}
\caption{The main stability regimes of one-component turbulent discs (see
  Sect.\ 2.1).  Also shown are the two-component cases illustrated in
  Fig.\ 2: H\,\textsc{i} in Regime A ($a_{1}=b_{1}=\frac{1}{3}$) plus
  $\mathrm{H}_{2}$ in Regime A ($a_{2}=0.1$, $b_{2}=0.3$), Regime B
  ($a_{2}=0.0$, $b_{2}=0.5$), or Regime C ($a_{2}=-0.1$, $b_{2}=0.7$).}
\end{figure}

Since Regimes A--C are fundamental to a proper understanding of Sects
2.2--2.4, we show them in Fig.\ 1.  Note, however, that this simple figure is
not meant to be a substitute for fig.\ 1 of Romeo et al.\ (2010), which
illustrates all seven stability regimes and their relation to the
phenomenology of ISM turbulence.

\subsection{Dispersion relation and general properties}

Until now we have considered H\,\textsc{i} and $\mathrm{H}_{2}$ separately.
How does the stability scenario change when H\,\textsc{i} and
$\mathrm{H}_{2}$ are considered together?  And how does it change when both
gas and stars are taken into account?  We will answer these questions here
and in Sects 2.3 and 2.4.

When H\,\textsc{i} and $\mathrm{H}_{2}$ are considered together, their
gravitational coupling changes how the disc responds to perturbations.  The
dispersion relation can be expressed in a form that is particularly useful
for discussing the stability properties of the disc:
\begin{equation}
\left(\omega^{2}-\mathcal{M}_{1}^{2}\right)
\left(\omega^{2}-\mathcal{M}_{2}^{2}\right)=
\left(\mathcal{P}_{1}^{2}-\mathcal{M}_{1}^{2}\right)
\left(\mathcal{P}_{2}^{2}-\mathcal{M}_{2}^{2}\right),
\end{equation}
where
\begin{equation}
\mathcal{M}_{i}^{2}\equiv
\kappa^{2}-2\pi G\Sigma_{i}(k)\,k+\sigma_{i}^{2}(k)\,k^{2},
\end{equation}
\begin{equation}
\mathcal{P}_{i}^{2}\equiv
\kappa^{2}+\sigma_{i}^{2}(k)\,k^{2},
\end{equation}
and $i=1,2$.%
\footnote{The dispersion relation of an $N$-component turbulent disc is
  $\sum_{i=1}^{N} (\mathcal{M}_{i}^{2}-\mathcal{P}_{i}^{2}) /
  (\omega^{2}-\mathcal{P}_{i}^{2}) = 1$, as can easily be inferred from
  eq.\ (22) of Rafikov (2001).  This equation cannot be expressed in a form
  similar to Eq.\ (4), and will not be used in the rest of the paper.}
Note that $\omega^{2}=\mathcal{M}_{i}^{2}(k)$ is the one-component dispersion
relation for potential-density waves [cf.\ Eq.\ (2)], while
$\mathcal{P}_{i}^{2}(k)$ describes sound waves modified by rotation (and
turbulence).  Since $\mathcal{M}_{i}^{2}(k)-\mathcal{P}_{i}^{2}(k)$
represents the self-gravity of component $i$, the right-hand side of Eq.\ (4)
measures the strength of gravitational coupling between the two components.

Eqs (4)--(6) are also applicable to two-component discs of gas and stars,
even though the stellar component is collisionless and non-turbulent.  This
is because stars can be accurately treated as a fluid when analysing the
stability of galactic discs (Bertin \& Romeo 1988; Rafikov 2001), and because
the equations above are valid whether each fluid is turbulent or not.
Remember, in fact, that the phenomenology of turbulence is encapsulated in
$\Sigma_{i}(k)$ and $\sigma_{i}(k)$ without altering the form of those
equations.  When the disc is made of gas (g) and stars ($\star$),
$\Sigma_{\mathrm{g}}(k)$ and $\sigma_{\mathrm{g}}(k)$ are given by Eq.\ (3),
while the stellar quantities are not.  $\Sigma_{\star}(k)$ is the reduced
surface density, $\Sigma_{\star}(k)=\Sigma_{\star}/(1+kh_{\star})$, where the
$k$-dependent factor results from the finite scale height of the stellar
layer (Vandervoort 1970; Romeo 1992, 1994; Elmegreen 2011).  In contrast,
$\sigma_{\star}$ is the radial velocity dispersion and does not depend on
$k$, since the pressure term in the dispersion relation is unaffected by disc
thickness (see again Vandervoort 1970).  The gaseous and stellar Toomre
parameters are then defined as
$Q_{\mathrm{g}0}=\kappa\sigma_{\mathrm{g}0}/\pi G\Sigma_{\mathrm{g}0}$ and
$Q_{\star}=\kappa\sigma_{\star}/\pi G\Sigma_{\star}$.

\begin{figure*}
\includegraphics[scale=.97]{fig2.eps}
\caption{The two branches of the dispersion relation, $\omega_{+}^{2}(k)$ and
  $\omega_{-}^{2}(k)$, vs.\ their one-component counterparts,
  $\mathcal{P}_{i}^{2}(k)$ and $\mathcal{M}_{i}^{2}(k)$, in stability regimes
  of galactic interest.  These quantities are measured in units of
  $\kappa^{2}$, the square of the epicyclic frequency, while $k$ is measured
  in units of $k_{\mathrm{T1,0}}=\kappa^{2}/2\pi G\Sigma_{1,0}$, the Toomre
  wavenumber of component $i=1$ at scale $\ell=\ell_{0}$.  The cases
  illustrated represent a disc made of marginally stable H\,\textsc{i} (in
  Regime A) and unstable $\mathrm{H}_{2}$ (in Regimes A--C).  The scaling
  exponents are specified in Fig.\ 1.  The other independent quantities are
  as follows: $k_{0}=8\,k_{\mathrm{T1,0}}$, $Q_{1,0}=1$,
  $\Sigma_{2,0}/\Sigma_{1,0}=1$ and $\sigma_{2,0}/\sigma_{1,0}=\frac{1}{2}$.
  These relations imply that $Q_{2,0}=\frac{1}{2}$ and
  $k_{0}=\frac{1}{2}\,k_{\mathrm{J2,0}}$, where $k_{\mathrm{J2,0}}=2\pi
  G\Sigma_{2,0}/\sigma_{2,0}^{2}$ is the Jeans wavenumber of component $i=2$
  ($\mathrm{H}_{2}$) at scale $\ell=\ell_{0}$.}
\end{figure*}

As Eq.\ (4) is quadratic in $\omega^{2}$, it can be solved with elementary
methods.  The discriminant is positive, so there are two real roots:
\begin{equation}
\omega_{\pm}^{2}=
\frac{1}{2}\left[\left(\mathcal{M}_{1}^{2}+\mathcal{M}_{2}^{2}\right)
\pm\sqrt{\Delta}\,\right],
\end{equation}
\begin{equation}
\Delta=
\left(\mathcal{M}_{1}^{2}-\mathcal{M}_{2}^{2}\right)^{2}+4
\left(\mathcal{P}_{1}^{2}-\mathcal{M}_{1}^{2}\right)
\left(\mathcal{P}_{2}^{2}-\mathcal{M}_{2}^{2}\right).
\end{equation}
This means that the dispersion relation has two branches that do not cross,
$\omega_{+}^{2}(k)\neq\omega_{-}^{2}(k)$, except possibly as $k\rightarrow0$
or $k\rightarrow\infty$.  The functions $\omega_{\pm}^{2}(k)$ satisfy two
basic properties, which constrain the gravitational instability of the disc
and generalize the stability constraints found in the classical two-component
case (Jog \& Solomon 1984a; Bertin \& Romeo 1988).  Such properties are
stated and proved below, and can easily be visualized with the help of
Fig.\ 2.  The cases illustrated represent a disc made of marginally stable
H\,\textsc{i} (in Regime A) and unstable $\mathrm{H}_{2}$ (in Regimes A--C).
\begin{itemize}
\item \emph{Property I:} $\omega_{-}^{2}(k)$ lies below both
  $\mathcal{M}_{1}^{2}(k)$ and $\mathcal{M}_{2}^{2}(k)$, i.e.\ a
  two-component self-gravitating disc is more unstable (or less stable) than
  each component, whether this is turbulent or not.  This can be proved by
  noting that $\Delta$ is larger than
  $(\mathcal{M}_{1}^{2}-\mathcal{M}_{2}^{2})^{2}$, so that
  $\sqrt{\Delta}>|\mathcal{M}_{1}^{2}-\mathcal{M}_{2}^{2}|$.  In turn, this
  implies that $\omega_{-}^{2}<\mathcal{M}_{\mathrm{min}}^{2}$, where
  $\mathcal{M}_{\mathrm{min}}^{2}$ is the smallest $\mathcal{M}_{i}^{2}$ for
  a given $k$.
\item \emph{Property II:} $\omega_{+}^{2}(k)$ is bounded by
  $\mathcal{P}_{1}^{2}(k)$ and $\mathcal{P}_{2}^{2}(k)$, i.e.\ this branch is
  always stable and represents sound waves modified by rotation (and
  turbulence).  To prove this, note that the inequality
  $\sqrt{\Delta}>|\mathcal{M}_{1}^{2}-\mathcal{M}_{2}^{2}|$ also implies that
  $\omega_{+}^{2}>\mathcal{M}_{\mathrm{max}}^{2}$, where
  $\mathcal{M}_{\mathrm{max}}^{2}$ is the largest $\mathcal{M}_{i}^{2}$ for a
  given $k$.  Note also that $\omega_{+}^{2}$ cannot be smaller than
  $\mathcal{P}_{\mathrm{min}}^{2}$ or larger than
  $\mathcal{P}_{\mathrm{max}}^{2}$, otherwise Eq.\ (4) would not hold.
  Therefore it must be $\mathcal{P}_{\mathrm{min}}^{2}\leq\omega_{+}^{2}\leq
  \mathcal{P}_{\mathrm{max}}^{2}$.
\end{itemize}

\subsection{\textmd{H\,\textsc{i}} plus $\mathrm{H}_{2}$}

In Sect.\ 2.1, we have summarized the main stability regimes of one-component
turbulent discs.  Let us now extend the discussion to two-component discs of
H\,\textsc{i} and $\mathrm{H}_{2}$, analysing three cases of galactic
interest (see again Fig.\ 2).

