text:
\section{Introduction}
\label{Intr}

Superconducting iron-based pnictides~\cite{KamiharaJAmChS2008}
attract considerable interest not only due to their high critical
temperatures, but also because of the rich physics of their electron
subsystem. The phase diagram in iron pnictides contains areas of
superconductivity, spin-density wave (SDW) order~\cite{DagottoNatPhys2012}, both commensurate~\cite{dong2008} and incommensurate~\cite{PrattICSDWed}, and even a phase with electronic nematicity.~\cite{KasaharaNature2012}

Moreover, these materials often demonstrate spin and charge inhomogeneity, exhibiting characteristic features of systems with electronic phase separation.~\cite{PSexp1,PSexp2,PSexp3,PSexp4,DagottoNatPhys2012,
DagottoPRB2010phys_reg} The origin of this phase separation is important for understanding the mechanisms driving numerous phase transitions in the phase diagram of iron pnictides.

The phase separation is quite ubiquitous, manifesting itself in different situations where the itinerancy of charge carriers competes with their tendency to localization. The latter is often related to some specific type of magnetic ordering, e.g. antiferromagnetic in manganites or low-spin state in cobaltites. The interplay between the localization-induced lowering of the potential energy and metallicity, providing a gain in the kinetic energy, favors an inhomogeneous ground state, such as nanosize ferromagnetic droplets on an antiferromagnetic insulating background. This type of phase separation has a long history (beginning from the seminal work of Refs.~\onlinecite{NagaevJETPL1967,KasuyaSSC1970}) in the fields of magnetic semiconductors and doped manganites. Electron correlations here also play an important role enhancing the tendency to localization.~\cite{DagottoScience2005} Moreover, it can be shown
that in strongly correlated electron systems with different types
of charge carriers, phase separation can appear even in the
absence of any specific order parameter.~\cite{SboychaPRB2007}

In this paper, we discuss a very different mechanism of phase separation, which is not directly related to electron correlations and could be more relevant in the case of iron pnictides. It is based on the imperfect nesting of different pockets of the Fermi surface. Indeed, it has been known that the SDW ground state in a model with two spherical Fermi surfaces of unequal radius~\cite{RicePRB70} can be unstable with respect to electronic phase separation.~ \cite{tokatly,AAgraphene_doped,OurRicePRB} Variations of the latter model have been used to describe SDW in chromium~\cite{RicePRB70} and graphene bilayer with AA stacking~\cite{AAgraphenePRL}. It is also analogous (but not identical) to the commonly used model of iron pnictides where one deals, roughly speaking, with elliptical rather than spherical electron and hole sheets of the Fermi surface. One can ask if a similar mechanism could apply to pnictides. In this paper, we demonstrate that the answer to this question is positive, and thus the charge inhomogeneity can result from a purely electronic mechanism. This finding is important for the interpretation of experimental data on charge inhomogeneity and for understanding the nature of the coexistence of the order parameters in iron pnictides.

For definiteness, we will focus here on iron pnictides, although iron chalcogenides also exhibit phase separation.~\cite{Bianconi1,Bianconi2} However, the physics related to the Fermi surface nesting may not be directly applicable to iron chalcogenides, especially to those containing alkaline atoms. Indeed, some chalcogenides do not have hole pockets, but nevertheless exhibit antiferromagnetism with rather high N\'eel temperatures.~\cite{chalcWang,chalcZhang,chalcMou}
Moreover, the electron correlation effects in chalcogenides seem to be more pronounced than in pnictides.~\cite{DagottoNatPhys2012}
Therefore, the case of iron chalcogenides requires a separate
consideration.

This paper is organized as follows. In Sec.~\ref{model} we discuss the choice of the model Hamiltonian. Section~\ref{sdw} deals with the study of homogeneous SDW order in the mean-field approximation. The instability of the homogeneous state is proved in Sec.~\ref{separation}, where the phase diagram is constructed as well. The results are discussed in Sec.~\ref{discussion}. In Sec.~\ref{Concl}, we summarize the main conclusions of the paper, list the assumptions used, and formulate possible tasks for future work.

\section{Model}\label{model}

\subsection{Kinetic energy}

Unlike cuprates, which are believed to be in the strong electron-electron interaction regime, iron pnictides may be described by a weak-interaction model (see, e.g., the discussion in Sec.~IIIA of Ref.~\onlinecite{stewart_rmp2011}). In this approach, the shape of the Fermi surface and the value of the Fermi velocity are the only relevant single-electron band parameters. In the literature, the Fermi surface of iron pnictides is typically described using two related approaches, which we briefly describe below. In Fig.~\ref{FermiSurface}(a), we plot the Fermi surface within the so called unfolded Brillouin zone,~\cite{stewart_rmp2011,RichardRPrPh201,RaghuPRB2008two-orb,
DaghoferPRL2008two-orb,DaghoferPRL2010three-orb,HuHaoPRX2012,ErChub,Calderon,Fink} which corresponds to the square lattice of iron atoms, with one Fe atom per unit cell and lattice constant $a$.  In this representation, two quasi-two-dimensional nearly-circular hole pockets are centered at the $\Gamma (0,0)$ point, one more circular hole pocket is located near the $\Gamma'\,(\pi,\,\pi)$ point, and two elliptical-shaped electron pockets are centered at the ${\rm M} (0,\pi/a)$ and ${\rm M} (\pi/a,0)$ points [see Fig.~\ref{FermiSurface}(a)]. At the same time, the actual unit cell of pnictides contains two Fe atoms since in the crystal lattice the pnictogen atoms are located in non-equivalent positions. The (folded) Brillouin zone corresponding to this unit cell is obtained by folding the Brillouin zone shown in Fig.~\ref{FermiSurface}(a) by dashed lines and consequent rotation by $45^{\circ}$. The Fermi surface in the folded Brillouin zone is shown in Fig.~\ref{FermiSurface}(b). In this figure, all three hole pockets are situated near the $\Gamma (0,0)$ point, while electron pockets represented by overlapping ellipses are located near the ${\rm M} (\pm\pi/\bar{a},\pi/\bar{a})$ points, with $\bar{a}=a\sqrt{2}$. Formulating our model, we will make several simplifications. First, we neglect the effects associated with non-equivalent positions of the Fe atoms. Consequently, the use of unfolded Brillouin zone is sufficient. Second, we will neglect the 3D structure of the material and study only the 2D model.

\begin{figure}[t!]\centering
    \includegraphics[width=0.98\columnwidth]{FigFSnew.eps}
\caption{(Color online) Schematic illustration of the Fermi surface of iron pnictides in the unfolded (a) and folded (b) Brillouin zone (BZ). We have three hole pockets located near the center of the folded BZ [shown by (blue) solid curves]. In the unfolded BZ, one of the hole pockets moves to the corner of the BZ. For the unfolded BZ (a), the electron pockets are elliptic [(red) dashed curves] and located near the $(0,\pi/a)$ and $(\pi/a,0)$ points, while in the folded BZ, they are represented by overlapping ellipses located at the corners. Arrows show the possible nesting vectors between hole an electron pockets, which give rise to the SDW order. (c) Illustration of the possible nesting at different doping levels.}
\label{FermiSurface}
\end{figure}

Thus, the Hamiltonian of the model has the form
\begin{eqnarray}
H = H_0 + H_{\rm int},
\end{eqnarray}
where the kinetic energy term $H_0$ is given by
\begin{eqnarray}
\label{H0}
H_0
=
\sum_{\mathbf{k}\lambda\sigma}
\varepsilon^{h}_{\lambda\mathbf{k}}
a^{\dag}_{\mathbf{k}\lambda\sigma}
a^{\phantom{\dag}}_{\mathbf{k}\lambda\sigma}+
\sum_{\mathbf{k}s\sigma}
\varepsilon^{e}_{s\mathbf{k}}
b^{\dag}_{\mathbf{k}s\sigma}b^{\phantom{\dag}}_{\mathbf{k}s\sigma}\,.
\end{eqnarray}
In this equation, $a^{\dag}_{\mathbf{k}\lambda\sigma}$,
$a^{\phantom{\dag}}_{\mathbf{k}\lambda\sigma}$
($b^{\dag}_{\mathbf{k}s\sigma}$, $b^{\phantom{\dag}}_{\mathbf{k}s\sigma}$) are the creation and annihilation operators for electrons in the hole-like (electron-like) bands $\lambda=1,2,3$ ($s=1,2$) with  spectra $\varepsilon^{h}_{\lambda\mathbf{k}}$  ($\varepsilon^{e}_{s\mathbf{k}}$).

To simplify our formalism, we assume that near the Fermi level the bands have quadratic dispersions. For circular hole-like bands we have ($\hbar = 1$)
\begin{eqnarray}
\label{Spec_hole}
\varepsilon^{h}_{1\mathbf{k}}&=&-\frac{v^{h}_{F}k^2}{2k_F}+
\frac{v^{h}_{F}k_F}{2}-\mu, \\
\varepsilon^{h}_{2\mathbf{k}}
&=&-\frac{v^{h}_{2F}k^2}{2k_F}+\frac{v^{h}_{2F}k_F}{2}
-\Delta\epsilon_{2}-\mu\,,\label{Spec_hole2}\\
\varepsilon^{h}_{3\mathbf{k}+\bar{\mathbf{Q}}}
&=&-\frac{v^{h}_{3F}k^2}{2k_F}+\frac{v^{h}_{3}k_F}{2}
-\Delta\epsilon_{3}-\mu\,,\label{Spec_hole3}
\end{eqnarray}
where $k_F$ is the Fermi momentum, $\mu$ is the chemical potential,
$v^{h}_{F}$ and $v^{h}_{2,3F}$ are the Fermi velocities for the hole bands, and $\bar{\mathbf{Q}}=(\pi/a,\pi/a)$. The energy shifts $\Delta\epsilon_{2,3}$ in Eqs.~\eqref{Spec_hole2} and~\eqref{Spec_hole3} determine the difference in radii of the hole pockets: for $\Delta\epsilon_{i}>0$ the radius of the hole pocket $i=2,3$ is smaller than that of the hole pocket $1$.

As mentioned above, the electron components of the Fermi surface are
elliptic.  For these, the dispersion near the Fermi surface is given by the following relations
\begin{eqnarray}
\label{Spec_electron1}
\varepsilon^e_{1{\bf k + Q_0}}
=
\varepsilon (k_x, k_y),
\quad
\varepsilon^e_{2{\bf k + Q_0'}}
=
\varepsilon (k_y, k_x),
\end{eqnarray}
where the function $\varepsilon$ is equal to
\begin{eqnarray}
\varepsilon (k_x, k_y)
=
\frac{v^{e}_{F}k^2}{2k_F}
-\frac{v^{e}_{F}k_F}{2}+
\frac{\alpha v^{e}_{F}}{k_F}\left(k_y^2-k_x^2\right)-\mu\, .
\end{eqnarray}
The centers of the elliptic bands are
$\mathbf{Q}_0=(\pi/a,0)$ and $\mathbf{Q}'_0=(0,\pi/a)$,
and $v^{e}_{F}$ is the Fermi velocity for the electron bands averaged over the Fermi surface. Note that in general $v^{h}_{F}\neq v^{h}_{2F}\neq v^{h}_{3F}\neq v^{e}_{F}$. The parameter $\alpha$ defines the ellipticity of the electron pockets. For the Fermi surface structure corresponding to Fig.~\ref{FermiSurface}(a,b), $\alpha$ is positive. In this case, the major axes of the ellipses are directed toward the $\Gamma$ point. For $\alpha<0$, the ellipses are rotated by $90^{\circ}$ around their centers.

\subsection{Interaction Hamiltonian}\label{interaction_ham}

Due to the multi-sheeted structure of the Fermi surface, the interaction Hamiltonian $H_{\rm int}$, in general, must include a number of terms describing interactions between charge carriers in different bands. However, since we are interested in the SDW
order, most of these terms may be omitted for they do not contribute to SDW phase transition \cite{RicePRB70}. For this reason, we ignore the electron-electron and hole-hole interactions.

