text:
\section{Introduction}

Clouds of cold bosonic atoms exhibit a variety of quantal
effects on the mesoscopic scale. The initial developments
dealt with dilute weakly interacting gases, and most of the
experimental results could be explained by means of the
Gross-Pitaevskii (GP)
equation~\cite{Leggett01,pethick2002,pitaevski2003,gatiobert2007}.
In recent years, the possibility of controlling the atom-atom
scattering length through Feshbach resonances opened a broad
range of possibilities for cold atomic clouds, connecting the
physics of cold atoms to the physics of strongly interacting
systems; for recent reviews see~\cite{Lewen2007,bloch-rmp}.

Here we consider Bosonic Josephson junctions (BJJ) as our
benchmark. The GP approach successfully predicted the existence
of Josephson tunneling phenomena in clouds of bosonic
atoms confined in a double-well potential~\cite{Smerzi97,Raghavan99}.
The physics of BJJ can be well understood by further assuming
a two-mode description of the condensate wave function, a
simplification which correctly explains the existence of
self-trapped states in BJJ when the non-linear interaction
strength is increased~\cite{Smerzi97}. This prediction was
later confirmed experimentally~\cite{Albiez05}. Very recently,
most of the semiclassical predictions of this two-mode
approach, dealing with the Rabi to Josephson transition,
have been confirmed in an internal Josephson experiment~\cite{tilman10}.

However, it is worth noting that the regime of applicability
of the quantized two mode approximation can extend further:
Recent examples are the experiments on BJJ, the production
of number squeezed states, and a non-linear atom
interferometer~\cite{esteve08,gross10}. These phenomena are
beyond GP, as they involve entangled states of the atoms in
the cloud, but can, however, be explained by a requantization
of the two-mode equations of GP, the Bose-Hubbard
model~\cite{Milburn97}. Thus, they are still two-mode physics,
albeit requantized.

We scrutinize here the predictions of the GP equation
when the non-linear interaction term is increased to set
the condensate beyond the limits of validity of the usual
two-mode truncation. Our focus is on a specific dynamical
configuration, the evolution of the BEC when initially
the majority of the atoms are located in one of the
wells. By studying the oscillations of the population
imbalance we find that increasing the non-linear coupling
the amplitude starts to increase, departing from the usual
self-trapping behavior. We demonstrate that this dynamics
can still be explained in terms of a few modes of the
effective GP potential, but that now it is the variation
of coupling between the second and third modes that
successfully explains the GP results.

The manuscript is organized as follows, first in section~\ref{sec1}
the time dependent GP equation and the usual
two-mode equations are presented, in section~\ref{sec2} we
present the results obtained increasing the number
of atoms, comparing the full time-dependent solutions
of the GP equations with two-mode predictions. Section~\ref{sec4}
contains a summary and conclusions.

\section{Theoretical description}
\label{sec1}

For definiteness, we consider a dilute gas of $N$ atoms
at zero temperature and perform our study in 1D.
Thus our results should be relevant to cigar-shaped
quasi-1D experiments. Setting $\hbar=m=1$ the evolution
is described by the GP equation,
\begin{equation}
\imath \frac {\partial}{\partial t} \psi(x,t)
=  -\frac {1}{2} \frac {\partial^2}{\partial x^2} \psi(x,t)
+  V_{\rm eff}[\psi(x,t)] \psi(x,t)\,.
\label{eq:gp}
\end{equation}
$\psi(x,t)$ is normalized to 1, and the time dependent
effective potential is
$V_{\rm eff}[\psi(x,t)]=V(x)+ \lambda_0 N |\psi(x,t)|^2\,.$
The relevant parameter in the GP equation is
$g_{1D}\equiv  \lambda_0 N$, which sets the importance
of the non-linear term. In this analysis we consider a
repulsive interaction, $\lambda_0 > 0$. Different values
of $N$ and $\lambda_0$ produce exactly the same GP evolution
provided $\lambda_0 N$ is kept fixed. The confining double-well
potential, $V(x)$, is generated by $V_{\pm} (x)= (x\pm 2)^2 $
connected by $V_p(x)=3 (1-x^2)$ in the interval $\mid x\mid \le 0.5$.

Eq.~(\ref{eq:gp}) is expected to provide accurate results
for large enough number of atoms. The recent calculations
reported in Ref.~\cite{ceder2009} show how the
exact 1D dynamics of the BJJ approaches the GP predictions as
the number of atoms is increased~\footnote{The authors of
Ref.~\cite{ceder2009} consider up to 100 atoms, far away from
the number of atoms considered in this work and in the experimental set up
of Ref.~\cite{Albiez05}, $N>1000$.}.