\subsubsection{$\mathrm{H}_{2}$ in Regime A}

The response of each component is driven by pressure at small scales and by
rotation at large scales, while self-gravity acts more strongly at
intermediate scales (see sect.\ 2.7 of Romeo et al.\ 2010).  This means that
the gravitational coupling between the two components is negligible as
$k\rightarrow0$ and $k\rightarrow\infty$, and so is the right-hand side of
Eq.\ (4).  Therefore the two branches of the dispersion relation behave
asymptotically as $\mathcal{M}_{1}^{2}(k)$ and $\mathcal{M}_{2}^{2}(k)$,
i.e.\ they converge to $\kappa^{2}$ as $k\rightarrow0$ and diverge positively
as $k\rightarrow\infty$.  Since the potentially unstable branch
$\omega_{-}^{2}(k)$ lies below $\mathcal{M}_{i}^{2}(k)$ (cf.\ Property I) and
$\mathcal{M}_{i}^{2}(k)$ has a minimum for $k>0$, $\omega_{-}^{2}(k)$ must
also have a global minimum below $\kappa^{2}$.  Thus the disc is stable \`{a}
la Toomre, like each component (see left panel of Fig.\ 2).

\subsubsection{$\mathrm{H}_{2}$ in Regime C}

The response of H\,\textsc{i} is similar to the previous case, while
$\mathrm{H}_{2}$ behaves differently (see sect.\ 2.5 of Romeo et al.\ 2010).
The self-gravity term gets dominant for large $k$ and makes
$\mathcal{M}_{\mathrm{H}2}^{2}(k)$ negative.  So $\omega_{-}^{2}(k)$ is also
negative in this limit (cf.\ Property I).  For small $k$,
$\mathcal{M}_{\mathrm{H}2}^{2}(k)$ is positive since it is dominated by the
pressure term ($b>1$) and/or the rotation term ($b\leq1$).  As neither
$\mathcal{M}_{\mathrm{H2}}^{2}(k)$ nor $\mathcal{M}_{\mathrm{HI}}^{2}(k)$ is
driven by self-gravity at large scales, the right-hand side of Eq.\ (4) is
negligible as $k\rightarrow0$.  So $\omega_{-}^{2}(k)$ is positive in this
limit, like $\mathcal{M}_{\mathrm{HI}}^{2}(k)$ and
$\mathcal{M}_{\mathrm{H2}}^{2}(k)$.  The disc is then unstable at small
scales and stable at large scales, like $\mathrm{H}_{2}$ itself (see right
panel of Fig.\ 2).

\subsubsection{$\mathrm{H}_{2}$ in Regime B}

The behaviour of $\mathrm{H}_{2}$ is intermediate between the previous two
cases (see sect.\ 2.3 of Romeo et al.\ 2010).  A similar flow of arguments
shows that the disc is in a phase of transition between stability \`{a} la
Toomre and instability at small scales, like $\mathrm{H}_{2}$ itself.  The
middle panel of Fig.\ 2 illustrates the phase of small-scale instability,
which occurs for $k_{0}\leq k_{\mathrm{J2,0}}=2\pi
G\Sigma_{\mathrm{H2,0}}/\sigma_{\mathrm{H2,0}}^{2}$ (see Hoffmann 2010 for a
detailed analysis).  Note how the two components contribute to the
gravitational instability of the disc, and how their coupling widens the
range of unstable scales.

\subsection{Gas plus stars}

This case involves three components: H\,\textsc{i}, $\mathrm{H}_{2}$ and
stars.  In nearby spiral galaxies, H\,\textsc{i} and $\mathrm{H}_{2}$ have
distinct domains: H\,\textsc{i} dominates the outer regions of the gas disc,
while $\mathrm{H}_{2}$ dominates the inner regions (e.g., Leroy et
al.\ 2008).  We can then consider H\,\textsc{i} and $\mathrm{H}_{2}$
separately.  This makes sense here because we already know how the
gravitational coupling between H\,\textsc{i} and $\mathrm{H}_{2}$ modifies
the main stability regimes of gas turbulence (see Sect.\ 2.3).  What we now
want to understand is the role that stars play in this stability scenario.
Let us then distinguish two cases:
\begin{enumerate}
\item \emph{Stars plus $\mathrm{H}_{2}$.}  Since the stellar component
  populates Regime A (like H\,\textsc{i}) and $\mathrm{H}_{2}$ populates
  Regimes A--C, this case is qualitatively similar to the set of cases
  analysed in Sect.\ 2.3.  So there are three stability regimes: stability
  \`{a} la Toomre, instability at small scales, and a phase of stability
  transition.  Note that such a variety of regimes is driven by
  $\mathrm{H}_{2}$ turbulence.  The stellar component can only modify the
  shape of the dispersion relation; it cannot change the type of stability
  regime.  Note also that there is a mismatch between two important scales.
  One is the characteristic scale of stellar instabilities,
  $L_{\star}=\sigma_{\star}^{2}/\pi G\Sigma_{\star}$, which is typically
  $\sim1\;\mbox{kpc}$ (see, e.g., Binney \& Tremaine 2008).  The other is the
  largest scale at which $\mathrm{H}_{2}$ turbulence has been observed,
  $L_{\mathrm{H2}}\sim100\;\mbox{pc}$ (e.g., Bolatto et al.\ 2008).  Since
  $L_{\star}$ is one order of magnitude larger than $L_{\mathrm{H2}}$, the
  stellar component cannot play a significant role in such stability regimes.
  Therefore this is essentially a one-component case, driven and dominated by
  $\mathrm{H}_{2}$.  In Sect.\ 3, we will show that such stability regimes
  can indeed be frequent in nearby star-forming spirals.
\item \emph{Stars plus \textup{H\,\textsc{i}}.}  As both components populate
  Regime A, this is a case of stability \`{a} la Toomre: $\omega_{-}^{2}(k)$
  has a global minimum, which determines whether the disc is stable for all
  wavenumbers or not (cf.\ Sect.\ 2.3.1).  In contrast to case (i),
  H\,\textsc{i} turbulence reaches scales as large as 1--10 kpc (e.g., Kim et
  al.\ 2007; Dutta 2011).  This makes it possible for the stellar component
  to `interact' with H\,\textsc{i} turbulence and contribute significantly to
  two-fluid instabilities, as in the classical case of stars plus
  non-turbulent gas.
\end{enumerate}

As discussed above, case (ii) represents the only stability regime in which
stars play a non-negligible role.  We then focus on this case, and analyse
how gas turbulence affects the onset of gravitational instability in the
disc, i.e.\ the local stability threshold and the corresponding
characteristic wavelength.  The effect of disc thickness is well known in
this context (Romeo 1992, 1994; Elmegreen 2011; Romeo \& Wiegert 2011).  So
we do not take that effect into account.

\subsubsection{The stability threshold}

As this is a Toomre-like case, the local stability criterion can be expressed
in the usual form $Q_{\mathrm{eff}}\geq1$, where $Q_{\mathrm{eff}}$ is the
effective $Q$ parameter.  In the classical case of stars plus non-turbulent
gas, $Q_{\mathrm{eff}}$ depends on three parameters: $Q_{\star}$,
$Q_{\mathrm{g}}$ and $s=\sigma_{\mathrm{g}}/\sigma_{\star}$.  For analysing
$Q_{\mathrm{eff}}$ in detail, it is useful to factor out the dependence on
$Q_{\star}$, $Q_{\mathrm{eff}}=Q_{\star}/\,\overline{Q}$, and study the
stability threshold $\overline{Q}$ as a function of $s$ and
$q=Q_{\mathrm{g}}/Q_{\star}$ (Romeo \& Wiegert 2011).  When gas turbulence is
taken into account via Eq.\ (3), $\overline{Q}$ depends on five parameters:
\begin{equation}
s_{0}\equiv\frac{\sigma_{\mathrm{g}0}}{\sigma_{\star}},\;\;\;
q_{0}\equiv\frac{Q_{\mathrm{g}0}}{Q_{\star}},
\end{equation}
$a$, $b$ and
\begin{equation}
\mathcal{L}_{0}\equiv\ell_{0}\,k_{\mathrm{T}\star},
\end{equation}
where $k_{\mathrm{T}\star}=\kappa^{2}/2\pi G\Sigma_{\star}$ is the stellar
Toomre wavenumber.  A general five-parameter study of $\overline{Q}$ is not
more useful than a targeted few-parameter analysis.  This is because $a$, $b$
and $\mathcal{L}_{0}$ are tightly constrained by observations, and because
their observed values fall within a single stability regime (remember that
this is a region of the parameter space where the disc has similar stability
properties).  For these reasons, we analyse $\overline{Q}$ as a function of
$s_{0}$ and $q_{0}$, choosing observationally motivated values of $a$, $b$
and $\mathcal{L}_{0}$: $a=b=\frac{1}{3}$, which is the typical scaling of
H\,\textsc{i} turbulence (see Sect.\ 1), and $\mathcal{L}_{0}=1.0\pm0.5$,
which are the median and $1\sigma$ scatter of $\mathcal{L}_{0}$ in the outer
discs of THINGS spirals (where H\,\textsc{i} dominates; see Sect.\ 3).  The
range $0.5\leq\mathcal{L}_{0}\leq1.5$ is also representative of clumpy
galaxies at intermediate and high redshifts.%
\footnote{Puech (2010) analysed two such galaxy samples at $z\approx0.6$ and
  $z\approx2$.  The median properties of the discs are summarized in his
  table 1 (see also his sect.\ 3.2).  Using those data, we find that the
  stellar Toomre wavenumber is
  $k_{\mathrm{T}\star}\approx0.3\;\mbox{kpc}^{-1}$ at $z\approx0.6$ and
  $k_{\mathrm{T}\star}\approx0.2\;\mbox{kpc}^{-1}$ at $z\approx2$.  The
  spatial resolution is $\ell_{0}\approx7\;\mbox{kpc}$ and
  $\ell_{0}\approx5\;\mbox{kpc}$ in the two cases (Puech, private
  communication).  This yields $\mathcal{L}_{0}\approx2$ at $z\approx0.6$ and
  $\mathcal{L}_{0}\approx1$ at $z\approx2$.  Thus, even at intermediate and
  high redshifts, $\mathcal{L}_{0}$ is remarkably close to unity and lies
  within the $1\sigma$ scatter computed from THINGS.}

\begin{figure}
\centering
\includegraphics[scale=1.]{fig3.eps}
\caption{Contour lines of the stability threshold,
  $\overline{Q}(s_{0},q_{0})=constant$, for discs of stars and turbulent
  H\,\textsc{i} vs.\ the classical case of stars plus non-turbulent gas.  The
  solid lines and the shaded regions correspond to the median and the
  $1\sigma$ scatter of $\mathcal{L}_{0}$ in the outer discs of THINGS
  spirals.}
\end{figure}