It is known~\cite{DagottoNatPhys2012} that magnetic order in pnictides is ``stripy". That is, the value of local magnetic moment oscillates along one of the crystal axes, remaining constant along the other axis. In the general case, each hole and electron bands are coupled to each other. However, to reproduce the striped magnetic structure it is sufficient to couple one electron and one hole band.~\cite{ErChub} For example, the SDW with oscillations along the $x$-direction occurs if we couple electrons in the hole band $1$ and electron band $1$, or electrons in the hole band $3$ and electron band $2$ [see the solid and dotted arrows in Fig.~\ref{FermiSurface}(a,b)]. In both cases, the nesting vectors will be nearly the same and equal approximately (exactly, for the commensurate SDW state) to $\mathbf{Q}_0=(\pi/a,0)$. Here we assume that only one hole band and one electron band take part in the formation of SDW order. For definiteness, assume that these are the hole band $\varepsilon^h_1$ and the electron band $\varepsilon^e_1$ (although our results remain the same for any pair of hole and electron bands). Consequently, only the interaction between $\varepsilon^h_1$ and $\varepsilon^e_1$ is crucial for the stabilization of the ordered phase. All other interaction terms will be discarded. As we will show below, even this simplified model allows to explain the experimental data on the commensurate and incommensurate SDW order as well as the phase separation. How our results change if we go beyond this simplification, will be discussed in Section~\ref{discussion}.

Keeping these considerations in mind, we split the model Hamiltonian into two parts, magnetic, $H_{\rm m}$, and nonmagnetic (``reservoir''), $H_{\rm r}$
\begin{eqnarray}
H&=&H_{\rm m}+H_{\rm r}\,,\label{Hmr}\\
H_{\rm m}&=&
\sum_{\mathbf{k}\sigma}
\left[
	\varepsilon^{h}_{1\mathbf{k}}
	a^{\dag}_{\mathbf{k}1\sigma}
	a^{\phantom{\dag}}_{\mathbf{k}1\sigma}
	+
	\varepsilon^{e}_{1\mathbf{k}}
	b^{\dag}_{\mathbf{k}1\sigma}
	b^{\phantom{\dag}}_{\mathbf{k}1\sigma}
\right]
\nonumber
\\
&&
+\frac{V_1}{\cal N}
\!\!\sum_{\mathbf{kk}'\mathbf{K}\sigma\sigma'}
\!\!\!
a^{\dag}_{\mathbf{k}+\mathbf{K}1\sigma}
a^{\phantom{\dag}}_{\mathbf{k}1\sigma}
b^{\dag}_{\mathbf{k}'-\mathbf{K}1\sigma'}
b^{\phantom{\dag}}_{\mathbf{k}'1\sigma'}\,,
\label{Hm}\\
H_{\rm r}&=&
\sum_{\mathbf{k}\sigma}
\left[
	 \sum_{\lambda=2,3}\varepsilon^{h}_{\lambda\mathbf{k}}
	a^{\dag}_{\mathbf{k}\lambda\sigma}
	a^{\phantom{\dag}}_{\mathbf{k}\lambda\sigma}
	+
	\varepsilon^{e}_{2\mathbf{k}}
	b^{\dag}_{\mathbf{k}2\sigma}
	b^{\phantom{\dag}}_{\mathbf{k}2\sigma}
\right]\!.
\label{Hr}
\end{eqnarray}
Here ${\cal N}$ is the number of Fe atoms in a layer, $V_1>0$ is the coupling constant characterizing the Coulomb interaction between the bands $\varepsilon^{h}_{1\mathbf{k}}$ and $\varepsilon^{e}_{1\mathbf{k}}$. Below we will refer to these bands as magnetic bands. The bands $\varepsilon^{h}_{2\mathbf{k}}$, $\varepsilon^{h}_{3\mathbf{k}}$, and and $\varepsilon^{e}_{2\mathbf{k}}$ will be called nonmagnetic, since in our model, they do not contribute to the magnetic order parameter.

Model~\eqref{Hmr} is a generalization of the Rice model, proposed in
Ref.~\onlinecite{RicePRB70} for the description of the incommensurate SDW order in chromium. The Hamiltonian of Ref.~\onlinecite{RicePRB70} has two bands, which participate in the magnetic transition, and a
``reservoir" (nonmagnetic bands corresponding to $H_{\rm r}$, where the subscript `r' stand for ``reservoir"). Unlike Eq.~(\ref{Hmr}), the bands responsible for magnetic ordering in the Rice model have a spherical Fermi surface; therefore, at certain filling, the nesting is perfect.

\section{Incommensurate SDW order}
\label{sdw}

\subsection{Mean-field equations}

We now consider Hamiltonian~\eqref{Hmr} in the mean-field approximation. As we pointed out above, the Coulomb interaction in iron pnictides is weak, therefore, we assume below that
\begin{equation}
\label{limitV}
V_1/\varepsilon_F\ll1\,,
\end{equation}
where the Fermi energy $\varepsilon_F$ is defined as
\begin{equation}\label{EF}
\varepsilon_F=\frac{v^e_F+v^h_F}{2}k_F\equiv v_Fk_F\,.
\end{equation}
The weak-coupling condition
Eq.~(\ref{limitV})
guarantees the applicability of the mean-field approximation.

We will study the stability of the following SDW order parameter:
\begin{equation}
\label{DeltaQ}
\Delta=\frac{V_1}{\cal N}\!\sum_{\mathbf{k}}
\left\langle
	a^{\dag}_{\mathbf{k}1\uparrow}
	b^{\phantom{\dag}}_{\mathbf{k}+\mathbf{Q}1\downarrow}
\right\rangle
=
\frac{V_1}{\cal N}
\!\sum_{\mathbf{k}}
\left\langle
	a^{\dag}_{\mathbf{k}-\mathbf{q}1\uparrow}
	b^{\phantom{\dag}}_{\mathbf{k}+\mathbf{Q}_01\downarrow}
\right\rangle,
\end{equation}
where the nesting vector ${\bf Q}$ is equal to
\begin{eqnarray}
\mathbf{Q}=\mathbf{Q}_0+\mathbf{q}.
\end{eqnarray}
When ${\bf q} = 0$, our SDW is commensurate, whereas if ${\bf q}$ is small, but non-zero, it is incommensurate. Other types of order parameter will be discussed in Sec.~\ref{discussion}.

Note here that different parts of each pocket of the Fermi surface have different orbital composition.~\cite{RichardRPrPh201,ScalapinoPRB2010,Suzuki2011}
The pairing is more favorable between those parts of the Fermi surfaces which have similar orbital character. Within our approach,  such feature can be accounted by introducing a momentum-dependent coupling $V_1$. Such a generalization would lead to a pronounced wave-vector dependence of the SDW order parameter, and could affect
the transition to the SDW state and the structure of the incommensurate SDW phase. However, the reliable calculation of the momentum-dependent $V_1$ is a complicated task going beyond the scope of the present study. Furthermore, unless the variation of $V_1$ is extremely strong, they do not affect phase separation qualitatively. Thus, we choose to work with a momentum-independent coupling constant.

\begin{comment}
The pairing is more favorable between parts corresponding to
similar orbital filling. In our model, such a situation corresponds
to the dependence of the interaction parameter $V_1$ on points on the coupled pockets. This should lead to the pronounced wave-vector
dependence of the SDW order parameter, and consequently to the
quite complicated magnetic structure. In our paper, we study a
simple type of SDW with the dependence only on one wave (nesting)
vector, which is consistent with available experimental data. This
means that our coupling constant $V_1$ corresponds to some averaging
over Fermi surface, and specific features of orbital composition
become averaged out.
\end{comment}

The magnetization corresponding to the SDW order parameter $\Delta$ lies in $xy$ plane. For the commensurate SDW case, in real space the ``stripy" order is observed. Namely, the magnetization direction remains constant when one moves along the direction normal to
${\bf Q}_0$. However, when one moves parallel to ${\bf Q}_0$,
the magnetization reverses its direction from one iron atom to the next iron atom. For incommensurate SDW, this ``stripy" pattern slowly rotates in the $xy$ plane: the local rotation angle $\phi ({\bf R})$ at the point ${\bf R}$ is equal to $({\bf q} {\bf R})$
[see panel (c) and (d) in Fig.~\ref{FigDeltaQ}].

In the mean-field approximation, the magnetic Hamiltonian
Eq.~\eqref{Hm} takes the form
\begin{eqnarray}
\label{HmMF}
H_{\rm m}^{\rm MF}
\!\!\!\!&=&\!\!\!\!
\sum_{\mathbf{k}\sigma}\!
\left[
	\varepsilon^{h}_{1\mathbf{k}-\mathbf{q}}
	c^{\dag}_{\mathbf{k}\sigma}
	c^{\phantom{\dag}}_{\mathbf{k}\sigma}
	\!\!+
	\varepsilon^{e}_{1\mathbf{k}+\mathbf{Q}_0}
	d^{\dag}_{\mathbf{k}\sigma}
	d^{\phantom{\dag}}_{\mathbf{k}\sigma}
\right.
\nonumber
\\
&&
-\left.
	\Delta\left(
		c^{\dag}_{\mathbf{k}\sigma}
		d^{\phantom{\dag}}_{\mathbf{k}-\sigma}
		+
		d^{\dag}_{\mathbf{k}\sigma}
		c^{\phantom{\dag}}_{\mathbf{k}-\sigma}
	\right)
	+\Delta^2/V_1
\right],
\end{eqnarray}
where we introduce the new operators
$c^{\dag}_{\mathbf{k}\sigma}=a^{\dag}_{\mathbf{k}-\mathbf{q}1\sigma}$,
$d^{\dag}_{\mathbf{k}\sigma}=b^{\dag}_{\mathbf{k}+\mathbf{Q}_01\sigma}$,
and $\Delta$ is assumed to be real. The Hamiltonian
Eq.~\eqref{HmMF}
can be easily diagonalized. The quasiparticle energies are
\begin{eqnarray}
\label{SpecD}
E^{(1,2)}_{\mathbf{k}}
&=&
\frac{
	\varepsilon^{e}_{1\mathbf{k}+\mathbf{Q}_0}
	+
	\varepsilon^{h}_{1\mathbf{k}-\mathbf{q}}
     }{2}\mp
\nonumber
\\
&&
\sqrt{
	\Delta^2
	+
	\frac{1}{4}
	\left(
		\varepsilon^{e}_{1\mathbf{k}+\mathbf{Q}_0}
		-
		\varepsilon^{h}_{1\mathbf{k}-\mathbf{q}}
	\right)^2
     }\,.
\end{eqnarray}
The grand potential $\Omega_{\rm m}$ (per one Fe atom) corresponding to $H_{\rm m}^{\rm MF}$ is ($k_B = 1$)
\begin{equation}
\label{OmegaM}
\Omega_{\rm m}
=
-2T\sum_{s}
\int\limits_{BZ}\!\!
\frac{
	v_0\;d^2\mathbf{k}
     }
     {
	(2\pi)^2
     }
\ln\left[
	1+e^{-E^{(s)}_{\mathbf{k}}/T}
  \right]
+
\frac{2\Delta^2}{V_1}\,,
\end{equation}
where $v_0$ is the volume of the unit cell, and the integration is performed over the 2D Brillouin zone. The SDW gap $\Delta$
and the nesting vector $\mathbf{Q}$ are found from the minimization of $\Omega_{\rm m}$
\begin{equation}
\label{EqDeltaQ0}
\frac{\partial\Omega_{\rm m}}{\partial\Delta}=0\,,\;\;\frac{\partial\Omega_{\rm m}}{\partial\mathbf{q}}=0\,.
\end{equation}

It will be shown below that in the weak-coupling limit
Eq.~(\ref{limitV}), the SDW order can exist only if the deviation from the perfect nesting is small, that is:
\begin{equation}\label{limits}
|\alpha|\ll1\,.
\end{equation}
In addition, the gap $\Delta$ is small compared to $\varepsilon_F$, and the deviation ${\bf q}$ of the nesting vector $\mathbf{Q}$
from the commensurate value $\mathbf{Q}_0$ is also small
\begin{equation}\label{limitQ}
|\mathbf{q}|
=
|{\bf Q} - {\bf Q}_0|
\sim
\Delta/v_F\ll k_F.
\end{equation}

Restricting ourselves to the limit of zero temperature, we can write the first of Eqs.~\eqref{EqDeltaQ0}
in the following form
\begin{equation}
\label{EqDelta}
1=\frac{V_1}{2}\int\!\!\frac{v_0\,d^2\mathbf{k}}
{(2\pi)^2}\frac{1-\Theta\left(E^{(1)}_{\mathbf{k}}
\right)-\Theta\left(-E^{(2)}_{\mathbf{k}}\right)}
{\sqrt{\Delta^2+\displaystyle\frac{1}{4}
\left(\varepsilon^{e}_{1\mathbf{k}+\mathbf{Q}_0}
-\varepsilon^{h}_{1\mathbf{k}-\mathbf{q}}\right)^2}}\,,
\end{equation}
where $\Theta(x)$ is the step function.