The standard two-mode
approximation~\cite{Smerzi97,Raghavan99,Ananikian2006}
is obtained by making the following ansatz for the wave
function:
$\Psi(x,t) = \Phi_L(x) \sqrt{N_L(t)} e^{\imath \phi_L(t)}
+ \Phi_R(x) \sqrt{N_R(t)} e^{\imath \phi_R(t)}$.
The left and
right modes ($\Phi_{L(R)}=1/\sqrt{2}(\Phi_1\pm \Phi_2)$)
are constructed from the ground state, $\Phi_1$, and the
first excited state, $\Phi_2$, of the stationary GP equation. These
in turn are obtained numerically by an imaginary time
evolution method. Then a set of equations relating the
population imbalance, $z(t)=(N_L(t)-N_R(t))/N$ and the
phase difference, $\delta\phi(t)=\phi_R(t)-\phi_L(t)$ are
easily derived~\footnote{These are the so-called standard
two mode equations. Similar conclusions are obtained by
using the improved two-mode equations of Ref.~\cite{Ananikian2006}
for the same double-well.},
\begin{eqnarray}
\dot{z}(t)&=& - 2{\cal K}\sqrt{1-z^2(t)} \,\sin {\delta\phi(t)}
\label{s2m} \\
\dot{\delta\phi(t)}&=&{ N U  z(t)}
+2{\cal K} {z(t)\over \sqrt{1-z^2(t)}} \, \cos{\delta\phi(t)}\,,\nonumber
\end{eqnarray}
where
\begin{eqnarray}
U &=&\lambda_0 \int\! dx \,\Phi_{L}^4 \nonumber \\
{\cal K}&=&  -\int d x
\left( (1/2)\partial_x\Phi_{L} \partial_x\Phi_{R}+\Phi_{L}
\,V(x)\,\Phi_{R}\right)
\end{eqnarray}
and  integrals involving mixed products of $\Phi_L \Phi_R$ of order larger
than one are neglected. Some authors characterize
the dynamics with the variable $\Lambda=N U /(2{\cal K})$.
In our double-well we find, using the modes computed at
$g_{1D}=0$, ${\cal K}=7.9\times10^{-3}$ and $U/\lambda_0=0.47$,
which gives $\Lambda=29.7 \lambda_0 N$. The critical value
of $\Lambda_c$ to have self-trapping within this two mode
approximation~\cite{Smerzi97}, for ($z(0)=1$,
$\delta\phi(0)=0$), is $\Lambda_c=2$, which translates
into a critical value for $g_{1D}^{(1,2)}=0.067$, where the
superscript $(1,2)$ refers to the states involved in the
tunneling dynamics.

\begin{figure}[t]
\includegraphics[width=0.98\columnwidth, angle=0, clip=true]{fig1.eps}
\caption[]{Maximum amplitude of the imbalance oscillations,
$z_{\rm  max}-z_{\rm min}$ computed with GP (circles)
as a function of $g_{1D}$. The solid (red) line
is the classical two-mode prediction using Eqs.~(\ref{s2m}).
The dashed (blue) line is a two-mode calculation
using modes (2,3) as explained in the text.
\label{fig:fig1}}
\end{figure}

\section{Results}
\label{sec2}

\begin{figure}[t]
\includegraphics[width=0.98\columnwidth, angle=0, clip=true]{fig2.eps}
\caption[]{(color online)
Effective potential $V_{\rm eff}(x,t)=V(x)+g_{1D} |\Psi(x,t)|^2$
for different values of $g_{1D}$. The bands are generated by
joining $V_{\rm eff}(x,0)$ and $V_{\rm eff}(x,t_{z_{\rm min}})$,
as explained in the text. The key to the various lines is
shown in each panel.
\label{fig:fig2}}
\end{figure}

In all the calculations, except those in
section~\ref{crit}, we have $\psi(x,t=0)=\Phi_L(x)$
(obtained by previously computing $\Phi_1$ and $\Phi_2$
of the GP for each $g_{1D}$), corresponding to the case
of all atoms being on the left well, $z(0)=1$, at $t=0$.
We study the dynamics for increasing values of $g_{1D} \ge 0 $,
going from the Rabi regime, $g_{1D}=0$, to the Josephson
and self-trapped dynamics, and further beyond the range
of validity of the usual two-mode approximation.

Results are shown in figure~\ref{fig:fig1}. There
we compare the numerically determined GP amplitudes of
$z(t)$, empty circles, with the semiclassical two mode
prediction of Eq.~(\ref{s2m}), solid (red). At
$g_{1D} < g_{1D}^{(1,2)}$ there is no self-trapping and $z(t)$
oscillates between $+1$ and $-1$, thus leading to a
constant maximal amplitude,
$A_z\equiv z_{\rm max}-z_{\rm min}=2$. With increasing
interaction strength, near $g_{1D}^{(1,2)}$, self-trapping
appears, the atoms become increasingly confined in the
left well, and $A_z$ decreases abruptly. In all this range
the semiclassical model predictions are very successful,
covering the well known Josephson and self-trapped regimes.
This range of $g_{1D}$ is the one recently explored
experimentally in Ref.~\cite{tilman10}.

With further increase of $g_{1D}$, deviations begin to
appear. Whereas the semiclassical two-mode model predicts a
smooth decrease of $A_z$, the GP calculations, empty circles, show
a smooth reappearance of tunneling between the two wells. This
is the new phenomenon that we will now discuss and interpret.