Fig.\ 3 shows a contour map of the stability threshold $\overline{Q}$ for
classical and turbulent discs.  Consider the classical case first, and look
at the contour levels $\overline{Q}=1.1$ and $\overline{Q}=1.4$.  Their slope
changes abruptly across the line $q_{0}=1$, showing that there are two
distinct stability regimes.  This fact has a simple explanation in terms of
star-gas decoupling (Bertin \& Romeo 1988; Romeo \& Wiegert 2011).  When
$s_{0}\la0.2$ and $q_{0}\sim1$, $\omega_{-}^{2}(k)$ has two minima: one at
small $k$, where the response of the stellar component peaks; and the other
at large $k$, where gas dominates.  For $q_{0}<1$, the gaseous minimum is
deeper than the stellar one, and therefore it controls the onset of disc
instability.  Vice versa, for $q_{0}>1$, it is the stellar minimum that
determines the stability threshold.  The line $q_{0}=1$ separates gas- from
star-dominated regimes even when $s_{0}\ga0.2$, but the transition is smooth
in this case since $\omega_{-}^{2}(k)$ has a single minimum.  In the
turbulent case, each contour level is on average shifted down.  As
$\overline{Q}$ increases in the same direction, this means that turbulence
lowers the stability threshold, i.e.\ it tends to stabilize the disc.  In
Sect.\ 3, we will evaluate the statistical significance of this effect.

\subsubsection{The characteristic wavelength}

The global minimum of $\omega_{-}^{2}(k)$ provides another useful stability
diagnostic: the least stable wavelength
$\lambda_{\mathrm{min}}=2\pi/k_{\mathrm{min}}$ (see Jog 1996 for the
classical case).  When the disc is marginally stable, the value of
$\lambda_{\mathrm{min}}$ is of particular interest.  It is the wavelength at
which instability first appears as $Q_{\star}$ drops below $\overline{Q}$.
This wavelength can be written as
$\overline{\lambda}=\overline{\Lambda}\,\lambda_{\mathrm{T}\star}$, where
$\lambda_{\mathrm{T}\star}=2\pi/k_{\mathrm{T}\star}$.  The characteristic
wavelength $\overline{\Lambda}$ depends on the same parameters as
$\overline{Q}$.  So we adopt the same approach as before, and analyse
$\overline{\Lambda}$ as a function of $s_{0}$ and $q_{0}$ for observationally
motivated values of $a$, $b$ and $\mathcal{L}_{0}$.

\begin{figure}
\centering
\includegraphics[scale=1.]{fig4.eps}
\caption{Contour lines of the characteristic wavelength,
  $\overline{\Lambda}(s_{0},q_{0})=constant$, for discs of stars and
  turbulent H\,\textsc{i} vs.\ the classical case of stars plus non-turbulent
  gas.  The solid lines and the shaded regions correspond to the median and
  the $1\sigma$ scatter of $\mathcal{L}_{0}$ in the outer discs of THINGS
  spirals.}
\end{figure}

Fig.\ 4 shows a contour map of the characteristic wavelength
$\overline{\Lambda}$ for classical and turbulent discs.  In the classical
case, the contour levels $\overline{\Lambda}=0.1$ and
$\overline{\Lambda}=0.2$ are truncated above $q_{0}=1$.  This tells us that
such short characteristic wavelengths occur only when stars and gas are
decoupled and gas dominates.  In fact, star-dominated instabilities appear at
longer wavelengths: $\overline{\Lambda}\ga0.3$ (Bertin \& Romeo 1988).  Note
also that the contour $\overline{\Lambda}=0.5$ is a separatrix.  Levels below
0.5 are on the left of this curve (and connected to the transition line),
while levels above 0.5 are on the right.  In the turbulent case, each contour
level below 0.3 is on average shifted to the right, i.e.\ in the direction of
increasing $\overline{\Lambda}$.  This means that turbulence shortens the
characteristic wavelength when stars and gas are decoupled and gas dominates.
An opposite, although weaker, effect is detectable for
$\overline{\Lambda}\geq1$.  Other regimes are also affected, but in a more
complex way.  This is especially true for $\overline{\Lambda}\sim0.5$, since
the separatrix of the parameter plane shifts to larger values.  Last but not
least, note how turbulence bends the transition line down, favouring
star-dominated regimes.  In Sect.\ 3, we will analyse these effects in
detail.

\section{APPLICATION TO THINGS SPIRALS}

We now consider a sample of twelve nearby star-forming spirals from THINGS:
NGC 628, 3198, 3184, 4736, 3351, 6946, 3627, 5194, 3521, 2841, 5055, and
7331.  For these galaxies, a detailed analysis by Leroy et al.\ (2008)
provides high-quality measurements of kinematics, as well as stellar and
gaseous surface densities, at a constant spatial resolution of 800 pc.

Leroy et al.\ (2008) also analysed the stability of those galaxies, treating
the ISM as a single non-turbulent component, gravitationally coupled to
stars, with surface density
$\Sigma_{\mathrm{g}}=\Sigma_{\mathrm{HI}}+\Sigma_{\mathrm{H2}}$ and velocity
dispersion $\sigma_{\mathrm{g}}=11\;\mbox{km\,s}^{-1}$.  Such a value of
$\sigma_{\mathrm{g}}$ fits the H\,\textsc{i} data well, but is twice as large
as the typical $\mathrm{H}_{2}$ velocity dispersion observed in nearby spiral
galaxies (Wilson et al.\ 2011).  To represent both H\,\textsc{i} and
$\mathrm{H}_{2}$ well, we choose $\sigma_{\mathrm{g}}=8\;\mbox{km\,s}^{-1}$.
This value lies within the $1\sigma$ scatter of $\sigma_{\mathrm{HI}}$
($11\pm3\;\mbox{km\,s}^{-1}$; Leroy et al.\ 2008) and $\sigma_{\mathrm{H2}}$
($6.1\pm2.9\;\mbox{km\,s}^{-1}$; Wilson et al.\ 2011), and therefore allows
us to carry out an unbiased stability analysis of THINGS spirals.

The constant spatial resolution of 800 pc used by Leroy et al.\ (2008) makes
their data particularly appropriate for analysing the effect of H\,\textsc{i}
turbulence at galactic scales.  H\,\textsc{i} dominates the gas surface
density in the outer disc, typically for $R>0.43\;R_{25}$, where $R_{25}$ is
the optical radius (Leroy et al.\ 2008).  We then treat gas as turbulent for
$R>0.43\;R_{25}$, and assume Larson-type scaling relations [see Eq.\ (3)]
with $\ell_{0}=800\;\mbox{pc}$,
$\Sigma_{\mathrm{g}0}=\Sigma_{\mathrm{g}0}(R)$ as tabulated by Leroy et
al.\ (2008), and $\sigma_{\mathrm{g}0}=8\;\mbox{km\,s}^{-1}$ (see above).
Concerning $a$ and $b$, we analyse the case $a=b=\frac{1}{3}$ in detail,
since it represents H\,\textsc{i} observations fairly well (see Sect.\ 1).
We have also studied the case $a=b=\frac{1}{2}$, as representative of
high-resolution simulations of supersonic turbulence (see Sect.\ 1), but here
we will only mention it when discussing the results of our stability
analysis.  Hereafter we will refer to the model described above as
\emph{Model 1}.

\subsection{The condition for star-gas decoupling}

\begin{figure*}
\includegraphics[scale=.98]{fig5.eps}
\caption{The parameter plane populated by THINGS spirals (Model 1), and the
  `two-phase region' where stars and gas contribute separately to the
  gravitational instability of the disc: neglecting gas turbulence (left),
  and taking into account H\,\textsc{i} turbulence for $R>0.43\;R_{25}$
  (right).  In the turbulent case, the solid lines and the shaded regions
  correspond to the median and the $1\sigma$ scatter of $\mathcal{L}_{0}$ in
  that radial range.  Data from THINGS are coloured according to the dominant
  component: $\mathrm{H}_{2}$ for $R\leq0.43\;R_{25}$, and H\,\textsc{i} for
  $R>0.43\;R_{25}$.}
\end{figure*}

In Sect. 2.4, we have seen that there is a region in the parameter plane where $\omega_-^2(k)$ has two minima. This is the {\textquoteleft}two-phase region{\textquoteright} introduced by Bertin \& Romeo (1988) and further investigated by Romeo \& Wiegert (2011).

Fig.\ 5 shows the two-phase region for classical and turbulent discs. Within this region, stars and gas are dynamically decoupled and the disc is susceptible to instabilities at two different wavelengths, where the responses of the two components peak. In the stellar phase the disc is more susceptible to long-wavelength instabilities, whereas in the gaseous phase it is dominated by short-wavelength instabilities. Along the transition line between the phases, neither component dominates and instabilities occur both at short and at long wavelengths. Outside the two-phase region, the two components are strongly coupled and instabilities occur at intermediate wavelengths.

We populate the parameter plane with measurements taken from the sample of spiral galaxies, and colour-code them by radius. We draw the turbulent two-phase region corresponding to the median and $1\sigma$ scatter of $\mathcal{L}_0$ for $R > 0.43 \; R_{25}$. Note the following points:

\begin{enumerate}

  \item The two-phase region of a classical disc is symmetric about $q = 1$. This symmetry is broken for a turbulent disc because gas (dominant for $q < 1$) follows turbulent scaling, but stars (dominant for $q > 1$) do not.

  \item The turbulent two-phase region is larger than the classical one. This follows from the fact that turbulence pushes the minima of $\omega_-^2(k)$ further apart, and the maximum between them further up, so as to favour star-gas decoupling.