When the lower band $E^{(1)}_{\mathbf{k}}$ is filled, while the upper band $E^{(2)}_{\mathbf{k}}$ is empty, the gap attains its maximum value $\Delta_0$. In this case, $\Theta(E^{(1)}_{\mathbf{k}})=\Theta(-E^{(2)}_{\mathbf{k}})=0$
for any $\mathbf{k}$, and Eq.~\eqref{EqDelta} becomes
\begin{eqnarray}
\label{EqDelta0}
1=\frac{V_1}{2}\int\!\!\!dE\,\frac{\bar{\rho}(E)}{\sqrt{\Delta_0^2+E^2}},
\end{eqnarray}
where the generalized density of states is defined as
\begin{eqnarray}
\label{Rho}
\bar{\rho}(E)=\int\!\!\frac{v_0\;d^2\mathbf{k}}{(2\pi)^2}\,
\delta\!\!\left(E-\frac{\varepsilon^{e}_{1\mathbf{k}
+\mathbf{Q}_0}-\varepsilon^{h}_{1\mathbf{k}}}{2}\right)\,.
\end{eqnarray}
Evaluating $\bar{\rho}(E)$, we set $\mathbf{q}=0$, since taking into account values of the order of $|\mathbf{q}|\sim\Delta/v_F$
gives only second-order corrections in Eq.~\eqref{EqDelta0}.

If $|E|\ll\varepsilon_F$, the function $\bar{\rho}(E)$ can be calculated explicitly using Eqs.~\eqref{Spec_hole} and~\eqref{Spec_electron1} for the band spectra
$\varepsilon^{e}_{1\mathbf{k}+\mathbf{Q}_0}$ and
$\varepsilon^{h}_{1\mathbf{k}}$. As a result, near the Fermi surface we obtain
\begin{equation}
\label{Rho0}
\bar{\rho}(E) \approx \bar{\rho}(0)
=
\frac{v_0 k_F^2}{2\pi\varepsilon_F}\,,\;\;\;\;\;|E|\ll\varepsilon_F\,.
\end{equation}
When the energy $E$ is of the order of the band width,
$\bar{\rho}(E)$ vanishes. This makes the integral in
Eq.~(\ref{EqDelta0}) convergent, and one can derive the usual BCS-like expression for the gap
\begin{equation}
\label{Delta0est}
\Delta_0
\approx
\varepsilon_F
\exp\!\left(\!
		-\frac{2\pi\varepsilon_F}{v_0 k_F^2V_1}
    \right)\,.
\end{equation}

If the sample is doped, then $E^{(1)}_{\mathbf{k}}>0$ or
$E^{(2)}_{\mathbf{k}}<0$, for some range of $\mathbf{k}$, and the equation for the band gap becomes
\begin{equation}
\label{EqDeltaX}
\ln\frac{\Delta_0}{\Delta}
=
\int\!\!\frac{\varepsilon_F\, d^2\mathbf{k}}{4\pi k_F^2}
\frac{
	\Theta\left(E^{(1)}_{\mathbf{k}}\right)
	+
	\Theta\left(-E^{(2)}_{\mathbf{k}}\right)}
   {\sqrt{\Delta^2+\displaystyle\frac{1}{4}\left(
			\varepsilon^{e}_{1\mathbf{k}+\mathbf{Q}_0}-
			\varepsilon^{h}_{1\mathbf{k}-\mathbf{q}}\right)^2}}\,.
\end{equation}
Substituting Eqs.~\eqref{Spec_hole} and \eqref{Spec_electron1}
into Eq.~\eqref{EqDeltaX}, and taking into account Eqs.~\eqref{limits} and~\eqref{limitQ}, after straightforward algebra we derive the equation for the band gap in the form
\begin{eqnarray}
\label{EqDeltaFin}
\ln\frac{1}{\delta}
=
\int\limits_{0}^{2\pi}\!\!
\frac{d\varphi}{2\pi}
\re \left\{
		{\rm cosh}^{-1}
		\left[
			\frac{\nu_0(\mathbf{p},\varphi)-\nu}{\delta}
		\right]
     \right\}\,,
\end{eqnarray}
where,
\begin{eqnarray}
\label{nu0}
\nu_0(\mathbf{p},\varphi)
&=&
p_x\cos\varphi+p_y\sin\varphi-\frac{\bar{\alpha}}{2}\cos2\varphi,\;\;
\\
\bar{\alpha}&=&\frac{\alpha\,\varkappa\,\varepsilon_F}{\Delta_0},
\label{alpha}
\end{eqnarray}
and we introduce the following dimensionless quantities
\begin{equation}\label{defs}
\varkappa=\frac{2\sqrt{v_F^ev_F^h}}{v_F^e+v_F^h},\;\;
\delta=\frac{\Delta}{\Delta_0},\;\;\nu=\frac{\mu}{\varkappa\Delta_0},\;\;
\mathbf{p}=\frac{\varkappa v_F\mathbf{q}}{2\Delta_0}\,.
\end{equation}

Transforming similarly the second of Eqs.~\eqref{EqDeltaQ0}, we obtain the equation for the nesting vector
$\mathbf{Q} = \mathbf{Q}_0+2\Delta_0\mathbf{p}/v_F\varkappa$,
\begin{eqnarray}
\label{EqQ}
\left(\begin{array}{c}\!\!p_x\!\!\\\!\!p_y\!\!
\end{array}\right)&=&\int\limits_{0}^{2\pi}\!\!\frac{d\varphi}{\pi}
\left(\begin{array}{c}\!\!\cos\varphi\!\!\\\!\!\sin\varphi\!\!
\end{array}\right)\sign\left(\nu_0(\mathbf{p},\varphi)-\nu\right)\times\nonumber\\
&&\re\sqrt{\left(\nu_0(\mathbf{p},\varphi)-\nu\right)^2-\delta^2}\,.
\end{eqnarray}

Equations~\eqref{EqDeltaFin} and~\eqref{EqQ} determine the SDW band gap $\Delta$ and the nesting vector $\mathbf{Q}$ as functions of $\mu$. However, experiments are performed at fixed doping, not chemical potential. Thus, we have to relate the electron density and $\mu$. The total number of electrons per iron atom, $n(\mu)$, is the sum of the number of electrons in the nonmagnetic and the magnetic bands
$n(\mu) = n_{\rm r}(\mu) + n_{\rm m} (\mu)$, where
\begin{eqnarray}
\nonumber
n_{\rm r}(\mu)
&=&
\frac{2}{\cal N}
\sum_{\mathbf{k}}
\left[
	 \sum_{\lambda=2,3}\Theta(-\varepsilon^{h}_{\lambda\mathbf{k}})
	+
	\Theta(-\varepsilon^{e}_{2\mathbf{k}})
\right],\\
n_{\rm m}(\mu)&=&-\frac{\partial\Omega_{\rm m}}{\partial\mu}.
\end{eqnarray}
The doping is defined by
\begin{eqnarray}
x(\mu)=n(\mu)-n(0).
\end{eqnarray}
Performing calculations similar to those described above, we obtain for the doping level
\begin{eqnarray}\label{EqX}
\frac{x}{x_0}&=&r\nu-\int\limits_{0}^{2\pi}\!\!\frac{d\varphi}{2\pi}\,
\sign\left(\nu_0(\mathbf{p},\varphi)-\nu\right)\times\nonumber\\
&&\re\sqrt{\left(\nu_0(\mathbf{p},\varphi)-\nu\right)^2-\delta^2}\,,
\end{eqnarray}
where
\begin{equation}\label{defs1}
x_0=\frac{2v_0k_F^2}{\pi\varkappa}\frac{\Delta_0}{\varepsilon_F},\;\;
r=\frac{(v^{h}_{2F})^{-1}+(v^{h}_{3F})^{-1}+
(v^{e}_{F})^{-1}}{(v^{h}_{F})^{-1}+(v^{e}_{F})^{-1}}\,.
\end{equation}
The first (second) term in Eq.~\eqref{EqX} is the nonmagnetic (magnetic) contribution $x_{\rm r}$ ($x_{\rm m}$) to the total doping $x$. The parameters $x_0$ and $r$ in Eq.~\eqref{defs1} have clear physical meanings: $x_0$ defines the characteristic scale of doping where SDW order exists, while $r$ is the ratio of the densities of states of electrons in the non-magnetic and magnetic bands.
Equations~\eqref{EqDeltaFin},~\eqref{EqQ}, and~\eqref{EqX} form a closed system of equations for the self-consistent determination of
$\Delta(x)$, $\mathbf{Q}(x)$, and $\mu(x)$.

\subsection{Results: Homogeneous state}
\label{results}

Our numerical analysis reveals that
Eq.~\eqref{EqDeltaFin} has no solutions if
$|\bar{\alpha}|>2.0$. Thus, the equality
$|\bar{\alpha}|=2.0$ determines the critical value of the ellipticity parameter $\alpha_c$: for a given coupling constant $V_1$, the SDW ordering occurs only if
\begin{eqnarray}
\label{alpha_c}
|\alpha| < \alpha_c = \frac{2 \Delta_0}{\varkappa \varepsilon_F}.
\end{eqnarray}
Conversely, this
condition~Eq.~(\ref{alpha_c})
may be re-formulated as a requirement on the
interaction strength: for given band parameters ($\alpha$, $\varkappa$,
etc.) the SDW is stable only if
\begin{equation}
\label{Vc}
V_1 > V_c=\frac{2\pi \varepsilon_F}{\displaystyle v_0 k_F^2
\ln \left(\frac{2}{|\alpha|\varkappa}\right)} \,.
\end{equation}

It is seen from Eqs.~\eqref{defs} and~\eqref{defs1} that the parameter $\varkappa$ only renormalizes the dimensionless quantities $\nu$, $\mathbf{p}$, and $x_0$. Thus, at fixed $\bar{\alpha}$ and $r$, it is enough to know the functions $\Delta(x)$, $\mathbf{q}(x)$, and $\mu(x)$ for $\varkappa=1$. For $\varkappa\neq1$ these functions are found by simple rescaling as $\Delta(x\varkappa)$, $\mathbf{q}(x\varkappa)/\varkappa$, and $\varkappa\mu(x\varkappa)$. For this reason, below we study only the $\varkappa=1$ case. Note that, typically, for a real material all Fermi  velocities are of the same order, thus $\varkappa \sim 1$.

\begin{figure}[t]\centering
    \includegraphics[width=0.98\columnwidth]{FigDeltaQa.eps}\\
    \includegraphics[width=0.98\columnwidth]{FigDeltaQb.eps}\vspace{6mm}\\
    \includegraphics[width=0.98\columnwidth]{FigSpinStrEH.eps}
 \caption{(Color online) Dependence of the normalized order parameter $\Delta/\Delta_0$ and wave vector $|\mathbf{q}|$
on the doping $x$, for $r=\varkappa=1$.
(a) Here $\bar{\alpha}=0.1$. The transition from commensurate to
incommensurate SDW state is of first order: both $\Delta$ and
$|\mathbf{q}|$ abruptly change at $x=x_1^{*}$. The dashed curves show the functions $\Delta(x)$ and $|\mathbf{q}(x)|$
corresponding to the metastable state. (b) Here $\bar{\alpha}=0.6$. The transition from commensurate to incommensurate SDW state is now of second order. Panels (c) and (d) show schematics of the incommensurate SDW spin structure. If $\alpha>0$, then panel (c) corresponds to hole doping ($x<0$) and (d) to electron doping
($x>0$). If $\alpha<0$, then panel (c) corresponds to electron
doping, while panel (d) corresponds to hole doping.}
\label{FigDeltaQ}
\end{figure}

The computed functions $\Delta(x)$ and $q(x)$ are shown in
Fig.~\ref{FigDeltaQ}(a) and (b) for $r=\varkappa=1$
and two different values of $\bar{\alpha}$.
At low doping, $|x|<x_1^{*}$, where the critical doping
$x_1^*$ depends on model parameters, all the extra charge goes to the nonmagnetic bands. As a result, the order parameter is independent of $x$, $\Delta(x)=\Delta_0$, $\mathbf{q}(x)=0$, and the chemical potential increases linearly with $x$,
\begin{eqnarray}
\mu(x)=\frac{\Delta_0 x}{rx_0}.
\end{eqnarray}
In such a regime, the system exhibits a commensurate SDW order.