Figure~\ref{fig:fig2} shows the effective potential
defined in Eq.~(\ref{eq:gp}) for several values of
$g_{1D}$ at two different times, $t=0$ and $t=t_{z_{\rm min}}$
which correspond to the time of the first minimum of
the population imbalance. In this way the band covers
the variation of the effective potential during the
simulation. When $g_{1D}\lesssim g_{1D}^{(1,2)}$ the non-linear
contribution is fairly small, and
$V_{\rm eff}(x,t) \simeq V(x)$ at all times. This
corresponds to the Rabi and Josephson regimes, with
maximal oscillations of the population. Increasing $g_{1D}$
further, $g_{1D}^{(1,2)} \lesssim g_{1D} \lesssim 3$, the value of
$V_{\rm eff}(x,t)$ in the left well is increased, but leaving
the value in the right well almost unchanged. This is a
direct consequence of self-trapping. In this regime, the
effective potential changes very little with time, see
fig.~\ref{fig:fig2} (a).  Further increasing $g_{1D}$,
$3 \lesssim g_{1D} \lesssim 5$, the potential on the
left well increases, and $V_{\rm eff}$ does begin to change
appreciably with time. Still, the dynamics remains
self-trapped but with larger oscillation amplitudes in $z(t)$.

\begin{widetext}

\begin{figure}[t]
\includegraphics[width=0.7\columnwidth, angle=0, clip=true]{fig3.eps}
\caption[]{(a) First four eigenvalues of $V_{\rm eff}$ at
$t=0$ and $t=t_{z_{\rm min}}$, thus generating the bands.
The dashed black lines are the first order perturbation
theory calculation described in the text. The dotted
line is the average energy of the initial
state, $\langle \psi(x,0)| H | \psi(x,0)\rangle$.
(b) Energy differences $E_2-E_1$ (violet band)
and $E_3-E_2$ (green band) compared to twice the
frequencies of oscillation of the population
imbalance computed with GP, empty circles. The solid
(red) line is the usual two-mode calculation using
Eqs.~(\ref{s2m}). The dashed (blue) line is a two-mode
calculation using modes (2,3) as explained in the
text. (c) and (d) depict the two relevant eigenstates
of the effective potential (computed at $t=0$) entering
into the dynamics for $g_{1D}=0.1$ and 3, respectively.
(e), (f), and (g) depict the normalized Fourier
transform of $z(t)$, $|z(\omega)|$, for
$g_{1D}=0.4, 1.4$ and $3$ respectively.
\label{fig:fig3}}
\end{figure}
\end{widetext}

\subsection{Analysis of the effective potential}

To clarify the discussion and further gauge the smallness
of the changes in the potential with time, we have
determined the first four stationary solutions of the
Schr\"odinger equation built with $V_{\rm eff}(x,t)$,
with $t$ a fixed parameter. Figure~\ref{fig:fig3} (a),
shows the eigenvalues thus found numerically. Two values
of the parameter $t$ have been chosen: $t=0$ and
$t=t_{z_{\rm min}}$, to form a band for each eigenvalue.
The band width is seen to remain very small for
$g_{1D} \lesssim 2.2$, in line with the largely time
independent $V_{\rm eff}$ depicted in Fig.~\ref{fig:fig2} (a).
For small interaction strengths, $g_{1D}\lesssim 2$,
two of the eigenvalues are practically independent of
$g_{1D}$: they correspond to states 1 and 3, mostly
located in the right well, which remains unchanged as
seen in Fig.~\ref{fig:fig2} (a). Their values are thus
close to the corresponding non-interacting harmonic
oscillator, $E_{1}^{ho}=\sqrt{2}/2$ and $E_{2}^{ho}=3 \sqrt{2}/2$.

The other two eigenvalues increase smoothly with the
interaction strength, they correspond to states 2 and
4 located mostly in the left well. The increase follows
the behavior of the effective potential shown in
figure~\ref{fig:fig2}. The almost linear increase
in energy of these two eigenvalues can be understood
treating the non-linear term as a perturbation, then
\begin{eqnarray}
\delta E_2&=&g_{1D} \langle \,\psi_1^{ho}|\,
|\psi_1^{ho}|^2\,|\psi_1^{ho}\rangle
=g_{1D}/(2^{1/4}\sqrt{\pi})\,,\nonumber \\
\delta E_4&=&g_{1D} \langle \psi_2^{ho}|\,
|\psi_1^{ho}|^2\,|\psi_2^{ho}\rangle=\delta E_2/2\,,
\label{eq:e24}
\end{eqnarray}
where $\psi_{1,2}^{ho}$ are the first two eigenfunctions
of the harmonic trap, $V(x)=(x+2)^2$:
\begin{eqnarray}
\psi_{1}^{ho}(x)&=& (\sqrt{2} /\pi)^{1/4}\, e^{-\sqrt{2}
  (x+2)^2\over 2} \,,\nonumber \\
\psi_{2}^{ho}(x)&=&2^{3/4} \, (x+2) \, \psi_{1}^{ho}(x)\,.
\end{eqnarray}
These estimates are shown in Fig.~\ref{fig:fig3} (a)
as dashed lines. \\
\\
As sketched above, in the conventional two mode picture
one considers only the lowest two stationary solutions
of the original GP equation,~(\ref{eq:gp}),
and self-trapping occurs due to a misalignment
of their eigenenergies that suppresses the (Josephson)
tunneling between the two states. The dynamics thus
involves two quasi-degenerate states arising from the
ground states of the unconnected wells.