  \item The transition line appears unaffected by the scatter of $\mathcal{L}_0$. This is because the shape of the two-phase region depends on $s$ and $q$, and $q$ is not affected by turbulence ($q=q_0$) if $a=b$.

  \item Turbulence increases the size of the stellar phase more than that of the gaseous phase. Recall that the boundary of the two-phase region is marked by the disappearance of the non-dominant peak, i.e. the gas peak in the stellar phase and vice versa. Since turbulence affects the gaseous peak more than the stellar peak, the size of the stellar phase is affected more than that of the gaseous phase. For $R > 0.43 \; R_{25}$, this causes a significant number of measurements to populate the stellar phase.

  \item For $R \leq 0.43 \; R_{25}$, we find that $f_2 = 61\%$ of all points populate the two-phase region, two-thirds of them in the gaseous phase. In such cases, the onset of gravitational instability is controlled by H$_2$. Turbulence is expected to play an important role in this process at scales smaller than about $100 \; \mathrm{pc}$ (see Sect. 2.4). For $R > 0.43 \; R_{25}$, only $4\%$ of all points populate this region for a classical disc. This fraction increases to $22\%$ for a turbulent disc with $a = b = \frac{1}{3}$, and to $52\%$ for $a=b=\frac{1}{2}$.

\end{enumerate}

\subsection{The effective $Q$ parameter}

\begin{figure*}
\includegraphics[scale=.99]{fig6.eps}
\caption{Radial profile of the effective $Q$ parameter,
  $Q_{\mathrm{eff}}(R)$, for THINGS spirals (Model 1): neglecting gas
  turbulence (left), and taking into account H\,\textsc{i} turbulence for
  $R>0.43\;R_{25}$ (right).  The disc is locally unstable for
  $Q_{\mathrm{eff}}<1$ (light grey shading).  For each measurement, we
  indicate whether the stability level is dominated by the stellar
  ($Q_{\star}<Q_{\mathrm{g}0}$) or the gaseous ($Q_{\mathrm{g}0}<Q_{\star}$)
  component.  Thick black lines and dark grey shading indicate the median and
  $1\sigma$ scatter of $Q_{\mathrm{eff}}$ in the two radial ranges.}
\end{figure*}

Fig.\ 6 shows radial profiles of the effective $Q$ parameter, $Q_{\mathrm{eff}} = Q_{\mathrm{eff}}(R)$, for our sample of galaxies. In the left panel, we neglect gas turbulence. On the right, we consider turbulent H\,\textsc{i} ($a=b=\frac{1}{3}$) for $R > 0.43 \; R_{25}$. Values of $Q_{\mathrm{eff}}$ smaller than unity mean gravitational instability. We indicate the median and $1\sigma$ scatter of $Q_{\mathrm{eff}}$ for radii smaller and larger than $R = 0.43 \; R_{25}$. We also colour-code the component that contributes more to disc instability according to the classical condition: gas for $Q_{\mathrm{g}0} < Q_\star$, and stars for $Q_\star < Q_{\mathrm{g}0}$ (Romeo \& Wiegert 2011).

For $R \leq 0.43 \; R_{25}$, $Q_{\mathrm{eff}}$ spans a wide range of values, with $13\%$ of points in the unstable regime. Here $56\%$ of points are gas-dominated and tend to be less stable than the star-dominated points (the median value of $Q_\mathrm{eff}$ is $Q_{\mathrm{eff,g}} \approx 1.3$ and $Q_{\mathrm{eff},\star} \approx 2.3$ in the two cases). For $R > 0.43 \; R_{25}$, the range spanned by $Q_{\mathrm{eff}}$ is tighter and only $4\%$ of measurements are in the unstable regime. Here the majority ($61\%$) of points are star-dominated, and there is no clear difference in $Q_{\mathrm{eff}}$ between star- and gas-dominated points ($Q_{\mathrm{eff,g}} \approx 1.3$ and $Q_{\mathrm{eff},\star} \approx 1.7$).

Introducing turbulent scaling for $R > 0.43 \; R_{25}$ only has a small effect on the measurements. For $a = b = \frac{1}{3}$, the median of $Q_{\mathrm{eff}}$ increases by $3\%$ and the $1\sigma$ scatter by $15\%$. For $a = b = \frac{1}{2}$, the median increases by $6\%$ and the $1\sigma$ scatter by $26\%$. This suggests that turbulence tends to stabilize the disc (the median increases), although the magnitude of this effect is small and depends on the non-turbulent value of $Q_{\mathrm{eff}}$ (the scatter increases).

The stabilizing effect of turbulence seems at odds with results from Romeo et al. (2010), who found that the stability of gaseous discs is unaffected by turbulence if $a = b$. The difference lies, of course, in the gravitational coupling of stars and gas. Consider the approximation for the effective $Q$ parameter introduced by Romeo \& Wiegert (2011):

\begin{equation}
\frac{1}{Q_{\mathrm{eff}}}=
\left\{\begin{array}{ll}
       {\displaystyle\frac{W}{Q_{\star}}+\frac{1}{Q_{\mathrm{g}}}}
                       & \mbox{if\ }Q_{\star}\geq Q_{\mathrm{g}}\,, \\
                       &                                            \\
       {\displaystyle\frac{1}{Q_{\star}}+\frac{W}{Q_{\mathrm{g}}}}
                       & \mbox{if\ }Q_{\mathrm{g}}\geq Q_{\star}\,,
       \end{array}
\right.
\end{equation}
\begin{equation}
W=
\frac{2\sigma_{\star}\sigma_{\mathrm{g}}}
     {\sigma_{\star}^{2}+\sigma_{\mathrm{g}}^{2}}\,.
\end{equation}
We see that, even if $Q_{\mathrm{g}} = Q_{\mathrm{g}0}$, the scaling $\sigma_{\mathrm{g}}  = \sigma_{\mathrm{g}0} ( \ell / \ell_0 )^{b}$ affects the weight factor $W(\sigma_\star,\sigma_{\mathrm{g}})$. The strength of this effect is determined by the power-law slope $b$. Therefore the effective $Q$ parameter of turbulent discs always differs from the classical case.

\subsection{The least stable wavelength}

\begin{figure*}
\includegraphics[scale=.98]{fig7.eps}
\caption{Radial profile of the least stable wavelength,
  $\lambda_{\mathrm{min}}(R)$, for THINGS spirals (Model 1): neglecting gas
  turbulence (left), and taking into account H\,\textsc{i} turbulence for
  $R>0.43\;R_{25}$ (right).  For each measurement, colour-coding indicates
  whether gas ($Q_{\mathrm{g}0}<Q_{\star}$) or stars
  ($Q_{\star}<Q_{\mathrm{g}0}$) dominate the stability level.  Thick black
  lines and dark grey shading indicate the median and $1\sigma$ scatter of
  $\lambda_{\mathrm{min}}$ in the two radial ranges.}
\end{figure*}

Fig.\ 7 shows radial profiles of the least stable wavelength, $\lambda_{\mathrm{min}} = \lambda_{\mathrm{min}}(R)$, for our sample. On the left we neglect gas turbulence, whereas on the right we consider turbulent H\,\textsc{i} for $R > 0.43 \; R_{25}$. Colour-coding indicates the component that dominates gravitational instability. As before, the median and $1\sigma$ scatter are indicated separately for small and large radii.

For $R \leq 0.43 \; R_{25}$, there is a clear gap between gas- and star-dominated points (the median value of $\lambda_\mathrm{min}$ is $\lambda_{\mathrm{min,g}} \approx 0.7 \; \mathrm{kpc}$ and $\lambda_{\mathrm{min},\star} \approx 8.2 \; \mathrm{kpc}$ in the two cases). So the gas-dominated points are characterized by much smaller values of $\lambda_{\mathrm{min}}$. The discrepancy is less significant for $R > 0.43 \; R_{25}$, apart from a few measurements close to $R = 0.43 \; R_{25}$ ($\lambda_{\mathrm{min,g}} \approx 3.9 \; \mathrm{kpc}$ and $\lambda_{\mathrm{min},\star} \approx 6.3 \; \mathrm{kpc}$).

Introducing a turbulent gas component for $R > 0.43 \; R_{25}$ causes a significant increase in $\lambda_{\mathrm{min}}$. For $a = b = \frac{1}{3}$, the median of $\lambda_{\mathrm{min}}$ increases by $28\%$ and the $1\sigma$ scatter by $34\%$. For $a = b = \frac{1}{2}$, the median increases by $41\%$ and the increase in $1\sigma$ scatter is again $34\%$. This suggests a tendency of turbulence to boost the least stable wavelength. As for $Q_{\mathrm{eff}}$, the magnitude of this effect depends on the non-turbulent value of $\lambda_{\mathrm{min}}$. There is a small number of gas-dominated measurements for which the least stable wavelength decreases, but these have large uncertainties.

Why does turbulence affect $\lambda_{\mathrm{eff}}$ more than $Q_{\mathrm{eff}}$? The answer is twofold. First, for a purely gaseous disc $\lambda_{\mathrm{min}}$ increases markedly with $Q_{\mathrm{eff}}$ (Romeo et al. 2010), so that any change in $Q_{\mathrm{eff}}$ will be amplified in $\lambda_{\mathrm{min}}$. Second, as stars are taken into account, gas-dominated points can enter the star-dominated regime, where $\lambda_{\mathrm{min}}$ is much larger (see Sect.\ 2.4). Both effects depend on the power-law slopes $a$ and $b$. They sum up and drive $\lambda_{\mathrm{min}}$ to significantly larger values.

\subsection{Robustness of the results}

Modelling the gas disc as a single component with an intermediate value of
$\sigma_{\mathrm{g}}$ is not the best that can be done.  Here we will no
longer follow this traditional approach.  We will model the gas disc as made
of two components, each with the more representative value of
$\sigma_{\mathrm{g}}$.  A simple way to do it is to treat the inner part of
the disc as $\mathrm{H}_{2}$ dominated and the outer part as H\,\textsc{i}
dominated.  We then set $\sigma_{\mathrm{g}}=6\;\mbox{km\,s}^{-1}$ for
$R\leq0.43\;R_{25}$ and $\sigma_{\mathrm{g}}=11\;\mbox{km\,s}^{-1}$ for
$R>0.43\;R_{25}$ (cf.\ introductory part of Sect.\ 3).