When $|x|=x_1^*$, the chemical potential touches the bottom (top) of the upper (lower) magnetic band. Upon further doping, electrons (holes) appear in the band $E^{(2)}_{\mathbf{k}}$ ($E^{(1)}_{\mathbf{k}}$). The SDW order becomes incommensurate,~\cite{ic_sdw} ${\bf q} \ne 0$. The order of the transition into the incommensurate state depends on the
parameters $\bar{\alpha}$ and $r$. If $r<r_1\cong0.38$,
the transition is of second order for any $\bar{\alpha}$,
while for larger $r$ it becomes of first order if
$|\bar{\alpha}|<\bar{\alpha}_1(r)$. In the case of first-order transitions, both $\Delta$ and $|\mathbf{q}|$ abruptly change at
$x=x_1^{*}$, see Fig.~\ref{FigDeltaQ}(a).

Electron doping ($x>0$) is in many respects similar to hole doping ($x<0$). Indeed, the functions $\Delta(x)$, $\mu(x)$, and $|\mathbf{q}(x)|$ obey particle-hole symmetry relations
\begin{eqnarray}
\Delta(-x)=\Delta(x),
\\
\mu(-x)=-\mu(x),
\\
|\mathbf{q}(-x)|=|\mathbf{q}(x)|.
\end{eqnarray}
In addition, these functions are independent of the sign of $\alpha$. However, the direction of the vector $\mathbf{q}(x)$ depends on the sign of $\alpha$ and on the type of doping. When $\alpha>0$,
the vector $\mathbf{q}(x)$ is parallel to the $x$ axis for electron doping and to the $y$ axis for hole doping. The direction of
$\mathbf{q}(x)$ is reversed if $\alpha<0$. Thus, the nesting vector
$\mathbf{Q} = (Q_x, Q_y)$ is given by the following formulas
\begin{eqnarray}
\label{Qdir1}
Q_x &=& \frac{\pi}{a}
+
\frac{2\Delta_0p(|x|)}{\varkappa v_F},
\quad
Q_y = 0,\;\;
\mbox{if }
	\alpha x>0,
\\
\label{Qdir2}
Q_x &=& \frac{\pi}{a},
\quad
Q_y = \frac{2\Delta_0p(|x|)}{\varkappa v_F},\;\;
\mbox{if }
	\alpha x<0.
\end{eqnarray}
How does the incommensurate SDW described by these equations look like in real space? Let us introduce the integer-valued vector
$\mathbf{n}=(n,m)$. Then the position of a given iron atom is equal to ${\bf R}_{\bf n} = a {\bf n}$. For the order parameter $\Delta$,
Eq.~(\ref{DeltaQ}), the SDW magnetization vector lies in the $xy$ plane: $S^z_{\bf n} = 0$. The in-plane components can then be expressed as
\begin{eqnarray}
\mathbf{S_n}=S_0
\Big(
	\cos(a\mathbf{Q \cdot n}),\,
	\sin(a\mathbf{Q \cdot n})
\Big),
\end{eqnarray}
where
$S_0=\Delta/V_1$.
Thus, we obtain
\begin{equation}\label{Sdir}
\mathbf{S_n}=S_0\left\{
\begin{array}{rccl}
&\!\!(-1)^n(\cos\phi n\,,&\!\!\sin\phi n )\!\!&\,,\;\;\alpha x>0\,,\\
&\!\!(-1)^n(\cos\phi m\,,&\!\sin\phi m )\!\!&\,,\;\;\alpha x<0\,,
\end{array}\right.
\end{equation}
where $\phi=a|\mathbf{q}|$.
These spin configurations are schematically shown in Fig.~\ref{FigDeltaQ} (c) and (d) for hole and electron doping, respectively. For positive (negative) $\alpha$, panel~(c) corresponds to $x>0$ ($x<0$), and panel~(b) corresponds to $x<0$ ($x>0$).

\section{Phase separation}
\label{separation}

In the previous section we assumed that the ground state of the model is homogeneous. Here we demonstrate that there is a part of the phase diagram where homogeneous states are not stable, and the true ground state is phase separated. To detect this instability, the chemical potential must be calculated.

The computed dependence of the chemical potential $\mu$ on doping $x$ is shown in Fig.~\ref{FigMu} for three different values of $\bar{\alpha}$ and $r=\varkappa=1$ for electron doping ($x>0$).
The dependence $\mu(x)$ for hole doping can be easily determined using particle-hole symmetry, as discussed in the previous section.

\begin{figure}[t]\centering
    \includegraphics[width=0.95\columnwidth]{FigMu1.eps}\\
    \includegraphics[width=0.95\columnwidth]{FigMu2.eps}\\
    \includegraphics[width=0.95\columnwidth]{FigMu3.eps}
 \caption{(Color online) Chemical potential $\mu(x)$ calculated at
$\bar{\alpha}=0.1$ (a), $\bar{\alpha}=0.5$ (b), and
$\bar{\alpha}=1.2$ (c). Here, $r=\varkappa=1$.
(a) and (b): the homogeneous state is {\it unstable} toward phase separation if $x_1<x<x_2$. The dashed (red) curve corresponds to the
$\mu_0$ found using the Maxwell construction. The shaded areas above and below $\mu_0$ are equal to each other. (c): $\mu(x)$ monotonically increases with $x$, no phase separation appears. The homogeneous commensurate ($\mathbf{q}=0$) and incommensurate ($\mathbf{q}\neq 0$) SDW, paramagnetic (PM), and inhomogeneous commensurate--incommensurate SDW (PS) states are separated by
vertical dotted lines.}\label{FigMu}
\end{figure}

The function $\mu(x)$ shown in Fig.~\ref{FigMu} demonstrates several peculiar features in the vicinity of the commensurate-incommensurate phase transition point $x_1^{*}$. Specifically, for low $\bar{\alpha}$, the function $\mu(x)$ is non-monotonic and multivalued near $x \approx x_1^*$ [see Fig.~\ref{FigMu}(a)]. At higher $\bar{\alpha}$, the multivaluedness disappears; however, the non-monotonicity remains [see Fig.~\ref{FigMu}(b)]. This vanishes at even higher values of $\bar{\alpha}$ [as in Fig.~\ref{FigMu}(c)].

We now observe that in Fig.~\ref{FigMu}(a) and Fig.~\ref{FigMu}(b)
there are finite ranges of doping where the chemical potential decreases as the doping increases. This means that the compressibility of the electronic system is negative and the homogeneous state is {\it unstable} with respect to separation into two
phases.~\cite{thermodyn} The phase transitions between homogeneous commensurate and incommensurate SDW phases, which we described in
subsection~\ref{results}, will be masked, at least partially, by the phase separation.

In the separated state there exist two phases, phase~$1$ and phase~$2$, with electron density $x_1$($<x_1^*$) and $x_2$($>x_1^*$), and with the volume fractions $p_1$ and $p_2$ satisfying the conditions $p_1+p_2=1$ and $x_1p_1+x_2p_2=x$. As one can see from Fig.~\ref{FigMu} (a,b), the phase $1$ is the commensurate and the phase $2$ is the incommensurate SDW state. The concentrations $x_1$ and $x_2$ are found from the equations~\cite{thermodyn}  $\mu(x_1)=\mu(x_2)\equiv\mu_0$ and $\Omega_1=\Omega_2$, where $\Omega_{1,2}$ are grand potentials in the phases $1$ and $2$. The latter condition means the equality of two shaded areas shown in Fig.~\ref{FigMu}(a,b) (the so-called Maxwell construction).

The range of doping $x$, where the phase separation exists, is largest when $\alpha=0$. In this case, our model is identical to the two-dimensional Rice model~\cite{RicePRB70}, for which the presence of the phase separation was shown in Refs.~\onlinecite{tokatly,OurRicePRB}. The range of the phase separation, $x_1<x<x_2$, shrinks if $|\bar{\alpha}|$ increases, and disappears at the critical value $\bar{\alpha}_c\cong1.15$. The phase separated state does not exist for $|\bar{\alpha}|>\bar{\alpha}_c$.

The obtained results are summarized in the phase diagram in the
($x,\bar{\alpha}$) plane shown in Fig.~\ref{FigPhDiag}. This phase diagram is calculated for $r=\varkappa=1$. It remains qualitatively the same if $r\neq0$. If the nonmagnetic bands are absent, $r=0$, the homogeneous commensurate SDW phase exists only when $x=0$. Consequently, the electronic concentration $x_1$ in the phase 1 is zero in the phase separated state for any $\bar{\alpha}$.

\begin{figure}[t]\centering
    \includegraphics[width=0.95\columnwidth]{FigPhDiag.eps}
\caption{(Color online) The phase diagram of the model~\eqref{Hmr} in the ($x,\bar{\alpha}$) plane; for $r=\varkappa=1$ and
$\alpha,x>0$. It is symmetric with respect to the replacement $x\to-x$ and/or $\alpha\to-\alpha$.  The boundary between incommensurate SDW and paramagnetic (PM) states shown by the dashed (red) curve corresponds to the first order and by the solid (red) curve to the second order phase transition. Solid (blue) lines indicate the boundaries of the phase separated (PS) state. The solid (black) curve (second order transition) and dashed (black) curve (first order transition) show the boundaries between commensurate ($\mathbf{q}=0$) and incommensurate ($\mathbf{q}\neq0$) homogeneous SDW phases. Note that phase separation partially masks the transition line between the homogeneous SDW states.
}
\label{FigPhDiag}
\end{figure}

Finally, we would like to draw the attention of the reader to an unexpected feature of the phase diagram in Fig.~\ref{FigPhDiag}.
Namely, the second-order incommensurate SDW-to-paramagnet transition line bends to the right, while all other transition curve in the phase diagram bend to the left. In other words, the value of doping where the transition from paramagnetic to incommensurate SDW phase occurs increases when the ellipticity parameter $\alpha$ increases. Interpreting this feature, however, one must keep in mind that the nesting quality is controlled not only by $\alpha$ but also by $\mu$ (or $x$). The parameter $\alpha$ controls the shape of the electron pocket, while $\mu$ (or doping) controls the relative areas of electron and hole pockets. Therefore, at larger doping levels, when the areas of the electron and hole pockets differ substantially, the electron and hole pockets could be better nested for larger ellipticity of the electron pocket.

\section{Discussion}
\label{discussion}

The most important result obtained here is the prediction of electronic phase separation in some range of doping. The separated phase consists of a mixture of commensurate and incommensurate SDW phases with different electronic concentrations. The phase separation in iron-based superconductors was observed in several experiments~\cite{PSexp1,PSexp2,PSexp3,PSexp4}. For example, the inhomogeneous state with a commensurate antiferromagnetic and nonmagnetic domains with characteristic sizes $\sim65$\,nm was
observed in the hole doped Ba$_{1-x}$K$_x$Fe$_2$As$_2$
compound.~\cite{PSexp1} Our theory predicts that the second phase is an incommensurate SDW rather than a nonmagnetic one. However, the proposed mechanism of phase separation can, in general, be consistent with the observations reported in Ref.~\onlinecite{PSexp1}.
We found that the thermodynamic potentials of the incommensurate SDW and the metastable paramagnetic phases are very close to each other in the doping range $x>x_2$. The incommensurate SDW phase can be destroyed by an additional reason not taken into account in our model, e.g., by disorder. In this case, the phase separation might occur between the commensurate SDW and the paramagnetic phases. In addition, the incommensurate SDW order parameter may be difficult to detect due to its weakness.