\subsection{Beyond the usual two-mode dynamics}

What is new here is that near $g_{1D} \simeq 2$
$(\Lambda \sim 60)$, the third eigenvalue becomes
aligned with the second and, since the corresponding
modes are located in different wells, tunneling of atoms
is again allowed. But now between modes 2 (left well)
and 3 (right well). This corresponds to the rise
of $A_z$ in figure~\ref{fig:fig1} beyond $g_{1D} \simeq 1$.
Figure 3a shows that by increasing the non-linear
interaction we go from the usual coupling between the
two lowest modes, 1 and 2, see panel (c), to a coupling
of the lowest mode of the left-well, 2, to the first
mode of the right well, 3, see panel (d). This coupling,
which is zero in absence of interaction, occurs due to
the large nonlinearity: it deforms the wave functions
enough to enable the coupling between the ground state
of one well and the first excitation in the other. It
is a large and clearly density dependent effect which
requires a change in the modes used and cannot be
accommodated by varying the parameters of the usual
two-mode picture. This effect is different in nature
from what was reported in Refs.~\cite{tonel2005,carr2007,carr2010}
where the alignment takes place due to the presence of
a large enough bias in the system. In our case, it
is clearly a dynamical phenomenon which happens even
for symmetric double-well potentials. The role played
here by the non-linear interaction in modifying the
single particle states is more similar to the interaction
blockade effect demonstrated for double-wells with
few atoms in optical superlattices \cite{cheinet08}.

Our result is also of different nature to the disappearance
of self-trapping reported in Ref.~\cite{meier01}. There,
the authors explore the population of low-energy
Bogoliubov excitations in the condensates of each of the
wells finding, using a schematic model, a departure
from self-trapping due to excitation of such low energy modes.
By using the time-dependent GP equation to determine
the condensate wavefunction, the low energy Bogoliubov
states are already incorporated into its time evolution.
See Eq. (8.43) and the discussion in section VIII.E in
Ref.~\cite{Leggett01}. Including them again along the
lines of Ref.~\cite{meier01} would be redundant.

To further confirm our picture, in panel (b) of
figure~\ref{fig:fig3} we compare the frequencies of
oscillation of $z(t)$~\footnote{These frequencies
correspond to those with the largest amplitudes in
the direct Fourier transform $|z(\omega)|$ of the
function $z(t)$, over one Rabi time.} found in the full
GP calculations, shown as empty circles, to the energy
differences of the first three modes~\footnote{The
energy of the fourth mode, see Fig.~\ref{fig:fig3},
shows a constant increase, without avoided
crossings in the range of $g_{1D}$ considered,
so that this mode remains mostly uncoupled to
the rest and we will ignore it.}. Up to $g_{1D} \simeq 1$ the
two mode description with
states 1 and 2 works very well, but beyond that, the
appropriate two mode model must involve states 2 and
3, and tunneling between wells increases again due
to the progressive alignment between the energies
of these two modes. The transition from (1,2) to
(2,3) takes place smoothly, with the region
$1\lesssim g_{1D}\lesssim 2$ having more than one
clear peak in the Fourier transform, $z(\omega)$, see
panel (f) of Fig.~\ref{fig:fig3}, but an extremely
small oscillation amplitude as seen in Fig.~\ref{fig:fig1}.
In this region, the dynamics is governed by the
first three modes coupled pairwise, (1,2) and
(2,3).

Above $g_{1D}\simeq 2$, the dynamics is dominated
by modes 2 and 3, depicted in panel (d) of
Fig.~\ref{fig:fig3}. The strongest frequency
extracted from the GP calculation now falls close to
the $E_3-E_2$ band (green). Following similar arguments
to those in the derivation of Eqs.~(\ref{s2m}) we can
write down the new two mode equations: We denote
the second and third modes of $V_{\rm eff}(x,0)$
as $\Phi_L$ and $\Phi_R$. A slight generalization of
Eqs.~(\ref{s2m}) leads to
\begin{eqnarray}
\dot{z}(t)&=& - 2{\cal K} \sqrt{1-z^2(t)} \,\sin {\delta\phi(t)} \\
\dot{\delta\phi(t)}&=&\Delta+N\,\bar{U}  z(t)
+2{\cal K} {z(t)\over \sqrt{1-z^2(t)}} \,
\cos{\delta\phi(t)}\, \nonumber
\label{s2mg}
\end{eqnarray}
where,
\begin{eqnarray}
\Delta&=&(E_L^0-E_R^0)+(U_L-U_R)/2\nonumber \\
\bar{U}&=&(U_L+U_R)/2 \nonumber \\
U_{L(R)} &=&\lambda_0 \int\! dx \,\Phi_{L(R)}^4  \\
E^0_{L(R)}&=&  \int d x
\left( (1/2)\partial_x\Phi_{L(R)} \partial_x\Phi_{L(R)}+\Phi^2_{L(R)}
\,V(x)\right)\,. \nonumber
\end{eqnarray}
Using $g_{1D}=1.2$ to build the modes gives,
$\Delta=-1.26$, $\bar{U}=0.35$, and ${\cal K}=-0.037$.
The prediction of this new two-mode model is shown by the
dashed (blue) lines in Fig.~\ref{fig:fig1} and
Fig.~\ref{fig:fig3}(b). As can be seen this (2,3) model
works well in the range $1 \lesssim g_{1D} \lesssim 3.5$,
giving a good account of both the dominant frequency
and the amplitude of the imbalance observed in the GP
simulations. The transition from (1,2) to (2,3)
coupling reflects also in the appearance of the node
of the $|\psi(x,t)|^2$ near $x=2$, obtained solving
the GP equations as seen in Fig.~\ref{fig:fig4}. This is
an observable feature which should be looked for
experimentally.