Besides $\sigma_{\mathrm{g}}$, there is another quantity that deserves
particular attention: the stellar radial velocity dispersion, which we now
denote with $\sigma_{R\star}$.  Leroy et al.\ (2008) inferred
$\sigma_{R\star}$ from the vertical velocity dispersion, $\sigma_{z\star}$,
assuming that $(\sigma_{z}/\sigma_{R})_{\star}=0.6$.  In turn,
$\sigma_{z\star}$ was inferred from the stellar exponential scale height,
$H_{\star}$, using the relation $H_{\star}=\sigma_{z\star}^{2}/2\pi
G\Sigma_{\star}$.  Gerssen \& Shapiro Griffin (2012) showed that
$(\sigma_{z}/\sigma_{R})_{\star}$ decreases markedly from early- to late-type
spirals.  The average Hubble stage of THINGS spirals is $\langle T\rangle=4$,
which corresponds to galaxy type Sbc (the mean and the median of $T$ are
equal).  The best-fitting model of Gerssen \& Shapiro Griffin (2012) then
yields $(\sigma_{z}/\sigma_{R})_{\star}=0.5$ (see their fig.\ 4).  Concerning
$H_{\star}$, the relation used by Leroy et al.\ (2008) is not correct.  It is
the total surface density in the disc that determines the stellar exponential
scale height: $H_{\star}=\sigma_{z\star}^{2}/2\pi G\Sigma_{\mathrm{tot}}$,
where $\Sigma_{\mathrm{tot}}=\Sigma_{\star}+\Sigma_{\mathrm{g}}$ (Bahcall \&
Casertano 1984; Romeo 1992).  In view of these facts, we set
$(\sigma_{z}/\sigma_{R})_{\star}=0.5$ and use the correct relation for
$H_{\star}$.

Finally, we implement gas turbulence as in Model 1, i.e.\ only for
$R>0.43\;R_{25}$, where the disc is H\,\textsc{i} dominated.  This is simply
because the constant spatial resolution of 800 pc used by Leroy et
al.\ (2008) is too coarse to probe the range of scales affected by
$\mathrm{H}_{2}$ turbulence [see Sect.\ 2.4, case (i)].  Hereafter we will
refer to the model described above as \emph{Model 2}.

\begin{table*}
\begin{minipage}{135mm}
\caption{Stability characteristics of THINGS spirals for Models 1 and 2.}
\begin{center}
\begin{tabular}{c c c c r r r r c r}
\hline

    Model
  & Radial Range
  & $a$ & $b$
  & $f_2$\textsuperscript{a}
  & $f_{2,\mathrm{g}}$\textsuperscript{b}
  & $f_\mathrm{u}$\textsuperscript{c}
  & $f_\mathrm{g}$\textsuperscript{d}
  & $Q_\mathrm{eff}$\textsuperscript{e}
  & $\lambda_\mathrm{min}$\textsuperscript{f} $\left[ \mathrm{kpc} \right]$\\

\hline

    $1$
  & $R \leq 0.43 \, R_{25}$
  & $0$ & $0$
  & $61\%$
  & $68\%$
  & $13\%$
  & $56\%$
  & $1.67 \pm 0.68$
  & $1.64 \pm 2.17$ \\

  & $R > 0.43 \, R_{25}$
  & $0$ & $0$
  & $4\%$
  & $100\%$
  & $4\%$
  & $39\%$
  & $1.50 \pm 0.46$
  & $4.76 \pm 1.67$ \\

  &
  & $1/3$ & $1/3$
  & $22\%$
  & $41\%$
  & $3\%$
  & $39\%$
  & $1.55 \pm 0.53$
  & $6.10 \pm 2.24$ \\

  &
  & $1/2$ & $1/2$
  & $52\%$
  & $9\%$
  & $3\%$
  & $39\%$
  & $1.59 \pm 0.58$
  & $6.70 \pm 2.23$ \\

  \hline

    $2$
  & $R \leq 0.43 \, R_{25}$
  & $0$ & $0$
  & $73\%$
  & $76\%$
  & $25\%$
  & $77\%$
  & $1.50 \pm 0.91$
  & $0.67 \pm 0.62$ \\

  & $R > 0.43 \, R_{25}$
  & $0$ & $0$
  & $4\%$
  & $100\%$
  & $0.5\%$
  & $39\%$
  & $1.99 \pm 0.57$
  & $9.32 \pm 3.40$ \\

  &
  & $1/3$ & $1/3$
  & $19\%$
  & $48\%$
  & $0.5\%$
  & $39\%$
  & $2.09 \pm 0.66$
  & $11.10 \pm 2.78$ \\

  &
  & $1/2$ & $1/2$
  & $52\%$
  & $5\%$
  & $0.5\%$
  & $39\%$
  & $2.14 \pm 0.72$
  & $12.00 \pm 2.43$ \\

\hline

\end{tabular}
\end{center}
\raggedright
\textsuperscript{a} Fraction of data that fall within the two-phase region.\\
\textsuperscript{b} Fraction of the data points in \textsuperscript{a} that populate the gaseous phase.\\
\textsuperscript{c} Fraction of data such that $Q_\mathrm{eff} < 1$.\\
\textsuperscript{d} Fraction of data such that $Q_{\mathrm{g}0} < Q_\star$.\\
\textsuperscript{e} Median and $1\sigma$ scatter of $Q_\mathrm{eff}$.\\
\textsuperscript{f} Median and $1\sigma$ scatter of $\lambda_\mathrm{min}$.\\
\end{minipage}
\end{table*}

Table 1 summarizes the dynamical differences between Model 2 and Model 1. On the whole, the stability diagnostics are moderately affected by the model. The most sensitive diagnostic is $\lambda_\mathrm{min}$, which differs by a factor of 2--3. $Q_\mathrm{eff}$ is more robust, with a difference well below a factor of 2. In Model 2, both $\lambda_\mathrm{min}$ and $Q_\mathrm{eff}$ are smaller for $R \leq 0.43 \; R_{25}$ and larger for $R > 0.43 \; R_{25}$.

Despite these differences, the effect of turbulence is comparable in the two models. For $R \leq 0.43 \; R_{25}$, $f_2$ and $f_{2,\mathrm{g}}$ are slightly larger in Model 2. So H$_2$ is more decoupled from stars and slightly more dominant. For $R > 0.43 \; R_{25}$, $f_2$ is almost identical in the two models, irrespective of the value of $a=b$. Turbulence increases the median value of $Q_\mathrm{eff}$ by less than 10\% in both models. In contrast, the median value of $\lambda_\mathrm{min}$ increases by 20--30\% in Model 2, i.e. less than in Model 1. Summarizing, the effect of H\textsc{i} turbulence in Model 2 is only slightly weaker than in Model 1. This points to the robustness of our results.

\section{DISCUSSION}

Our results cannot be directly compared with those of Shadmehri \& Khajenabi
(2012), hereafter SK12.  This is partly because of the wider scope of our
paper, which embraces a brand-new application to THINGS spirals, and because
most of the analysis carried out by SK12 cannot be easily interpreted.

SK12 analysed five stability regimes of gas turbulence: $a>1$ and
$b<\frac{1}{2}\,(1+a)$; $a=1$ and $b\neq1$; and Regimes A--C.  The first
regime corresponds to a fractal dimension $D=a+2$ higher than 3, and is
therefore beyond the natural range of $a$ (see fig.\ 1 and sect.\ 3 of Romeo
et al.\ 2010).  In the second regime, the volume density is scale-independent
($D=3$), so the medium is incompressible and hence subsonic.  Cold
interstellar gas is instead dominated by compressible structures and
supersonic motions.  Therefore even this regime is of marginal interest (see
again fig.\ 1 and sect.\ 3 of Romeo et al.\ 2010).  Regimes B and C are
populated by $\mathrm{H}_{2}$ turbulence, which manifests itself at scales
less than $L_{\mathrm{H2}}\sim100\;\mbox{pc}$.  In turn, $L_{\mathrm{H2}}$ is
one order of magnitude smaller than the characteristic scale of stellar
instabilities.  Therefore stars play a negligible role in these stability
regimes [see Sect.\ 2.4, case (i)].  SK12 reached the opposite conclusion.
But this is because they assumed Larson-type scaling relations even at kpc
scales, disregarding the type of turbulence associated with such regimes.
Regime A is populated by both $\mathrm{H}_{2}$ and H\,\textsc{i} turbulence.
While the $\mathrm{H}_{2}$ case raises the same issue as Regimes B and C, the
H\,\textsc{i} case is conceptually simpler.  H\,\textsc{i} turbulence
manifests itself at all scales of galactic interest, so stars can play a
significant role in this stability regime [see Sect.\ 2.4, case (ii)].  SK12
reached a similar conclusion.  However, even in this case, their approach is
different from ours.  They chose $a$, $b$ and $\mathcal{L}_{0}$ so as to
sample Regime A, and studied the dispersion relation numerically.  We have
instead examined the whole regime analytically (see Sect.\ 2.3.1).  We have
then chosen observationally motivated values of $a$, $b$ and
$\mathcal{L}_{0}$, and analysed the onset of gravitational instability in the
disc (see in particular Sects 2.4.1 and 2.4.2).

In conclusion, there is a fundamental difference between our analysis and
that of SK12.  Our analysis takes into account the astrophysical relevance of
the various stability regimes, as well as the tight constraints imposed by
observations of ISM turbulence in the Milky Way and nearby galaxies.  These
are important aspects of the problem, which are missing from their analysis.

\section{CONCLUSIONS}

Our analysis of THINGS spirals shows that H\,\textsc{i} turbulence has a
triple effect on the outer regions of galactic discs: (i) it weakens the
coupling between gas and stars in the development of disc instabilities, (ii)
it makes the disc more prone to star-dominated than gas-dominated
instabilities, and (iii) it typically increases the least stable wavelength
by 20--40\% (the steeper the H\,\textsc{i} scaling relations, the larger the
effect).  This is in contrast to the typical 3--8\% increase predicted for
the effective $Q$ parameter.  The effect of H\,\textsc{i} turbulence is in a
sense complementary to the effect of disc thickness.  In fact, disc thickness
increases the effective $Q$ parameter by 20--50\% (Romeo \& Wiegert 2011) but
hardly changes the least stable wavelength (Romeo 1992, 1994) or the
condition for star-gas decoupling (Romeo \& Wiegert 2011).