The geometry of the emergent inhomogeneities and their characteristic sizes are beyond the scope of the present study. The electron concentrations in separated phases are different; hence, the inhomogeneities are charged and one should take into consideration the electrostatic contribution to the total energy. The characteristic sizes of the inhomogeneities are controlled by the interplay between the long-range Coulomb interaction and the energy of the surface between the phases. In the simplest case, the
structure of the inhomogeneous state corresponds to the droplets of one phase embedded in the matrix of another phase. However, depending on the properties of the system, other geometries are possible, such as alternating layers of different phases, stripes,
etc.~\cite{Coulomb_refs} When disorder is present in the sample, it also affects the structure of the inhomogeneous phase.

In our study we chose the order parameter $\Delta$, Eq.~(\ref{DeltaQ}). In the literature, a different order parameter is also discussed.~\cite{tokatly,gorkov_teit_prb2010} This order parameter is not homogeneous: SDW gap experiences periodic
modulations in real space. When the state with such an order parameter is doped, the extra charges go to the places where the gap
locally vanishes.
The latter type of order may be more stable than Eq.~(\ref{DeltaQ}). However, for several reasons we decided to avoid such an option.
Specifically, analytical calculations with inhomogeneous gaps become very complicated. Further, the choice of the order parameter affects somewhat the phase diagram and, in particular, the region of the phase separation; however, the inhomogeneous region does not disappear. In addition, we must remember that the relative stability of different order parameters is likely a non-universal quantity, which depends on a variety of microscopic parameters (e.g., details of the band structure, interaction, disorder). Therefore, the type of suitable order parameter cannot be deduced without input from experiments.

It follows from the phase diagram in Fig.~\ref{FigPhDiag} that the smaller effective ellipticity parameter $\bar{\alpha}$, the larger the region of the phase separation. The SDW gap $\Delta_0$ increases with increasing coupling potential $V_1$. Therefore, a stronger coupling is more favorable for phase separation since $\bar{\alpha}\propto\alpha/\Delta_0$ [see Eq.~\eqref{alpha}].

Our mean-field approach is not applicable in the limit of strong coupling, where the use of Hubbard-like models is more appropriate. The phase separation in such models is a common
phenomenon~\cite{Dagbook,Nagbook,KaKuUFN2001,LittlwNature2005,
DagottoNJP2005,OvchinUFN2009,KugelPRL2005,DagottoScience2005,SboychaPRB2007}.
Thus, we expect that the existence of phase separation in our model is not an exclusive feature of the weak-coupling regime.

The model studied here predicts an incommensurate SDW phase for both
electron and hole doping in the range of dopant concentrations scaled by the parameter $x_0$, Eq.~\eqref{defs1}. From the latter equation we conclude that $x_0\ll 1$ if the weak-coupling condition, Eq.~(\ref{limitV}), is met.
Thus, we predict the existence of the incommensurate SDW order for small doping, $x\ll 1$.

The incommensurate SDW phase is characterized by the vector
$\mathbf{q}=\mathbf{Q}-\mathbf{Q}_0$. Our calculations show that there are only two possible equilibrium directions of $\mathbf{q}$: it can be either parallel, or perpendicular to $\mathbf{Q}_0$, depending on the type of doping and the sign of the ellipticity parameter $\alpha$ [see Eqs.~\eqref{Qdir1} and~\eqref{Qdir2}].
It is clear, however, that both the magnitude and direction of $\mathbf{q}$ is sensitive to the shape of the Fermi surface, which is simplified in the present calculations. In real materials, the shape of the hole pockets deviates from perfect circles. Moreover, the spectrum of the hole and electron bands depend on the transverse momentum, $k_z$, which is completely neglected in the model considered here. In particular, the electron bands have corrugated
structure~\cite{GraserEll1,BrouetEll2}, that is, the major axis of the ellipses are rotated by $90^{\circ}$ when $k_z$ varies from $0$ to $\pi$. Nevertheless, we believe that the model studied here captures the main features of the incommensurate SDW state in pnictides.

Indeed, the observation of the incommensurate SDW phase with $\mathbf{q}$ perpendicular to $\mathbf{Q}_0$ in the electron doped
Ba(Fe$_{1-x}$Co$_x$)$_2$As$_2$ was recently reported in Ref.~\onlinecite{PrattICSDWed}. The measured value of $|\mathbf{q}|$ was about $0.02$--$0.03$ for the concentration range $0.056<x<0.06$.
Such values of $x$ and $\mathbf{q}$, as well as the direction of
$\mathbf{q}$ (corresponding to $\alpha<0$), are consistent with our theory.

The short-range incommensurate SDW phase was described in
Ref.~\onlinecite{LuoSRICed} for the electron doped
BaFe$_{2-x}$Ni$_x$As$_2$. In general, one must be cautious interpreting this experiment using our model, since the observed short-range SDW correlations do not correspond to our long-range SDW order. However, we note that the measured vector $\mathbf{q}$
was perpendicular to $\mathbf{Q}_0$, which is also consistent with a negative $\alpha$.

We found no experimental work reporting the observation of the
incommensurate SDW phase in the hole-doped pnictides. However,
double-peaked spin fluctuations at $\mathbf{Q}=\mathbf{Q}_0\pm\mathbf{q}$
have been observed~\cite{LeeICSFhd,CastellanICSEhd}
in the hole-doped Ba$_{1-x}$K$_x$Fe$_2$As$_2$
compound in a wide doping range. In these
measurements~\cite{LeeICSFhd,CastellanICSEhd}
the vector $\mathbf{q}$ was found to be parallel to
$\mathbf{Q}_0$, which, again, corresponds to $\alpha<0$ in our model.

Note that, in general, all electron and hole parts of the Fermi surface interact with each other. Each $i$th pair of these interacting electron-hole surfaces are characterized by the nesting vector $Q_{i}$, coupling constant $V_i$, and ``de-nesting'' parameter $\alpha_i$. However, the $i$th interaction contributes to the SDW order only if $V_i$ exceeds some critical value (see Section~\ref{results}). All other charge carriers do not contribute to the ``magnetic'' interaction and form a reservoir. It is rather quite probable that among the various iron pnictides there exist systems with such reservoirs. However, the existence of the reservoir is not necessary for the nucleation of the incommensurate AFM order or for phase separation.

We limit our consideration to only one type of interaction. Even this simple case corresponds to the experimentally-observed SDW symmetry both for commensurate and incommensurate phases. Also, ``switching on'' additional interactions may be necessary in the future, if the incommensurate AFM ordering with different symmetry would be observed. However, let us emphasize that the qualitative results of our work remain unchanged.

\section{Conclusions} \label{Concl}

We considered a model with imperfect nesting of the Fermi surface suitable for the description of iron pnictides. We show that an incommensurate SDW phase arises at finite doping. We demonstrate that two spin configurations can arise in the system depending on the model parameters. It was shown that the homogeneous state is unstable toward phase separation into commensurate and incommensurate SDW phases in a specific doping range. These results are in qualitative agreement with the recent experimental observation of the incommensurate SDW order and phase separation in doped superconducting pnictides.

The main achievement of this paper is the demonstration that a simple model approximating the Fermi surface of pnictides implies the existence of electronic phase separation even in the weak-coupling regime, that is, in the absence of strong electron correlations. This is an important finding for the interpretation of the experimental data on phase inhomogeneity of iron pnictides: it proves that a purely electronic model with moderate interaction is sufficient to explain the observed inhomogeneities.

There are several features of pnictides which we incorporate into our approach. Let us briefly recall them.

First, we need a Fermi surface with sufficient nesting (poor nesting implies no phase separation). The ARPES data~\cite{RichardRPrPh201}support the assumption that at least some sheets of the Fermi surface nest adequately.

Second, the interaction between electrons in the nested bands must not be too weak: the ground state of the parent compound should be the homogeneous SDW state. There is plenty of experimental evidence that a broad class of iron pnictides are in such a state at zero doping. However, to make our Hamiltonian analytically tractable, we discarded all interaction constants except one, $V_1$. Further, $V_1$ was assumed to be momentum-independent.

Third, following Rice~\cite{RicePRB70}, we included non-magnetic (``reservoir") bands into our model. This is a simple way to account for those sheets of the Fermi surface which do not nest with some other sheets. The Fermi surface pockets, which may serve as the reservoir, are seen by ARPES (like ``propellers'', see, e.g.  Ref.~\onlinecite{BorisenkoJPSJ2011}). In addition, the finite conductivity of pnictides even in the undoped SDW state may be easily explained by non-magnetic bands (although, other explanations are also possible).

Clearly, our model, being quite simple and generic, cannot predict whether a particular material exhibits phase separation. One can attempt devising a more elaborate model. For example, instead of a single coupling constant $V_1$, a set of spin-dependent couplings
$V_{\alpha \beta}^{\sigma \sigma'}$, which describe the interaction of electrons in the band $\alpha$ and the band $\beta$, may be introduced. Other refinements, e.g., 3D structure of the material, orbital content of the Fermi surface states~\cite{ScalapinoPRB2010,Suzuki2011} (the latter introduces a pronounced momentum dependence of the interaction), are possible as well.

Yet, such a detailed investigation can be counterproductive. Indeed, our analysis clearly shows that the phase separation is a non-universal feature of the model. That is, its presence depends on the parameters of the Hamiltonian. It is very likely that a study of a a more complex model, while being quite costly in terms of effort, will bring up the same conclusion about the non-universality of phase separation. Thus, in the situation where accurate knowledge of the microscopic parameters is absent, one would not be able to reliably establish the presence of phase separation for a given material. Keeping these circumstances in mind, we emphasize that the main purpose of our study is to introduce the mechanism of phase separation in iron pnictides. However, the problem regarding the instability of the homogeneous state for a particular material has to be solved on an individual basis by the analysis of the specific feature of its electronic structure.

\section*{Acknowledgments}

This work was partially supported by the ARO, RIKEN iTHES Project,
MURI Center for Dynamic Magneto-Optics, JSPS-RFBR contract no. 12-02-92100, Grant-in-Aid for Scientific Research (S), MEXT Kakenhi on Quantum Cybernetics, the JSPS via its FIRST program, and by the Russian Foundation for Basic Research (projects 11-02-00708, 11-02-00741, and 12-02-00339). A.O.S. acknowledges support from the RFBR project 12-02-31400 and the Dynasty Foundation.

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    cfsetispeed(&options, B9600);
    cfsetospeed(&options, B9600);
    options.c_cflag &= ~CSIZE;
    options.c_cflag |= CS8;
    options.c_oflag &= ~OPOST; //raw output

    /*
     * Enable the receiver and set local mode...
     */

    options.c_cflag |= (CLOCAL | CREAD);

    /*
     * Set the new options for the port...
     */

    tcsetattr(fd, TCSANOW, &options);
    if(tcsetattr(fd, TCSAFLUSH, &options) < 0){
	perror("init_serialport: Couldn't set term attributes");
    }
    unsigned char data;
    data = 0x31;

    int n = write(fd, &data, 8);
    if (n < 0)
      fputs("write() of 8 bytes failed!\n", stderr);

    close(fd);

}

redpajama_set_name: RedPajamaGithub


Please visit regularly to learn about new events and promotions.
Check out these upcoming events. Please contact Carly Manino at maninoc@natfuel.com to suggest your own.
Old-school fun with popular board, card and parlor games from the late-1800s and early-1900s. A selection of craft beers will also be available. Tuesday from 5:30 - 8 p.m.
On the second Sunday of each month, museum admission for the entire family is just $5 and includes an array of programming. 10 a.m. - 5 p.m.
Over 50 regional artists with unique jewelry, prints, pottery and more. Fri: Noon- 8 p.m.; Sat: 10 a.m. - 5 p.m.
Don your finest hat and enjoy a traditional three course tea complete with scones, strawberries, elegant little cakes and listen to Platters Chocolate Factory about the fine art of chocolate making. 2 - 4 p.m.
Fairy-themed crafts and activities, magic shows, balloon animals, music, a scavenger hunt and more. 10 a.m. - 4:30 p.m.
Enjoy the beautiful cherry blossoms and many events taking place.
To benefit Ten Lives Club Cat Adoption Group. Meal includes unlimited pancakes, topping bar, sausage links, coffee, tea or juice. Raffles, 50/50 and more.
* For more information, please contact Carly Manino, Corporate Communications, 814-871-8199 or maninoc@natfuel.com.