Further increasing $g_{1D}$, $g_{1D}\gtrsim 6$, our
initial state has an average energy above the
barrier, see dotted line in Fig.~\ref{fig:fig3} (a),
thus facilitating the flow of atoms
between the wells.
At high enough $g_{1D}$ a certain equilibration of
the imbalance can be expected, in line with
Ref.~\cite{ceder2009}, mostly due to the sizeable
contributions from  modes with energies above the
barrier.

\begin{figure}[t]
\includegraphics[width=0.95\columnwidth, angle=0, clip=true]{fig4.eps}
\caption[]{Density of atoms along the $x$ direction at
a given time $t=t_{\rm Rabi}/10$ for several values of $g_{1D}$. The
bands are built by joining the calculations at two different
values of $g_{1D}$.
\label{fig:fig4}}
\end{figure}

\subsection{Critical $g_{1D}^{(2,3)}$ for $z(0) < 1$}
\label{crit}

Until now we have considered only cases with a maximally imbalanced
initial condition, $z(0)=1$. For other initial conditions,
$z(0)< 1$ we can estimate the critical value for the
tunneling between modes (2,3), $g_{1D}^{(2,3)}$,
using similar arguments to the ones leading to Eq.~(\ref{eq:e24}).
The value of $g_{1D}^{(2,3)}$ for $z(0)=1$ corresponds to the one
for which the second energy level (the first of the most
populated well) equals the third energy level (the second
of the less populated well). Thus fulfilling $E_1^{ho}+\delta E_2 = E_3$,
which can easily be solved giving,
$g_{1D}^{(2,3)}=2^{3/4}\sqrt{\pi}\sim 2.98$, in good agreement with
Figs.~\ref{fig:fig2} and ~\ref{fig:fig3}.

Similarly, we can estimate the critical value, $g_{1D}^{(2,3)}$,
for an initial state with a certain population imbalance
$z_0\equiv z(0) >0$. In this case, assuming the system
remains mostly self-trapped, we can define the fraction
of atoms on the left well, $p_L \equiv (1+z_0)/2$, and on the
right well, $p_R \equiv (1-z_0)/2$. We can use a similar argument
as before and assume the wave function of the system is
essentially a harmonic oscillator wave function at each
side of the trap. We assume, the left well stays mostly
on the ground state, while the right side is promoted to
the first excited one. Treating again the non-linearity
as a perturbation, we have,
($E_1\equiv E_{1R}$, $E_2\equiv E_{1L}$, $E_3\equiv E_{2R}$,
$E_4\equiv E_{2L}$),
\begin{eqnarray}
\delta E_1  &=&
g_{1D} p_{R} \langle \psi_{1}^{ho} | |\psi_{2}^{ho}|^2 |\psi_{1}^{ho}\rangle
=g_{1D}p_{R}/(2^{5/4}\sqrt{\pi}) \,,\nonumber \\
\delta E_2  &=&
g_{1D} p_{L} \langle \psi_{1}^{ho} | |\psi_{1}^{ho}|^2 |\psi_{1}^{ho}\rangle
=g_{1D}p_{L}/(2^{1/4}\sqrt{\pi}) \,,
\nonumber \\
\delta E_3  &=&
g_{1D} p_{R} \langle \psi_{2}^{ho} | |\psi_{2}^{ho}|^2 |\psi_{2}^{ho}\rangle
=(3/2) \delta E_1 \,,
\nonumber \\
\delta E_4  &=&
g_{1D} p_{L} \langle \psi_{2}^{ho} | |\psi_{1}^{ho}|^2 |\psi_{2}^{ho}\rangle
=(1/2)\delta E_2\,.
\end{eqnarray}
The critical condition would correspond to have
$E_{2}\sim E_{3}$, that is $E_2^{ho}+\delta E_3 = E_1^{ho}+\delta E_2$
\begin{equation}
{3\over \sqrt{2}} + {3\over 2} {g^{1c}_{1D} p_R\over
2^{5/4}\sqrt{\pi}}
=
 {1\over \sqrt{2}} + {g^{1c}_{1D} p_{L}\over 2^{1/4}\sqrt{\pi}} \,,
\end{equation}
which gives,
\begin{equation}
g^{(2,3)}_{1D}= {4\; 2^{3/4}\sqrt{\pi} \over 4 p_L-3 p_R }\,.
\end{equation}
For $p_R\ll 1$ we have,
$
g^{(2,3)}_{1D} \sim 2^{3/4} \sqrt{\pi} \left[1 +  (7/4) p_R\right]\,.
$
Thus, for $z(0)$ close to 1, the critical value, $g_{1D}^{(2,3)}$, grows
linearly with the initial fraction of atoms in the less populated well.