Our analysis of THINGS spirals also suggests that $\mathrm{H}_{2}$ turbulence
has a significant effect on the inner regions of galactic discs.  For
$R\la0.4\,R_{25}$, i.e.\ where $\mathrm{H}_{2}$ dominates over H\,\textsc{i},
60--70\% of the data fulfil the condition for star-gas decoupling and
70--80\% of these points represent gas-dominated stability regimes.  In such
cases, the onset of gravitational instability is controlled by
$\mathrm{H}_{2}$.  Turbulence is expected to play an important role in this
process at scales smaller than about 100 pc (see Sect.\ 2.4).  If $a=0$ and
$b=\frac{1}{2}$, then $\mathrm{H}_{2}$ turbulence drives the disc to a regime
of transition between instability at small scales and stability \`{a} la
Toomre, as was first pointed out by Romeo et al.\ (2010) in the case of
one-component turbulent discs.  Since this is a regime of transition, even
small deviations from the standard $\mathrm{H}_{2}$ scaling laws ($a=0$ and
$b=\frac{1}{2}$) can have a strong impact on the gravitational instability of
the disc.  This is true even when the mass densities of H\,\textsc{i} and
$\mathrm{H}_{2}$ are comparable, since small-scale instabilities are more
actively controlled by $\mathrm{H}_{2}$ (see Sect.\ 2.3).

\section*{ACKNOWLEDGMENTS}

We are very grateful to Oscar Agertz, Christoph Federrath, Mathieu Puech and
Joachim Wiegert for useful discussions.  We are also grateful to an anonymous
referee for constructive comments and suggestions, and for encouraging future
work on the topic.  ABR thanks the warm hospitality of both the Department of
Physics at the University of Gothenburg and the Department of Fundamental
Physics at Chalmers.

redpajama_set_name: RedPajamaArXiv


text:
One Voice is the fourth full-length studio album from New York hardcore band Agnostic Front. It was released in 1992 on Relativity Records. It marks a three-year absence from recording – the last album was Live at CBGB in 1989 – after Roger Miret's term of imprisonment. However, the comeback was short-lived as after Last Warning (another live album), the band split up and did not record again until 1998.

Musically, the band continued their lean towards crossover thrash which earned the interest of Roadrunner Records who distributed this and their next album under license. After a three-year lay off,  two line-up changes had taken place – Matt Henderson replacing Steve Martin on guitar, and Craig Setari replacing Al Peters on Bass.

Track listing

Personnel
Agnostic Front
 Roger Miret – vocals
 Vinnie Stigma – lead guitar
 Matt Henderson – rhythm guitar
 Craig Setari – bass
 Will Shepler – drums
Production
 Armand Majidi – backing vocals
 Jamie Locke – piano
 Produced by Don Fury
 Engineered and mixed by Jamie Locke
 Assistant engineered by Joe Pires

References

External links
Flex! Discography album entry
Discogs album entry

1992 albums
Agnostic Front albums
Albums produced by Don Fury
Roadrunner Records albums

redpajama_set_name: RedPajamaWikipedia


Found the weakest link. Blew the headgasket on the number 2 cylinder into the water jacket today at 11AM. finished the job by 4pm. The gasket was a NOS aftermarket piece from the early 70's that I didn't feel good about installing last year. The new gasket is a modern production improved unit that I have much more faith in.
On a positive note I replaced the soft valve springs with some considerably stiffer ones.


We have always been an outdoor loving family and now that Bram has joined our family, we have even more reason to get out and about in the fresh air. Cocker Spaniels are renowned for having bags of energy and sharing a home with him for the last couple of months, I would definitely agree with that.
During the Summer holidays I felt like I needed a season ticket to our local Trespass store as I was in there so often buying kit for our many camping trips so I was delighted when they contacted me to ask if we would like to review anything from their outdoor clothing range. I have been looking for a new coat to keep me warm on my dog walks but also bright and cheerful so that I can be seen.
The Trailwind 3 in 1 jacket from Trespass is comprised of a Tres-tex fabric outer shell and inner down jacket making it suitable for use in multiple types of weather.
Externally, offering both windproof and waterproof protection, you'll not have worry about moisture leaking in through the taped seams of the outer coat. With a hood as well, adjustable features mean you get a comfortable fit while 2 zip pockets will give you some storage space that is easy to access.
The inner down jacket has been filled with down insulation that uses natural fibres to absorb heat meaning you'll be kept warm with it on. Coming in 2 colours, you can wear both jackets together or as individual pieces giving you 3 types of coat in 1 style.
What I think . . .
Our Trespass delivery arrived just as I was about to put on my walking boots to take Bram out for his morning walk, it seemed silly to not put on my new Trailwind straight away so I took off the tags, popped it on and we went on our way. I'm a very tactile person and the first thing I noticed was how soft and comfortable the jacket felt with the inner down jacket.
I must admit I have been quite lucky and haven't had the opportunity to wear my outer jacket in the rain yet but I live in the UK so of course that will happen soon enough. It is windproof though and I can testify to that as I have been on plenty of windy walks.
My favourite part of the jacket is definitely the inner down jacket which I have worn regularly on it's own. It is warm and comfortable with long sleeves (I have long arms) and the high neck keeps me cosy too. I love having the choice of wearing it alone or with the outer jacket for extra warmth and protection.
The Rhythmic men's softshell trainers are a part of the Trespass specially designed DLX range, which has been created for those who want great performing outdoor wear.
Additionally, these hiking trainers have a Phylon cushion midsole, which helps to keep your feet comfortable. Further, the Vibram sole of these trainers is very hard wearing and durable meaning they can withstand tough terrain.
As they are a softshell style trainer, it means they are much easier to move about in, ideal for adventurers. Wear these walking trainers with a pair of hiking socks and gaiters for even more protection and comfort.
What Simon thinks . . .
The first thing I noticed about my boots was how lightweight they were. We will often walk Bram across the fields and did lots of walking off-track over the Summer often carrying Albie in a backpack. On those days when it's a bit wet under foot boots can quickly become heavy when weighed down by mud so it helps if they are a little lighter to start with. They feel more like a sturdy trainer with ankle support than a traditional inflexible hiker. When walking through wet grass it was great to see the water droplets just roll off the waterproof outers and even in cold weather my feet have been toasty even without my hiking socks on. I like the style of them as they look sleek being all black, but have the silver reflective stitching and reflective stripes down the heel so will pick up the lights when walking Bram at night through the winter. I am really looking forward to a decent hike in these to put them truly through their paces.
As you can see, Simon found his walking boots so comfortable they were perfect for chasing the kids. I think he was practicing being a superhero or something!
DISCLAIMER: We were provided with these items from Trespass in exchange for this post. All words, images and opinions are my own and may not be copied without my permission. I have not been instructed what to write.


Cavity type Pressure Transducers | Tokyo Measuring Instruments Laboratory Co., Ltd.
The PW-PA pressure transducer can make stable high-accuracy measurement over a long period of time. It is widely used in production lines and plants and to measure liquid pressure, air pressure, and so forth in laboratories.
Measurement moves in the plus direction with regard to an increase in pressure.
The PWH-PA high-capacity pressure transducer has a sealed structure made with high-strength stainless steel.Owing to this structure, stable high-accuracy measurement can be made over a long period of time. It is used to control plant or production lines, to measure jack pressure, and for various other applications.
The PW-PAH pressure transducer is designed to measure pressure of fluids like oil and water or gases like air in high temperature. Since it is constructed small, it can be used in a narrow space. These models line up five ranges of 2, 5, 10, 20 and 50MPa.


Detail of cat from the hunting scene (fowling scene) from the tomb of Nebamun, Thebes, Egypt, 18th dynasty, ca. 1400-1350 BCE.
Ra, in the form of a Great Cat, slays the snake-god Apep. Thebes, wall painting from the tomb of Inher-kha, c. 1164-1157. Image courtesy Wikipedia.
It is unsurprising to me that cats could be associated with Ra, the sun-god. In ancient Egypt, domesticated cats were useful for getting rid of vermin, like rats, mice and snakes (especially cobras). Since the sun-god Ra was the greatest enemy of Apep (Apophis), the evil cobra-god of darkness, it makes since to me that cats would be associated with Ra. The wall painting from the tomb of Inher-kha, which shows the sun-god battling Apep, is from the New Kingdom, which is considered to be the time period in which "the cat achieved full apotheosis" in funerary texts and contexts.2 The story of Ra battling Apep is found in the Litany of Ra, which explains how Apep attacked the solar boat as it passed through the sky during the night. Ra overcame Apep, which allowed the sun to continue its journey and be reborn at dawn.
However, Ra was not the only deity associated with cats in ancient Egypt. At the British Museum I also saw the so-called Gayer-Anderson bronze cat on display in another area of the museum. The museum label for the bronze cat explained that this cat was probably associated with the goddess Bastet, the cat-goddess. The British Museum also owns a bronze statuette of the cat-goddess Bastet, although I didn't find this statue on display during my recent visit. Cats were important to the cult of Bastet, and were bred on an industrial scale by the first millenium BC.
Bastet is a mother-goddess with protective and maternal attributes, as shown in the bronze statuette of the cat goddess with four kittens at her feet. Even Bastet's name, which means "she-of-the-ointment-jar", suggests a soothing character on part of the goddess.3 Bastet's associations with ointment also connect her protective qualities to health: she provides protection from contagious diseases. I wonder if ancient Egyptians ever made the association with how their domestic cats fought vermin (that carry disease), which is similar to how the goddess Bastet protected people from contagious diseases.
Detail of sarcophagus of Prince Thutmose's cat, limestone, sarcophagus height 64 cm, New Kindgom, Dynasty 18, reign of Amenhotep III. Image courtesy Wikipedia via Larazoni.
Do you have a favorite depiction of a cat in ancient Egyptian art? Do you know of other religious or cultural associations for ancient Egyptian cats?
1 Museum label for "Nebamun hunting in the marshes," London, British Museum, August 13, 2013.
2 Ian Shaw and Paul Nicholson, The Princeton Dictionary of Ancient Egypt, 2nd ed., s.v. "Cat." (Princeton, New Jersey: Princeton University Press, 2008), p. 70.
3 Bastet is seen to be in opposition to the aggressive lioness-headed goddess Sekhmet. See "Bronze figure of the cat-headed goddess Bastet," from http://www.britishmuseum.org/explore/highlights/highlight_objects/aes/b/bronze_figure_of_bastet.aspx. Accessed August 26, 2013.
4 Shaw and Nicholson, p. 70.
5 The sarcophagus of Prince Thutmose's cat refers to the cat as an Osiris, which indicates that the cat "would be able to reach the netherworld and be judged in the Hall of Truth there." See Zahi Hawass, Tutankhamun: The Golden King and the Great Pharaohs (Washington, D.C.: The National Geographic Society, 2008), p. 122.