A new update for SocketTools is available for download. Version 8.0.8010.1864 was released on December 10, 2013. This is a complete product release that incorporates fixes from the previous general release, as well as all subsequent hotfixes.


text:
Vibrant Treasures: Botanical Illustrations from the 16th to 20th Centuries: Pierre-Joseph Redouté
Les roses, par P.J. Redouté, avec le texte par Cl. Ant. Thory. Paris, Imprimerie de Firmin Didot, 1817-24. Pierre Joseph Redouté, 1759-1840. Antwerp: Belgium, De Schutter S.A., 1974.
Pierre-Joseph Redouté learned painting from his father, but left home at age 13 to train in Liège. In the Netherlands he studied the botanical works of Jan van Huysum and Rachel Ruysch, leaning how to illustrate the individual flowers with grace and precision, which was what his later patrons demanded for scientific purposes, rather than elaborate flower-pieces intended purely for aesthetic pleasure. In 1782 he moved to Paris and furthered his knowledge with engraving while painting the flowers in the Royal gardens. He eventually came to the attention of Empress Josephine Bonaparte and for whom he painted his famous wok, Les Roses. After her death Redouté fell on hard times and in 1840, died of a cerebral hemorrhage. [Stern, William. Redouté, Pierre-Joseph. Oxford Art Online / Grove Art Online - Biographies. Accessed March 8, 2011. Michigan State University Libraries.]
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Next: Covers - Beauty inside and out >>

redpajama_set_name: RedPajamaCommonCrawl


text:
1997 WK13 (asteroide 37796) é um asteroide da cintura principal. Possui uma excentricidade de 0.15703640 e uma inclinação de 5.01535º.

Este asteroide foi descoberto no dia 24 de novembro de 1997 por Yoshisada Shimizu e Takeshi Urata em Nachi-Katsuura.

Ver também
 Lista de asteroides
 Asteroide da cintura principal

Ligações externas

Asteroides da cintura principal
Objetos astronômicos descobertos em 1997

redpajama_set_name: RedPajamaWikipedia


text:
WikiMili
The Custard Boys
This article needs additional citations for verification . Please help improve this article by adding citations to reliable sources. Unsourced material may be challenged and removed.
Find sources: "The Custard Boys" – news · newspapers · books · scholar · JSTOR (December 2009) ( Learn how and when to remove this template message )
First edition (publ. Rupert Hart-Davis)
The Custard Boys is a 1960 British novel by John Rae, focusing on the lives of children in a small village in World War II Norfolk [1] dealing with an influx of war refugees. It is sometimes compared[ by whom? ] to Lord of the Flies , and was adapted to make the film Reach for Glory in 1962 (which was passed with an 'X' certificate at the time by the British Board of Film Censors), and again for a second film carrying the original name in 1979, directed by Colin Finbow.
Karel Reisz was a Czech-born British filmmaker, one of the pioneers of the new realist strain in British cinema during the 1950s and 1960s. Two of the best-known films he directed are Saturday Night and Sunday Morning (1960), a classic of kitchen sink realism, and the romantic period drama The French Lieutenant's Woman (1981).
Bird's Custard is the brand name for the original powdered, egg-free imitation custard powder, now owned by Premier Foods. Custard powder and instant custard powder are the generic product names for similar and competing products. The product is a powder, based on cornflour, which thickens to form a custard-like sauce when mixed with milk and heated.
Albert Gordon MacRae was an American actor, singer and radio/television host who appeared in the film versions of two Rodgers and Hammerstein musicals Oklahoma! (1955) and Carousel (1956) and who played the leading man opposite Doris Day in On Moonlight Bay (1951) and sequel By The Light of the Silvery Moon (1953).
A heartbeat is one cardiac cycle of the heart.
Brian Gibson was an English film director.
William Thomson Hay was an English comedian who wrote and acted in a schoolmaster sketch that later transferred to the screen, where he also played other authority figures with comic failings. His film Oh, Mr. Porter! (1937), made by Gainsborough Pictures, is often cited as the supreme British-produced film-comedy, and in 1938 he was the third highest-grossing star in the UK. Many comedians have acknowledged him as a major influence. Hay was also a keen amateur astronomer.
if.... is a 1968 British satirical drama film produced and directed by Lindsay Anderson, and starring Malcolm McDowell as Mick Travis, and also starring Richard Warwick, Christine Noonan, David Wood, and Robert Swann. A satire of English public school life, the film follows a group of pupils who stage a savage insurrection at a boys' boarding school. The film was the subject of controversy at the time of its release, receiving an X certificate for its depictions of violence.
A road movie is a film genre in which the main characters leave home on a road trip, typically altering the perspective from their everyday lives. Road movies often depict travel in the hinterlands, with the films exploring the theme of alienation and examining the tensions and issues of the cultural identity of a nation or historical period; this is all often enmeshed in a mood of actual or potential menace, lawlessness, and violence, a "distinctly existential air" and is populated by restless, "frustrated, often desperate characters". The setting includes not just the close confines of the car as it moves on highways and roads, but also booths in diners and rooms in roadside motels, all of which helps to create intimacy and tension between the characters. Road movies tend to focus on the theme of masculinity, some type of rebellion, car culture, and self-discovery. The core theme of road movies is "rebellion against conservative social norms".
Tudor Grange Academy is a co-educational Academy and technology college located in Solihull, West Midlands, England. Formerly known as Tudor Grange Grammar School and Tudor Grange Secondary School. It was originally a boys' grammar school for around 650 boys. A girls grammar school was built later and both original schools now form part of the current academy.
Cream is a dairy product.
Tunes of Glory is a 1960 British drama film directed by Ronald Neame, based on the 1956 novel and screenplay by James Kennaway. The film is a "dark psychological drama" focusing on events in a wintry Scottish Highland regimental barracks in the period immediately following the Second World War. It stars Alec Guinness and John Mills, featuring Dennis Price, Kay Walsh, John Fraser, Duncan MacRae, Gordon Jackson and Susannah York.
Reach for Glory is a 1962 British film adaptation of John Rae's 1961 novel, The Custard Boys, directed by Philip Leacock. It received a United Nations Award.
John Rae was a British educator, author and novelist. He was headmaster of Taunton School (1966–1970) and then Head Master of Westminster School (1970–1986).
Douglas John Cardew Robinson was a British comic, whose career was rooted in the music hall and Gang Shows.
David Liam McCormack is an Australian musician and singer-songwriter. He is best known as frontman of Brisbane-based rock group Custard, and for voicing the character Bandit in the animated children's series Bluey.
Camping coaches were holiday accommodation offered by many railway companies in the United Kingdom and the Republic of Ireland from the 1930s. The coaches were old passenger vehicles no longer suitable for use in trains, which were converted to provide sleeping and living space at static locations.
Sir Morien Bedford Morgan CB FRS, was a noted Welsh aeronautical engineer, sometimes known as "the Father of Concorde". He spent most of his career at the Royal Aircraft Establishment (RAE), before moving to Whitehall for ten years as the Controller of Aircraft within the Ministry of Aviation. He spent the last years of his life as master of Downing College, Cambridge.
A Poke in the Eye is the title of the first show in what later became the Secret Policeman's Ball series of benefit shows for human rights organization Amnesty International, although it pre-dated by three years the first show to bear that name. The film of the show was titled Pleasure at Her Majesty's which is sometimes mistakenly thought to be the title of the actual benefit show.
Harriet Frank Jr. was an American screenwriter and producer. Working with her husband Irving Ravetch, Frank received many awards during her career, including the New York Film Critics Circle Awards and the Writers Guild of America Award, and several nominations.
Starlift is a 1951 American musical film released by Warner Bros. in directed by Roy Del Ruth and written by Karl Lamb and John D. Klorer. The film stars Janice Rule, Dick Wesson, Ron Hagerthy and Ruth Roman. Starlift was made during the beginning of the Korean War and centers on an Air Force flyer's wish to meet a film star, and her fellow stars' efforts to perform for injured men at the air force base.
↑ "068. RAE (John) The Custard Boys, London, Rupert Hart-Davis, 1960".
This article about a World War II novel first published in the 1960s is a stub. You can help Wikipedia by expanding it.
See guidelines for writing about novels. Further suggestions might be found on the article's talk page.
This page is based on this Wikipedia article