\subsection{Possible experimental conditions}
\label{sec3}

The phenomena presented in the previous sections
rely on the adequateness of the Gross-Pitaevskii
equation to describe the physics at large enough
values of $g_{1D}$. The predicted reappearance of
tunneling of atoms through the barrier beyond
the usual self-trapped region as we increase $g_{1D}$
requires quantum fluctuations to be minimized during
the whole process. Thus, we need to estimate with
realistic conditions whether the system can be brought
to such $g_{1D}$ values while remaining mostly condensed.

We consider $N$ atoms of $^{87}$Rb trapped inside an axially
symmetric trap, characterized by $\omega_\perp$, and
its associated length $a_\perp= (\hbar / M \omega_\perp)^{1/2}$.
The double-well potential is built with a frequency
$\omega_x$ inside each well. The scaled 1D coupling,
$\hat{g}$, can be written in the weakly interacting
limit~\footnote{As discussed in Ref.~\cite{sala02}, Eq.~(\ref{eq:gp})
can be obtained from the 3D GP one in the weakly interacting limit.
For the strongly interacting limit the corresponding 1D
reduction would correspond to
$\tilde{V}_{\rm eff}=V(x) + \tilde{\lambda}_0 \sqrt{N} |\psi(x,t)|$.
We have checked that the phenomena described in the paper are
also present in such reduction.} as~\cite{sala02},
\begin{equation}
\hat{g}={4 \pi \hbar^2 a_s  \over 2 \pi a_\perp^2  M} =
{2 \hbar a_s   \omega_\perp  } \,.
\end{equation}
To obtain meaningful estimates we consider the elongated
trap conditions of Ref.~\cite{gio08}:
$\omega_x=2 \pi 44.7$ Hz and $\omega_\perp= 2 \pi 1100$ Hz.
For these we can estimate the dilution factor, $\eta= n_{1D} a_s$,
where $a_s$ is the s-wave scattering length and $n_{1D}$ is
the one-dimensional density. In the Thomas-Fermi limit, this
estimate is given by
\begin{equation}
\eta = (g_{1D})^{2/3} {\omega_x \over \omega_\perp} {1\over 3^{1/3} 2^{5/3}} \,,
\end{equation}
and for the trap conditions considered,
$
\eta \sim   9 \times 10^{-3} (g_{1D})^{2/3}\,.
$
Thus, an elongated trap ensures the diluteness of the
gas along the direction of the barrier, which is a
necessary condition for the validity of the Gross-Pitaevskii approximation.
The diluteness on the longitudinal direction also ensures the non-excitation
of transverse modes of the elongated trap. This can be checked by
comparing the transverse chemical potential with the transverse
quantum, $\hbar \omega_\perp$. The transverse chemical potential
can be written as, see Eq.~(10) of ~\cite{paul07},
$
\mu_\perp = \hbar \omega_\perp ( 1+  2 \eta)
$
which is well below $2 \hbar \omega_\perp$ for the values of
$g_{1D}$ considered in this work provided the trap is
cigar-shaped.

This excitation of the third mode (the first excited
state of the less-populated well) should show up
macroscopically
in the experiments as an increase in the amplitude
of oscillations of the population imbalance above
a certain value of the interaction strength.
Simultaneously, a node should appear in the center
of the atomic cloud sitting in the less populated
well, see Fig.~\ref{fig:fig4}.

Experimentally, the challenge is twofold: first one
needs to build a double-well potential with a
single-particle spectrum close to the one described
here, see Fig.~\ref{fig:fig3}a.
This can be achieved by modifying the parameters of the
optically produced double-well used in Ref.~\cite{Albiez05}.
Secondly, one needs to increase the number of atoms to have a
non-linear term able to scan the
transition described in this article.
Such an experiment is within
reach with current experimental setups~\cite{oberp}.

\section{Conclusions}
\label{sec4}

We have demonstrated the possibility of exciting
higher modes of the double-well potential through
the dynamics. We have considered an initially
imbalanced population and have shown
that for a broad range of interaction energies
the system remains self-trapped but not due to
the dynamics of the two lower states of the
Gross-Pitaevskii equation, as usually accepted, but
of another mechanism involving a third state. This
transition from the coupling between the first two
(1,2) to the next two (2,3) states can be well
characterized and understood by analyzing the
static properties of the effective potential
(including interactions) which due to the fact
that the system remains mostly self-trapped does
not vary substantially with time.

\begin{acknowledgments}

We thank D.W.L. Sprung for useful remarks and a
careful reading of the manuscript. M. M-M, is
supported by an FPI grant from the MICINN (Spain).
B.J-D. is supported by a CPAN CSD 2007-0042
contract. This work is also supported by Grants
No. FIS2008-01661, and No. 2009SGR1289 from
Generalitat de Catalunya.
\end{acknowledgments}

redpajama_set_name: RedPajamaArXiv


text:
movie, "The Chronicles of Narnia: The Lion, the Witch and the Wardrobe", director: Andrew Adamson, scene with: William Moseley, fairy tale, novel by Clive Staples Lewsi
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movie, "The Chronicles of Narnia: The Lion, the Witch and the Wardrobe", director: Andrew Adamson, scene with: William Moseley, fairy tale, novel by Clive Staples Lewsi, Interfoto, 00529625
MOVIE, The Chronicles of Narnia - The Lion, The Witch And The Wardrobe