With the start of the school year in February, schools are teaching indigenous languages for the first time in Bolivia. This is required by the 2010 Avelino Siñani-Elizardo Pérez Law (Spanish), which covers the "traditional knowledge" of students' communities.
Students will be taught Spanish, plus a foreign language (English, French or Portuguese) and a local language.
See "Bolivia: Indigenous languages taught in school" for more.
English is used as the official language of Nigeria to tie together communication among the ethnic groups who speak hundreds of languages (522 living languages by Ethnologue's count).
The London Irish Centre is offering three courses that start over the next week or so, a beginner's course, an improver's course and a comfortable speaker's course. The courses are eight weeks long and cost 80 pounds.
See "Summer Irish Language Classes" for more details.


text:
Trump and his cabinet/buffoonery- Get your bunkers ready!
By brandymac27,
November 15, 2016 in The Tailgate
Llevron
That's a pretty ****ing cool job lol. The 10 y/o me is pissed that I ****ed my life up like this
skinsmarydu
10 minutes ago, Llevron said:
Ikr? All I did was make sure I didn't have to worry about food. Pfft.
Cooked Crack
Long n Left
14 minutes ago, Cooked Crack said:
This dumb **** is going to do all he can to get more Americans killed. He'll then probably blame Biden for any terrorist acts.
TheGreatBuzz
4 hours ago, Bang said:
well, at least I'm not the only pessimist (re: realist) here any more.
There is only one way these things ever end. (Does not include: everyone seeing the light, changing their minds and deciding to go along with the rule of law.)
C'mon I have been right there with you the whole time!
BRAVEONAWARPATH
GoSkinsGo
They are not evil by stupidity they are actively trying to be evil. WTF.
PokerPacker
The Run Stopper
1 hour ago, GoSkinsGo said:
This surprises you?
5 hours ago, PokerPacker said:
I honestly thought the majority was just lack of compassion and ability to plan long term. The evil was a side effect.
Boy was I wrong, evil was the driving force.
Oh, come on.
I figured all along that "losing the records" was part of the plan all along. That the evil people who set out to come up with a way to take people's children away from then, that'll teach 'em, knew when they started that the first judge they saw would order them to undo it. And their plan for when that day came was "Gee, Your Honor, we just can't comply with this order you just gave us, because we lost our homework."
Tip of the iceberg. I bet a LOT of records are going to be missing.
Thats what the pardons are for.
LadySkinsFan
The Millers don't have souls.
25 minutes ago, LadySkinsFan said:
Polar bears are badass. Polar bears (at least I'm positive that the males do) will also eat their own young. Nature is both beautiful and ugly
Beloved Tailgate News Anchor
Omphaloskeptic
8 hours ago, Die Hard said:
They also like playing with dogs.
They need to override his veto in one last humiliation.
At least we know who Biden and company need to fire on January 20, 2021 at 1:00pm.
Trump Pentagon Nominee Boosted Calls For Martial Law This Week
The President's nominee for a top Pentagon job boosted calls for martial law on Wednesday.
And that's just one piece of the off-the-walls social media presence of Scott O'Grady, Trump's nominee to become assistant secretary of defense for international security affairs, CNN reported. O'Grady's nomination was sent to the Senate on Monday.
O'Grady also retweeted numerous false claims that Trump had in fact won a second term in office, by a landslide, and described Joe Biden's winning the presidency as a "coup" attempt carried out in coordination with Chinese President Xi Jinping, according to CNN's review.
The Pentagon nominee, if confirmed, would serve through the end of Trump's presidency.
On Wednesday, O'Grady retweeted an article about Michael Flynn's call for martial law in light of the election results. Then, he retweeted another message from the same account that had shared the article, CNN found.
"I don't know who needs to hear this," read the message that O'Grady retweeted. "But calling for martial law is not a bad idea when there is an attempted coup against the president and this country happening right now."
Like other Pentagon officials in the wake of Trump's purge of top Defense Department officials, O'Grady's social media is full of conspiracy theories and outrageous claims — like the assertion that former President Barack Obama is a "sworn socialist" and that former Secretary of Defense James Mattis is a "traitor."
Click on the link for the full article
Fergasun
The Dirtbags
Re: Defense Boards
What's funny is that these shenanegans will prolly get reversed on Jan 21. Trump is so incompetent, he should have made these ideological changes in his first year.
The Biden transition team should reach out to the board members and apologize.
Also, how does politicizing the DoD help your 2024 run?
dfitzo53

redpajama_set_name: RedPajamaCommonCrawl


text:
Cole Swindell Had Us at the New Music Video for "She Had Me At Heads Carolina"
Cole Swindell's latest single from his album Stereotype is "She Had Me At Heads Carolina."
Cole recently released the music video for the track – and it includes a very special cameo.
Jo Dee Messina, who sings the 1996 hit that inspired Cole's new single, is playing the role of the bartender in the music video.
While wearing a Cole Swindell T-Shirt, Jo Dee shares the story behind how her song "Heads Carolina, Tails California" ended up on her debut album – which Tim McGraw co-produced.
That latest minute addition has gone on to be a 90s country classic and inspired Cole Swindell's 2022 revision, "She Had Me At Heads Carolina."
Photo Courtesy of Cole Swindell


text:
Optus Go Places Mobile App Offers Restaurant Discounts
Angus Kidman
Fancy 20 per cent off at a nearby restaurant? Optus' new Go Places app includes discount vouchers for "thousands" of restaurants — but the vouchers themselves aren't free.
The deal works like this: you pay $39.99 for a year's access to discount vouchers, which can be used as often as you like at participating restaurants by flashing your mobile at the waitstaff before requesting the bill. If you're a more casual diner, you can buy a single voucher for $2.99, which must be used within 24 hours. For a 20 per cent saving, you'd only have to spend more than $15 to be ahead on a single voucher, which isn't much in restaurant terms.
You can download a free version of the app to see if it covers enough restaurants to be worth your while. While Optus customers won't incur data charges using the app, you can download it on any applicable handset, regardless of which network you use.
Unusually in this day and age, while Android, BlackBerry and Symbian users are catered for immediately, the iOS version isn't complete, though Optus has said it is in development.
craigbaldie @Craig
I noticed on the screen shots on the optus site that its related to the Entertainment group www.entertainmentbook.com.au which I have had for a number of years
RVG Guest
Despite what you say in the article, it is an Optus only app
brent3000 @brent3000
Oct 7, 2011, 12:31pm
No surprise... another carrier not supporting WP7...
Mark Guest
Oct 10, 2011, 4:52pm
Hey Brent - WP7 is a great platform and for sure Go Places will be out on it as soon as it establishes itself in Australia early 2012.


The compact, high output UP-DRAFT II produces a concentrated mist at flow rates as low as 5 LPM. Nebulizes at angles up to 45 to accommodate special treatment requirements. 8 cc capacity. Anti-spill design prevents loss of medication in any position. Cap and jar screw apart for easy cleaning. Available in a variety of prepackaged configurations.


text:
een plaatsnaam
Carnegie (Oklahoma)
Carnegie (Pennsylvania)

een achternaam
 Andrew Carnegie (staalbaron)
 Dale Carnegie
 James Carnegie
 Charles Carnegie

overig
 Carnegie Stichting
 Carnegie Stichting (Nederland)
 Carnegie Hall
The Carnegie Hall Concert
 Carnegie Hall Tower
 Carnegie Medal
 Medaille van het Carnegie Heldenfonds
 Carnegie Wateler Vredesprijs
 Carnegie Mellon University
 Carnegie Science Center
 Carnegie (schip), een onderzoeksschip