text:
Creating the Perfect Super Bowl Ad
29 Jan 2013Research & Ideas
by Kim Girard
Professor Thales S. Teixeira says TV viewers lose purchasing interest when ads get too caught up in entertainment. His advice for the perfect pitch: tie together a good story and a compelling brand.
Super Bowl Sunday is sure to bring the usual barrage of clever soda, beer, and car ads featuring everyone from Vegas showgirls selling Coca-Cola to pop celebrity Psy charming us to buy pistachios Gangnam-style.
But at a whopping $3.7 million per 30-second spot, perhaps it's time for advertisers to question whether ads, including the over-the-top Super Bowl spots, have become too entertaining, says Thales S. Teixeira, an assistant professor in the Marketing unit at Harvard Business School.
In upcoming research, Why, When and How Much to Entertain Consumers in Advertisements? A Web-based Facial Tracking Study, Teixeira and colleagues question whether advertisers are striking the right balance between entertaining and promoting their brands. Could companies entertain less and get consumers to buy more?
Teixeira's research offers insight to modern-day Don Drapers, perhaps showing advertisers ways to spend ad dollars more shrewdly.
"They need to use entertainment judiciously," he says. "It's very expensive. They have to ask: Why do we need to entertain so much?"
During an interview in his office, Teixeira, who has analyzed why ads go viral, reviews a quick history of the use of entertainment in advertising. In 1963, British advertising pioneer David Ogilvy, in his book Confessions of an Advertising Man, argued that ads should be all business, selling products by informing consumers rather than entertaining them. A few Ogilvy classic lines that reflected the information-only mantra included: "At 60 miles an hour the loudest noise in the new Rolls-Royce comes from the electric clock," and the straightforward "man in the Hathaway shirt."
By 1985, Ogilvy changed his tune, agreeing that a little fun is fine, Teixeira says. (Proof of that attitude is clear in Ogilvy's award-winning Sprite Shower campaign, which features men, women, and children splashing under Sprite-logo showers on a Brazilian beach.)
Teixeira does not argue that entertainment—fun content, creative stories, upbeat music—isn't used effectively in ads. But many companies don't use entertainment to their best advantage. To find out what works, Teixeira went directly to consumers, partnering with the MIT Media Lab and Waltham, MA-based Affectiva, which has developed the first online facial tracking system for testing advertising.
The research team worked with 275 randomly selected people, showing them a sample of 82 ads for 30 brands in their homes or workplaces.
The research relied on webcams that track visible changes on a person's face as they watch an ad, responding to funny, or amusing content. The software detects the slightest deviations of facial movement in the eyes, cheeks, and mouth, tracking whether a person smiles, grins, or breaks out in laughter. Continuously measuring smile responses and facial cues allowed the team to determine a person's interest in viewing the ad and their intent to purchase the brand.
The ad watchers were monitored remotely, a setup intended to be unobtrusive and provide a more natural out-of-lab environment, Teixeira says. Also, participants were allowed to skip through commercials they didn't want to watch. They viewed ads in three product categories: confectionary (Skittles, Snickers, M&Ms, and others), beverage (including Coke, Pepsi, Mountain Dew), and alcohol (Budweiser, Dos Equis, Captain Morgan, etc.). The team built a model relating the amount of entertainment a participant experienced with both their viewing interest and their intent to purchase a brand.
Entertaining Only So Far
Results determined that the level of entertainment increases a viewer's interest in watching an ad. After a certain amount, however, that persuasiveness starts to decrease and advertisers lose the link to the brand and the power to influence buying. In other words, too much entertainment can actually reduce viewers' desire to buy.
These observations can help companies strategize. Ideally, an advertiser that seeks acquiring customers should entertain initially to capture attention, but also introduce the brand early on, and follow up with a moderate amount of entertainment, Teixeira says.
"If you want to persuade consumers as do Pepsi, Skittles, and Coke, it's about getting people to associate your brand with fun," he says. "But you have to show the brand and then entertain. That's when the conditioning occurs. The other way around—entertain then brand—doesn't work as well."
Three Pepsi MAX ads from Super Bowl 2011 viewed in Teixeira's study show that Pepsi does not always maximize its entertainment/purchase intent balance, he says.
Pepsi MAX's Torpedo Cooler ad (also known as "Catch"), for example, featuring a beer can-shooting ice chest, scored low (13th percentile) on both entertaining and purchase intent, according to Teixeira's facial tracking study. Pepsi Max's First Date, an ad portraying gender differences of a couple on their first date, fared a bit better. Viewers found it extremely entertaining—as she judges him as possible marriage material, he is thinking of the bedroom rather than the altar—and 81 percent viewed it until the end . Yet it fell short for purchasing intent in the low 22nd percentile score. "First Date has too much entertainment," Teixeira says. "People view but are not very persuaded by this ad."
The most successful Pepsi MAX effort, Love Hurts, features a woman trying to get her husband to eat better by snatching a burger from his mouth and kicking him under the dinner table when he orders fries. Sitting on a park bench, the couple agree that drinking Pepsi MAX is OK—until a pretty jogger waves at the husband. The wife throws her can at her hubby, missing him and hitting the jogger instead. The viewers found the ad moderately entertaining yet it generated a high purchasing intent in the 77th percentile, "striking a balance between entertaining viewers to grab their attention and maximizing the brand's persuasiveness," Teixeira says.
Importantly, he adds, all three ads had exactly the same amount of information content on Pepsi MAX.
Advertisers should pay attention to that balance, taking into account not only how soon into the ad that the brand is presented, but also how the branding aligns with the entertainment. Many advertisers choose to show the brand name at the end, when it's too late. Others entertain too much, failing to connect the entertainment parts effectively to the brand.
If the balance is off, Teixeira says, entertainment competes with brand awareness and reduces purchase intent. But when entertainment follows the brand introduction a cooperating effect is created, which increases both interest in the brand and intent to buy. The idea is aligned with Pavlov's theory of classical conditioning, he says. If you show somebody a stimulus (the brand) and then you show qualities (fun) right after, people better associate those two things.
Finally, advertisers should consider the stage of the consumer purchasing cycle they aim to impact: do they want to create awareness, interest, or spark a purchase? If the goal is to simply create a buzz, then entertain as much as possible—as many advertisers will do during the Super Bowl. If the intent is to convert consumer interest to purchases it might be time to reduce the volume on talking babies and dancing monkeys and up the attention on brand.
Teixeira is now talking with companies that are trying to connect television ad campaigns with online viral advertising. "What companies tell me is that they want to relate this research to viral advertising—to get people's attention and then to get them sharing. They want to understand how to use these media collectively, such as by spending money on the Super Bowl to get attention and then saving money by using viral ads to get engagement," he says.
In whatever medium, the trick remains the same: strike a balance that holds consumer attention optimally in both media. "If you entertain too much on TV, you're wasting an expensive opportunity to sell."
I am surprised that this article makes no reference to the power of evoking emotions and feelings in TV commercials. The importance of emotionally connecting with consumers in a way that is brand relevant whilst resonating with one's core target audience is key to building brand affinity. The correlation between TV commercials and its ability to drive purchase intent also needs to be further examined. Any good TV commercial will need to be futher bolstered by other media and - for example - breakthrough point of sale at the retail level in order to re-trigger the brand memory at the moment of purchase.
Jared Latigo
Owner, Jaredlatigo.com
I would be interested to know whether the people in the research were known to have been advocates of the brand previous the advertising being presented. I believe the we purchase more from companies we love and align with more so than we do because of ads. So it would skew the research a bit if the people had all previously believed in the company and bought from them as opposed to maybe hating what they stood for or created in general.
Good article and very interesting for sure.
Kapil Kumar Sopory
Company Secretary, SMEC(India) Private Limited
A very interesting research which focuses on the relationship between advertisements and better sales due to what and how the display takes place. We have our TV programs with regular ads. in between. Ads appear in newspapers, magazines, etc. as well.
I have always felt that an ad which primarily focuses on the product yields to better sales outcome. The more the extraneous - music, comedy, etc. - the more is the focus shifted and the product somewhat lost sight of. Hence, a fair mix is recommended.
Demand and Consumers
Media and Broadcasting


Simply stated, water is life. Some microbial organisms, for example, can exist in the complete absence of oxygen. However, no form of life can exist and function in the absence of water. It is truly the essence of life. Thus, adequate supplies of freshwater of good quality are obviously a critical requirement for human health and well-being, and economic development. Indeed, humans use freshwater for a wide range of purposes, including drinking water, irrigation, power generation, commercial and sports fisheries, recreation and transportation.
Freshwater systems also offer aesthetic pleasures, and are also of spiritual significance in some cases. Freshwater also maintains the terrestrial and aquatic ecosystems upon which humans depend for their health, well-being and livelihoods, as well as maintaining the integrity of the ecosystems that provide these services in the first place. Indeed, life as we know it would not be possible without this irreplaceable, and unfortunately easily degraded commodity.
To this end, the International Institute for Sustainable Water Resources (IISWR) was established to be an active participant in providing practical information, experience, and guidance regarding freshwater issues and the ecosystems that provide this critical resource. Its activities focus on the accurate assessment and integrated management of freshwater resources for sustaining the life-supporting ecosystem services they provide, as well as considering the scientific, social, economic and policy aspects of these activities.


What is the Tidy Garden Scheme?
The Tidy Garden Scheme is a gardening service for tenants or leaseholders who would like help looking after their garden.
Our annual service starts at £400, which equates to just under £8 per week. Customers are welcome to pay weekly by Direct Debit.
Lawn mowing - fortnightly from April to September.
Shrub pruning and weeding - monthly from October to March.
Hedge trimming - twice a year.
One-off garden projects - to bring your garden back to an easy to maintain condition.
Tree works - pruning, reduction and felling.
We can arrange a suitable instalment payment scheme for these works by Direct Debit. Please note that Introductory tenants will need to pay for one-off works in full.
The work is carried out by friendly and reliable gardeners from our partner at Continental Landscapes.
All gardeners are fully trained, qualified and work to the latest health and safety regulations.
Please note that the Tidy Garden Scheme is not available to tenants who have any debt with Wolverhampton Homes or Wolverhampton City Council or tenants who have applied to buy their home under the Right to Buy.
If you'd like to join our Tidy Garden Scheme or you'd like a quote for a one-off job, please fill in the form and we will contact you.


So, who's excited about the upcoming Spring: From the Bay to the Mountains conference? Hands? Hands?
You know my hand is raised. And I'm doubly excited about staying at the new Christiane Inn at the Clagett Center and participating in all the fun activities planned! In case you don't know what activities I'm talking about, I thought I'd do a giant ALL THINGS CONFERENCE post today to get you up to speed.
Did you see Susan's Hear ye, Hear ye! We need your legal questions post regarding how any questions you might have about contracts, structuring your business, or copyright and intellectual property can be submitted early? Conference presenter and attorney Razvan Miutescu will be answering as many as them as possible.
–EB Lewis, Caldecott winning illustrator. Ask anyone who's heard him. Don't miss the chance to be in the room with this generous, articulate, most talented, Artistrator. You'll remember why you started doing what we do in the first place.
– Heather Alexander, Agent from Pippin Properties representing both authors and illustrators will give a talk on How to Build Your Brand: For Illustrators A discussion of styles, social media, and how to focus your efforts to break into illustrating for children's books.
– Emily Feinberg, Assistant Editor, Roaring Brook Press, Using picture books as a medium, Emily will discuss the interplay between the writer and the illustrator for an entire intensive on Sunday. She's speaking on nonfiction picture books on Saturday.
– Legal Eagle Razvan E. Miutescu will introduce the key issues involved in contracts, business organization, and intellectual property/copyright. SEND YOUR QUESTIONS TO MDDEWV@SCBWI.ORG ahead of time. Raz will tailor his talk to match our areas of interest.
Sarah Maynard also sent out a message regarding the fun KIDLIT TRIVIA NIGHT she's cooked up!
Start your conference weekend with a bang! Join us on Friday at 7 pm and battle for the title of KIDLIT TRIVIA CHAMPIONS! Rounds will include topics ranging across the children's book spectrum from picture books to YA novels and their creators as well as some SCBWI trivia. Prizes will be awarded! Location at the Claggett Center to be announced.
After a day filled with craft and business, join us on Saturday night at 7 pm in Monocacy Hall for a fun community activity where we will take the often solitary task of writing and illustrating for children and make it a group effort in a game of Round Robin Story & Art. Following the game, we will move across the courtyard into the Christiane Inn for a Mix & Mingle with wine and light snacks.
These events are included with your Saturday conference registration.
Please RSVP, for one or both events, by emailing Sarah Maynard at sarahmdm@gmail.com by Tuesday, March 24.
And finally, if you have not yet registered for all this awesomeness, there's still time! Just go here but don't dally … registration closes tomorrow, March 19th!
Happy writing and drawing and I can't wait to see you at the conference!
This entry was posted in Conference Information, Interviews: Agents & Editors, Interviews: Authors, Interviews: Illustrators. Bookmark the permalink.
1 Response to All Things Conference!
Also, use the hashtag #bay2m to tweet!


Hello, I am at the hotel resting before tomorrow's race. I arrived last night but it took forever to get to the hotel because of a cab situation, and then Jaime and I went to the lobby for a drink..or drinks.
Afterwards I met up with Jaime to eat breakfast and then to go to the expo. I was not disappointed with it. There were a decent number of vendors but I told myself that I was not going to buy anything. Well, I just bought another red flower by Fellow Flowers and one of their shirts. So cute!
I got taped! I've been having some slight discomfort in my IT band so someone from KT tape helped me out.
The medals! The one on the right is for the marathon and the other one is for the half marathon.
The start line. See the Marriott sign? That is our hotel.
Off to get more rest. Just Keep Running!


text:
BBC production workers' union demand £20,000 minimum wage
Gerry Morrissey, leader of Bectu - now part of the Prospect union - said something should be done about low pay
The union representing low-paid production workers at the BBC is stepping up demands for a minimum salary of £20,000.
Bectu said it was "unjustifiable" for the corporation to focus on the earnings of those on more than £150,000 when thousands of engineers, technical and other production staff were paid a fraction of that amount.
Gerry Morrissey, leader of Bectu - now part of the Prospect union - said something should be done about low pay.
He told the Press Association: "We have had a claim in for two years for a minimum wage of £20,000 rather than the current £16,000.
"It is totally unacceptable that the BBC is prepared to pay senior management and others many times that amount.
"There should be a lot more focus on giving low-paid staff a decent living wage."
Peter Capaldi with David Bradley - the current and first Doctors (Image: BBC)
Mr Morrissey said more than 2,500 production staff were paid less than £20,000.
The BBC has revealed which of its talent are paid more than £150,000, with DJ Chris Evans topping the list with earnings of more than £2 million.
Fiona Bruce earns between £350,000 and £399,000 but fellow news host Huw Edwards is on £550,000 to £599,999.
The BBC's political editor Laura Kuenssberg is on £200,000 to £249,000, below news presenter George Alagiah (£250,000-£299,000) and Radio 4's PM host Eddie Mair (£300,000 - £349,000).
News host Sophie Raworth is on £150,000 to £199,000.
BBC Breakfast presenter Naga Munchetty is in the £150,000 to £199,999 bracket, and her colleague on the show Dan Walker, who also works on Football Focus and fronted slots from the Rio Olympics, took home between £200,000 and £249,000.
Their fellow BBC Breakfast presenters Louise Minchin and Charlie Stayt do not make the £150,000 bracket.
In sport, Match Of The Day host Gary Lineker is paid in the £1,750,000 to £1,799,999 bracket. He had earlier revealed that he had turned down higher pay offers from commercial broadcasters.
Writing on Twitter, the former England striker said he had stuck with the Beeb "because I love and value my job and BBC Sport."
BBC boss claims top-earning stars are paid at "discount" rates
But Wimbledon's Sue Barker earns between £300,000 and £349,999, behind Alan Shearer (£400,000 and £449,999).
Clare Balding is paid between £150,000 to £199,999, putting her in the same list as Jonathan Agnew, Jonathan Davies and John McEnroe.
Presenters John Inverdale and Gabby Logan are on between £200,000 and £249,000.
Radio 2 Breakfast DJ and former Top Gear host Evans earns between £2.2 million and £2,249,999.
Graham Norton is listed as between £850,000 and £899,999 - but as the list only includes cash from licence fee payers, that does not include his chat show, for which the BBC pays an independent production company, which in turn pays his salary.
Strictly Come Dancing host and Radio 2 DJ Claudia Winkleman earns between £450,000 and £499,000.
BBC star salaries revealed - with a shocking pay gap between men and women
Strictly judge Darcey Bussell earns between £150,000 and £199,999, putting her in the same band as Craig Revel Horwood.
But Bruno Toniolo, who also worked on Eurovision: You Decide, and former head judge Len Goodman earn more at £200,000 to £249,999.