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I was searching for a Property and found this listing (MLS® #C4233749). Please send me more information regarding #526 500 Allen St Se, Airdrie, Alberta, t4b 1j6. Thank you!
I'd like to request a showing of #526 500 Allen St Se, Airdrie, Alberta, t4b 1j6 (MLS® #C4233749). Thank you!


text:
OneFour
Admission & show times
"the biggest thing in hip hop right now…" GQ
"Australia's first drill rappers…" Radar Station
"Australia's most exciting rappers…" Vice
With a string of viral singles and videos racking up over 30 million streams, drill collective OneFour have announced their first ever headline in New Zealand this December.
From the streets of Western Sydney to the world at large, OneFour are carving out a reputation for energy charged storytelling and world-class production. Their songs depict a life of adversity and conflict that few outsiders have access to. Yet, as Australia's first drill group, they proudly represent the Greater Western Sydney district of Mt Druitt to a growing fanbase all around the world, awakening audiences to the often-overlooked talent that come from working-class communities across the country.
Dubbed as 'Australia's most exciting rappers' by Vice - OneFour will be bringing their unique sound, shaped by a life of adversity and conflict, to fans in Auckland, performing at the Powerstation on Thursday December 5th.
It's the end of the beginning for this crew. While their feet are firmly planted in the streets that raised them, their sights are set on being the first Australian Rap group to really crack open the UK and US markets.
THIS SHOW IS LICENSED R18 ONLY. A valid photo ID will be required - any current passport, a current New Zealand driver's license, a HANZ 18+ card or Kiwi Access Card. - FOR MORE INFO ON AGE RESTRICTIONS CLICK HERE.
Spot the Difference - ONEFOUR
Video of Spot the Difference - ONEFOUR
The Message - ONEFOUR
Video of The Message - ONEFOUR


text:
fragments shored against my ruins, or, three reviewable atlanta exhibitions i shall not review
Three Atlanta Exhibitions About Which I Shall Not Write Reviews
From the lumpy sculptures in the front to the broken clay vessels scattered across the floor in the back, adjacent to the wall text of a poem by Pessoa, "Movable Types" (the Art Papers-curated exhibition at Ponce City Market through September 28) raises questions that I don't feel the slightest inclination to have answered, much less to answer through my own research. It's useful to have the explanation of the wall grid of images depicting cherry stems, but it's enough to enjoy them as glyphs of some alphabet or algorithm I'll never understand.
The pun on "movable type" indicates the deliberately uncertain or slippery place of the exhibition in terms of form and language alike: it is a type of exhibition that resists being made conceptually immobile, or out of play rather than playfully in play, always. Like movable type, its components will be reused for other purposes (in fact the broken ceramics in the back will be distributed like some latter-day version of a Tibetan sand mandala, except that unlike the transient order of the mandala, the work began with an act of disordering that was itself a form of order...as in Wallace Stevens' poetic assertion in "Connoisseur of Chaos," "1. A violent order is a disorder; and / 2. A great disorder is an order. These / Two things are one. (Pages of illustrations.)"
I'm very glad I don't have to write a review of the exhibition, because it would entail re-reading Georges Bataille and re-upping my recollections of what the famous "Informe" exhibition was all about, and I just don't want to do any of that right now.
But I think it would be great for folks who happen to be in the vicinity of Ponce City Market during gallery hours to stop by and ask, if they are so inclined, to have the show explained to them. But first and foremost, to look at all the stuff that I don't feel up to explaining in detail. I especially don't feel like trying to describe the videos. But the slippery quality of description is part of what the show is about. Or maybe not about, for "aboutness" itself is the problem. Ludwig Wittgenstein thought that a philosophical problem took the form of "I don't know my way about," but it might rather be "I don't know about my way," or worse, "My way doesn't know about me."
"Alice: Curiouser and Curiouser," at Cherrylion Studios through September 26, is a curious kind of show in a couple of different ways. Walking into it may give the feeling of falling down a rabbit hole, but apart from that, the exhibition is not really an homage to Lewis Carroll's most memorable creation.
It's an independent exhibition of 9 members of a critique group of women artists, as curated by Michelle Pizer of Pizer Fine Arts. It, too, deserves the level of review I simply cannot write under duress, though it holds up perfectly well without one.
In fact, it is the variety of visual pleasure in this small exhibition that makes it singularly worth seeking out in the two days or so that are left to seek it out (if you read this as soon as it is posted, which most of this note's potential readers are unlikely to do). Patty Nelson Merrifield's witty taxidermy sculptures alone are worth the price of admission. (Admission is free, of course, so that is less high praise than I had meant to convey with that cliché. Please insert smiley-face emoticon here.)
People who already know Linda Mitchell's work will find new and quite different iterations of it. Ditto for Edie Morton's encaustics, Mary Anne Mitchell's photographs, and Chris Dolan's drawings...Dena Light is only one of the artists who are less likely to be familiar to gallerygoers, and the same goes for Shannon Davis, Deborah Hill, and Julie Grant, all of whom contributed singularly interesting works to this diverse yet tightly curated exhibition.
And that detail-less observation brings me to:
Henry Callahan's "Beyond Abstraction: Expressing Nature," at Reinike Gallery through September 27, is a show that will not be helped in the slightest by this note regarding its existence, for its most likely interested viewers do not read Facebook and are unlikely to find a notice on a blog.
These are loose, diversely painted evocations of places in nature, eminently worth the analysis I cannot at present give them, although they are also works which it is more important to match up with an audience than to provide with a discerning critical analysis. There are those to whom these paintings will speak deeply, and there are those who are likely to remain unresponsive to the set of aesthetics these paintings embody. That is simply a fact of human psychology and personal predilections.
It is highly unlikely that more than a handful of viewers would find "Movable Types" and "Beyond Abstraction" equally appealing, though it is possible to imagine someone who would find equal pleasure in the shattered ceramic shards of the one and the darker range of paintings in the other. (It is possible to imagine this because I did it.)
And this pathetic expression of complete exhaustion does little more than acknowledge the existence of these exhibitions and show off a few photographs (left unlabeled because with few exceptions I have no information regarding them).
And there are still more bodies of work in current and recent exhibitions that deserve extremely detailed and serious analysis, not least analysis of the mismatch between work and probable audience—this latter would be different in every city in which the work might be exhibited.
Given my interest in how different very small parts of the planet respond differently to different artistic stimuli (cf. the earlier, programmatic essays on this Counterforces blog), I am fascinated by the Atlanta-centric problem of critical and audience response to a particular species of painting.
The genre I have in mind seems to combine representational references (usually modestly specific ones), geometric abstraction, biomorphic abstraction, and gestural painterliness in one big, sometimes chaotic but just as often complexly organized canvas.
And the general response thus far has been betwixt and between; scarcely anyone seems to know what to say about it, or if they do they haven't stepped forward to say so. And audiences seem equally indifferent when they are not bewildered.
But all that will have to wait for some other exhausted evening, or some less sleep-deprived writer.
Posted by littlejoke at 8:57 PM
Counterforces and Other Little Jokes
Blogs may be more like private journals with megaphones than reasoned contributions to public life.
—Russell Jacoby, author of The Last Intellectuals
fragments shored against my ruins, or, three revie...
a deliberately loopy recommendation to attend or c...
Byzantine Things in the World, a Year Later: a Bel...
an incredibly tiny essay on art reviewing
littlejoke