text:
Call our expert team on 01964 529512 or Email sales@fisheruk.co.uk
AGHE
Butchery Units
Factory Extensions
FSA Approved Plants
Temperature controlled storage
HACCP Consultancy
Extension to modular farm shop
Butchery facility for Knepp Wild Range Meat
AGHE facility
FSA approved Meat Cutting Plant
The Devil's Kitchen production facility
Native Beef Butchery unit
Venison Processing Facility
The Sausage Shop Country Farm Meats
Abattoir Extension
EC Approved Cutting Plant
Meat Processing & Packing Plant
Butchery Expansion
Game Larders
Meat Rail Systems
Fisher Modular Construction UK Ltd
Unit 3, Warren Park,
Beeford, Driffield,
East Yorkshire,
YO25 8BD
E: sales@fisheruk.co.uk
The Devil's Kitchen is the plant-based spin-off from Forest Green Rovers (FGR), which is recognised by FIFA and the United Nations as the world's greenest football club. Since turning vegan in 2015, FGR has built a reputation for its award-winning food.
The Devil's Kitchen project is one of the latest initiatives from the Forest Green Rovers chairman and Ecotricity founder, Dale Vince. It launched with a Fisher UK modular production facility being installed in 2018 with the aim of bringing plant-based food to primary school children and improving nutritional standards.
Its popularity grew rapidly, quickly expanding into secondary schools, colleges and universities and in 2021. The Devil's Kitchen now supplies around 10% of schools nationwide – and reached 200,000 school dinners in November last year. Dale Vince, Founder of Devil's Kitchen, said: "Kids love the food, and football fans from all over the country have been asking if they can get them at home – so we're excited to have recently gone nationwide with Ocado. Today, food is such an important issue and veganism is a growing choice – both for our health and the future of our planet, and with Veganuary and Meat Free Mondays bigger than ever – it's time to bring a taste of Forest Green Rovers into homes everywhere."
All Devil's Kitchen products are 100% plant-based and made with pea protein, not soya. They are also free of the 14 major food allergens (such as nuts, seeds, gluten and soya), making them accessible to everybody, as well as being free from palm oil, MSG and all artificial ingredients.
Take a look at the factory here :
Jon Fisher, Managing Director at Fisher UK, was able to consult with the team at The Devil's Kitchen from an initial concept of the production facility.
The main reason for The Devil's Kitchen opting for a Fisher UK unit was that they needed a solid three metres of height to house their state-of-the-art Reiser production line equipment.
The Fisher UK solution offered greater ceiling height than other modular options examined in the research process.
The Fisher UK plans meant that The Devil's Kitchen could apply for temporary planning permission, which was very helpful as a stepping stone for permanent planning permission.
The need to move quickly, coupled with the option to extend or move the unit, meant that down time would be minimal compared to a traditional extension. This was crucial for a business with such aggressive scale-up plans.
Another buying factor was that if necessary, the unit could be repurposed as the business grows e.g. used as a test bed for new ideas or as a prep kitchen for Forest Green Rovers.
"I'm a real fan of Fisher UK and really like their products – they are wholly fit for purpose and futureproof for the long haul.
The accuracy of the build off- plan was so precise, in fact, millimetre perfect. This enabled the unit to be built off-site at the Fisher UK factory until it was ready to be placed in its target position on installation day.
"We had to build a factory that was half a meter off the ground in accordance with building regs, owing to being positioned on a floodplain.
The Fisher UK modular factory was craned into position on pre-scored concrete pads to achieve the required distance from ground level and satisfy planning permissions.
The best thing about this production facility is that it could be sold in the future as would hold a resale value or relocated anywhere required.
There is also the option to bolt-on more components to the unit as an when required as the business grows."
Barry Jordan
Fisher Modular Construction (UK) Ltd make extension and expansion affordable because the modular units are manufactured off-site, which results in much lower costs than traditional methods of construction.
A Fisher UK solution offers shorter build programmes and much less disruption to existing operations. A new building from Fisher UK can also be purchased through third party asset finance companies.
Talk to our team about Production facilities
Do you need advice or want to enquire about our bespoke Production facilities?
Just get in touch, we're always happy to help.
Email sales@fisheruk.co.uk
Take a look through a selection of videos showing some of our recently completed projects.
Our modular construction solutions can serve a wide range of applications.
Give us a call on 01964 529512 or head over to our contact page to send us a message.
Stand Alone Units
© 2022 Fisher UK. Web Design Manchester by Designers Up North


text:
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redpajama_set_name: RedPajamaGithub


Drama and beauty abound on the plains of Africa and in this superb collection of images, Australian photographers Kym and Tonya lllman present an intimate insight into Earth's greatest wilderness. This lavish book is the result of thousands of hours spent on safari in Kenya, Tanzania, Rwanda, Botswana, Zimbabwe and South Africa. The lllmans' innovative, and sometimes controversial, approach includes cameras buried at the edges of waterholes, mounted on aerial drones and on remote controlled buggies, with many lost to lions and elephants in the process. They have spent days concealed in photographic hides to capture low level shots and have chartered helicopters to photograph wildlife and vistas not accessible by land. Each photograph is accompanied by the fascinating story behind its capture. In a final section the lllmans discuss the various elements that ensure a successful safari, from both a sightseeing and photographic viewpoint. This splendid collection of photographs is an unforgettable record of Africa in all its untamed beauty and raw motion. From the brutality of the food chain to playful shots of animals at their most uninhibited, from majestic sunsets to brooding landscapes, there is no greater theatre than nature itself. This is Africa on Safari.


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Deep Thoughts » The Gunner Tampico: Exploring Mexico's 20th Century Underwater Cultural Heritage
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The Gunner Tampico: Exploring Mexico's 20th Century Underwater Cultural Heritage
February 23rd, 2020, 3:39PM
Posted In: Deep Thoughts, Nautical Headlines
By Roberto Junco
ACUA Board Member
Underwater archaeologists of the National Institute of Anthropology and History (INAH) have confirmed the identity of a historic ship sunk in combat 105 years ago, the wreck of the gunner Tampico, participant of the first air to sea battle in history. Although not well known, the Mexican Revolution (1910-1921) was also fought at sea.
Tampico, 1908. Library of Congress.
Archaeologists from the Underwater Archeology Office (SAS) of INAH, working with Mexican Navy personnel, located this 'tomb of war' during the first of two field sessions, held from March 30 to April 2, 2019. Using the Mexican Navy's Oceanographic Research Vessel Río Tecolutla, the team obtained three-dimensional images of the seabed using multibeam sonar. The sonar revealed the presence of an anomaly that corresponded to the dimensions of the revolutionary gunner, at 60m long x 10m breadth.
Multibeam sonar image of Tampico. Photo courtesy INAH.
Guided by the Navy side scan sonar, the team returned to the site on September 8, 2019 and made two 40-meter dives that confirmed the identity of Tampico. In this first visit to the site, 105 years after its last sighting, the ship is in a considerable state of deterioration. In future dives, a 3D model will be developed to help monitor the wreck.
Side scan sonar image of Tampico. Courtesy INAH
Both the Tampico and its enemy, the gunner-transport Guerrero, the former built in the shipyards of New Jersey, USA, and the latter in Liverpool, England, were part of a project by Bernardo Reyes, Minister of War and Navy, who in the early twentieth century modernized the naval fleet of Mexico. In 1913, when Victoriano Huerta rose to power after deposing President Francisco I. Madero, a large part of the federal forces remained faithful to him, which included the fleet of gunner and gunner-transports; the latter, with greater military capacity.
On February 22, 1914, Hilario Rodríguez Malpica, the first lieutenant on Tampico, led a rebellion in Guaymas, Sonora, and with other officers imprisoned the ship's captain. After releasing those who did not support the revolutionary cause, the new captain went to Topolobampo, then controlled by revolutionary General Venustiano Carranza's troops. The central government ordered punishment for the rebels and on March 3, Guerrero began a blockade of the port. A day later, Guerrero opened fire on Tampico.
A second encounter occurred on March 13, when Tampico tried to leave Topolobampo. The attacks resumed on March 31; the federal forces had placed two obsolete ships (Democrata and Oaxaca) to hinder the eventual flight of the revolutionaries. From March 31 until April 22, intermittent fire continued between Guerrero and Tampico, with an almost fatal blow to the latter. If it had not been for the help of the biplane Sonora, from which hand bombs were thrown that failed to damage, but scared away Guerrero, the outcome may have been different. Because of the help from Sonora, Guerrero, Oaxaca, and Democrata, were forced to return to the port of Guaymas. From April 22 to June 10, everything possible was done to refloat Tampico. The ship finally left on June 14, for Mazatlan where repairs could continue on one of its two damaged boilers. Some 30 nautical miles out, the working boiler also failed leaving the ship adrift.
Two US destroyers, USS Preble and USS Perry, witnessed the battle; their records were key to determining the survey area. Captain Rodríguez Malpica requested help from USS Preble, but it was denied for neutrality reasons. Motionless, the men on Tampico spotted Guerrero at 05:00 on June 16, 1914, and following not far behind, USS New Orleans.
NAVY and INAH personnel going through the survey areas. Photo courtesy INAH.
At 07:48, Guerrero began firing. Unlike Tampico, the ship could move to avoid incoming fire. During the battle, a fire started on Tampico and at 09:50, captain Malpica gave orders to leave the ship and open its bottom valves to take it to the seabed. Boarding the lifeboats, the men tried to reach land, but were intercepted by Guerrero. It was in that extreme situation that Hilario Rodríguez Malpica took his gun, and pulled the trigger.
After the sinking, Guerrero, USS Preble, USS Perry, and USS New Orleans lowered their flags to half-mast in honor of the "Captain de Ship", Rodriguez Malpica and his fallen men. Finding Tampico is the first step to investigate and make visible an important but overlooked episode of the Mexican Revolution. The story is just beginning.
View of a portion of Tampico's engine. Photo courtesy INAH.


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NEW YORK -- Depending on who you ask the question of whether Microsoft developers are remaining Microsoft developers can elicit a myriad of responses. Oracle Corp. made a slew of announcements concerning its developers at Internet World on Wednesday, one of which implies that the ark of developers sailing around Redmond is losing passengers and that their life rafts are heading south to Oracle HQ.
"For the first time in a decade, Microsoft's developer community is up for grabs," says Jeremy Burton, vice president of Internet platform marketing for Oracle Corp. "They want to get to know the fashionable technologies." Burton says those include Java, XML and Linux.
Oracle cites a 1,000 percent increase in membership, from 40,000 to 400,000, of the Oracle Technology Network (OTN, http://technet.oracle.com) as evidence of the Microsoft exodus. On Wednesday, Oracle increased its commitment to OTN by launching a new site with expanded professional resources, software and support for developers. Developers can now take part in topic-based communities and find as "Ask Oracle" forum for direct interaction with Oracle experts.
Oracle also reports that more than 50 percent of new OTN members since February 1999 identify themselves as former Windows-only developers.
Also announced were the availabilities of Oracle Application Server 4.0.8 (OAS) and Oracle JDeveloper 3.0 and their support for Oracle's new Business Components for Java (BC4J). Similar to Microsoft Foundation Classes (MFCs) for building desktop applications, BC4J makes building Java server applications easier and more productive. The new version also has increased support for Enterprise JavaBeans (EJBs), Java Servlets and Java Server Pages (JSPs).


This article discusses the cause and potential resolutions of the "Errno 22 Invalid Argument" ShadowSnap backup error.
This error may be triggered during backup job initialization when the ShadowSnap software on a protected machine cannot properly access files shared through the Samba protocol by the Datto device to transfer backup job metadata.
This error may also occur on encrypted agents before data transfer is initiated over iSCSI.
Force a new backup. If the backup fails, continue with the steps below.
Log in to the Datto device's web interface.
Click the Protect tab in the main menu bar at the top of the page.
Click the Configure Agent Settings link for the agent experiencing the error.
Enable Share Compatibility Mode: Click the Share Compatibility Mode check box.
Force a backup of the agent from the Protect tab.
If the backup continues to fail, proceed to the next step.
If the preceding steps did not resolve the error, uninstall and reinstall the Shadow Snap agent on the server by following the process in the Reinstalling the ShadowSnap Software article.
If you are unable to resolve the issue using the steps in this article, please contact Datto Technical Support.