Clear Input Field Value When Selected?
The trick is that all three values (I have bolded them) must be the same or else it won't work. See? That's it. Now you can try it at your website.
This entry was posted in Miscellaneous and tagged clear input field value when selected?. Bookmark the permalink.


Clémence attended on the 20th of April a new event for National Geographic's 'Genius: Picasso' Premiere where she was interviewed among her costars of the show. You can watch one full interview here.
EDIT: Added brand new production stills and promotional pictures in UHQ!
To finish off today, we added Genius videos, caps and pictures. We will upload episode 1 screencaps soon! Video Promos here, here and here.
I'm so sorry for the lack of updates everyone, but we are here to stay and will bring you a few new posts today! Clémence wore Miu Miu to the Tribeca premiere of Genius, and we bring you brand new pictures thank you to our friend James!
Clémence has joined the french campaign Fondation Des Femmes. #Maintenant On Agit means Now We Act. It is a fundraising campaign which aims to ease the access to justice for women who are victims of violence and sexual abuses and supply financial and technical means to the organisations supporting them. Plenty of committed public actors promote the program and provide their support, #MaintenantOnAgit campaign is the opportunity to offer an effective answer to those who took a legal action for sexual. Find more about this campaign here.
Clémence alongside 4 more actors will make their first steps as directors for the Adami Cannes 2018 Talents, which are celebrating 25 years. The event will take place in Cannes in May.


text:
Q: SQL pivot table query and hookup query in hierarchical format Table-1
Resource    Rank1   Rank2   Rank3   Rank4
Critical    3         3         6    12
High        8         8        12     24

Table-2
Name     Issue      SLC
RAM     Critical    Rank1
KIRAN   Critical    Rank2
BASS    High        Rank3
LOUT    Critical    Rank4
chinna  High        Rank1
lavanya Critical    Rank3
babau   High        Rank4
rani    Critical    Rank2

Expected out should
Name    Issue       SLC   values RESOURCEMISS
RAM     Critical    Rank1   3      Resource
KIRAN   Critical    Rank2   3      Resource
BASS    High        Rank3  12      Resource
LOUT    Critical    Rank4  12       Resource
chinna  High        Rank1  8      Resource
lavanya Critical    Rank3   6      Resource
babau   High        Rank4  24    Resource
rani    Critical    Rank2  3     Resource

This should not be like [RESOURCEMISS]='Resoure'

A: A somewhat ugly solution, using a correlated subquery to lookup each rank and issue:
SELECT
    Name,
    Issue,
    SLC,
    (SELECT CASE WHEN t2.SLC = 'Rank1' THEN t1.Rank1
                 WHEN t2.SLC = 'Rank2' THEN t1.Rank2
                 WHEN t2.SLC = 'Rank3' THEN t1.Rank3
                 WHEN t2.SLC = 'Rank4' THEN t1.Rank4 END
     FROM table1 t1
     WHERE t1.Resource = t2.Issue) "values"
FROM table2 t2;

Demo
I don't know what database you are actually using (MySQL or SQL Server), but it might not even matter much, given your current design.  Your schema is not normalized, and ideally the rank number should be an actual value in a column somewhere, rather than the column name itself.  It seems that @strawberry has suggested one refactor of your design which makes it much easier to proceed, using just a single inner join.

A: Consider a solution along the following lines (anything markedly different from this is frankly wasting your time):
DROP TABLE IF EXISTS table1;

CREATE TABLE table1
(resource VARCHAR(12) NOT NULL
,slc_rank INT NOT NULL
,val INT NOT NULL
,PRIMARY KEY(resource,slc_rank)
);

INSERT INTO table1 VALUES
('Critical',1,3),
('Critical',2,3),
('Critical',3,6),
('Critical',4,12),
('High',1, 8),
('High',2, 8),
('High',3,12),
('High',4,24);

DROP TABLE IF EXISTS table2;

CREATE TABLE table2
(name VARCHAR(20) NOT NULL
,resource VARCHAR(12) NOT NULL
,slc_rank INT NOT NULL
,PRIMARY KEY(name,resource,slc_rank)
);

INSERT INTO table2 VALUES
('RAM','Critical',1),
('KIRAN','Critical',2),
('BASS','High',3),
('LOUT','Critical',4),
('chinna','High',1),
('lavanya','Critical',3),
('babau','High',4),
('rani','Critical',2);

SELECT x.*
     , y.val
  FROM table2 x
  JOIN table1 y
    ON y.resource = x.resource
   AND y.slc_rank = x.slc_rank;
+---------+----------+----------+-----+
| name    | resource | slc_rank | val |
+---------+----------+----------+-----+
| babau   | High     |        4 |  24 |
| BASS    | High     |        3 |  12 |
| chinna  | High     |        1 |   8 |
| KIRAN   | Critical |        2 |   3 |
| lavanya | Critical |        3 |   6 |
| LOUT    | Critical |        4 |  12 |
| RAM     | Critical |        1 |   3 |
| rani    | Critical |        2 |   3 |
+---------+----------+----------+-----+

A: Think you could try something like this:
SELECT
    Name
    Issue
    SLC
    Values.value
FROM
    Table-2
LEFT JOIN
    (
        SELECT 'Rank1' descrip, Rank1 value FROM Table-1
        UNION ALL
        SELECT 'Rank2' descrip, Rank1 value FROM Table-1
        UNION ALL
        SELECT 'Rank3' descrip, Rank1 value FROM Table-1
        UNION ALL
        SELECT 'Rank4' descrip, Rank1 value FROM Table-1
    ) as Values
ON Values.descrip = Issue

based on Mysql Convert Column to row (Pivot table )

redpajama_set_name: RedPajamaStackExchange


Time was... is... will be... Unaware, we alternatively flow with, or resist time. We obey its imposing disciplines when we catch a plane. Times inevitable march frequently awakens distress in some with a second look in the bathroom mirror. The typical American, obviously a victim of time, roots for victory at game's end, mentally fracturing the seconds with one eye on the clock. By contrast, the Oriental waits patiently, it is in his nature to conserve and merge with time.
We perceive and comprehend earthly activity through our five senses by means of time. Literally speaking, time-sense, or lack of it, brings in, or takes us out of this world. When we are deeply engrossed in pleasurable activity, time really flies. Time travel, where one moves forward or backward on a controlled wave of time, I believe, can occur within the higher planes of life, if a high intelligence so desires, indeed it's a reachable goal living in these strata of human existence. But consciously moving oneself, others, or things physically forward or backward in time... Ah! That's another matter.
Consider "bi-location", where the mystic appears in human form at two distinct locations within a measured period of day. Again, to support the idea of time - perhaps non-time events - we have reports of "teleportation" , the instant transference of material substances through solid matter outside the scope of known physical laws.
The late western mystic, Joel Goldsmith, and others, have described experiences of "instantaneity". Joel spoke of an incident where he, himself, and with passengers in an automobile, were transported immediately from a point on the Pasadena Arroyo Seco Parkway to central Culver City, California. The entire trip, according to Joel, consumed less than five minutes, a dubious feat attainable by any speeding race-car on deserted freeways.
Instantaneity apparently comes with more frequency to those living i four-dimensional consciousness, a state of being acquired through long periods of meditation and various physical-mental disciplines (the Pyramid form seemingly accelerates psychic energies associated with higher levels of awareness). Attainment follows repeated thought desire, and emotion toward the higher state in that order, coupled with selfless dedication in its pursuit - but not always.
Rewarding instantaneity, I once had a similar experience - not completely of this world. For years I've been seeking a logical explanation - in particular to the first of three such happenings beginning in 1971. Later investigation revealed the surprising frequency of instantaneous occurrences encountered by others.
A lightening-like twenty minute auto trip on a Saturday night from Laguna Beach to Mira Loma, California normally would have required at least forty-five minutes. At first, I thought my watch had stopped, it hadn't. I even considered the possibility of some monstrous joke, with someone conspiring at either end to set watches and clocks ( including my own ), ahead or behind, as the case may have been. But of course, that wasn't so and I can only describe some of the latter part of the trip as lying outside the region of conscious memory.
It took more than two years of persistent study to partially find out the how and why of this strange episode living in and out of time. Instantaneity (as I later came to understand it) altered time during the brief excursion along the road - where I was suddenly vacuumed into a peculiar time frame, a warp as it were, where the normal progression of moments, past, present and future, all joined to become one unit.
Unlike cross-country "trance" driving, where one loses time-sense; then, later, in studying a road map, finds one has driven fifty miles further than realized - failing to recall, even, one or more small towns driven through en route. And where one observes one's watch and dashboard clock registering the actual time lapsed... No, with instantaneity measured speed, travel distance and clock-time never jibe. My body transporting vehicle must have been momentarily propelled out of earths ordinary succession of moments and into the timeless sphere of another dimension.


Pain is a common complaint in the medical practice. It is defined as an unpleasant sensory and emotional experience associated with actual or potential tissue damage; or described in terms of such damage. It is a subjective measurement. Description of the pain includes eight characteristics namely the site, character, severity, radiation, temporal relationship, associated symptoms, aggravating and relieving factors. Depending on the temporal relationship of the pain it is further classified as acute and chronic pain, and this article points out the differences between these two terms.
The pain, which persists past the time of healing or for more than about 3 months, is called the chronic pain. Sometimes acute pain can become chronic if it persists after 10-14 days of the onset.
Pain pathway comprises afferent and efferent fibers where C fibers are responsible for carrying the chronic, so called visceral pain.
Most of the time chronic pain is associated with the psychological disturbances. Clinically a patient with chronic pain commonly presents with the limitation of social, mental and psychological activities, subdued, sad or sleepy in his facial expressions or with vegetative symptoms such as sleep disturbances, irritability or with loss of appetite.
Chronic pain is poorly localized, and it is dull and vague in its character. It is often periodic and builds peaks. The pain may be referred to other areas associated with internal factors and often associated with nausea, vomiting and ill feeling.
Management includes non pharmacological and pharmacological therapies.
Acute pain, which is also known as somatic pain, is of sudden onset.
Large myelinated A delta fibers are responsible for carrying the acute pain.
Clinically a patient with acute pain presents with increased autonomic activity, which is manifested as tachycardia, hypertension, sweating, reduced intestinal mortality, increased rate and reduced depth of respiration and with facial grimaces. Acute pain can also be exacerbated by psychological factors such as sleeplessness, anxiety, depression or anger. As mentioned above acute pain can become chronic or it can be superimposed on chronic pain.
Acute pain is well localized, and the radiation may follow the distribution of somatic nerves. It is sharp and defined in its character, and it hurts where the stimulus is associated with the external factors. Acute pain is often a constant pain and nausea and vomiting are uncommon unless it is of deep somatic pain to bone involvement.
Management of acute pain includes the drug therapy; mainly opioids and non steroidal anti inflammatory drugs and the regional blockers.
• While acute pain is of sudden onset and resolves within a short time, chronic pain is of insidious onset and persists past the time of healing or for more than about 3 months.
• In acute pain, the site is well localized, but chronic pain is poorly localized.
• Radiation of the acute pain may follow the distribution of somatic nerve, but radiation of chronic pain is diffuse.
• Acute pain is sharp and defined in its character, but chronic pain is dull and vague.
• Acute pain is often constant, but chronic pain is often periodic and builds peaks.
• Chronic pain is often associated with nausea, vomiting and ill feeling but acute pain is usually not.