Unique Dining Room Chair Leg Protectors is free HD wallpaper. This wallpaper was upload at May 14, 2017 upload by Juan I. Boggs in Dining Room Chairs.
You can download Unique Dining Room Chair Leg Protectors in your computer by clicking resolution image in Download by size:. Don't forget to rate and comment if you interest with this wallpaper.
The dining room is among the most important rooms in a home and also the one of the only areas which joins everyone collectively. The dining area is meant for entertaining, whether you're hosting guests for a big celebration or having a quiet family dinner. The dining room seats will be among the very first pieces of furniture your visitors will visit and more importantly will be sitting , so it's crucial to have a dining area that is both appealing in appearance and welcoming.
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This article is all about dining room seats. Mixing and matching chairs, fashion, and comfort are discussed.
The dining room chair you select can increase the total staging impact of your dining room. Below are a few suggestions about how you're able to pick out the dining room chair. Everything comes down to finding balance between function and form.
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Dining Room Chair Covers are a basic and effortless way to alter the appearance of any dining room seat. The most important plus is that they are really simple to install and remove.
One of the hottest trends in home decor these days is the upsurge in popularity of modern dining room chairs. If you check out the latest home decorating magazines or see the house renovation television shows you'll notice that more and more people are turning to trendy and funky seats because of their dining rooms. While traditionally classic seats still have their location, the availability of fabulous and fun furniture for your dining area is definitely a trend that's well worth exploring.
Ever wonder if their is a piece of furniture which should not be made out of wicker? Well living room seats are one of those bits. But why? I tell them it isn't really that difficult to do once they understand the upholstery process of doing things.
The use of dining room chair slipcovers has been quite popular with big hotels and restaurants that want to have the very best dining experience for their customers. Basically, the dining cover slips and recliner slip cover can be used easily because it may be attached to the seats using stitches and other house based materials and materials. This is easy to do and can be done by anyone.
Ever wonder exactly what are the simple things you can do to make those hottest sitting areas keep their comfort? Check out them here.
First time buyers are often confused when they are attempting to choose the style, colours, fabrics which will compliment their style and tastes as well as provide a functional space for entertaining and family. The dining room chairs are an essential portion of the dining area table and are great methods to compliment the table with modern overtones. The dining room is the most used area of the home by family in addition to guests.
In the current world it is rarely necessary to leave your house. Thanks to the Internet, there isn't much you cannot purchase from the comfort of your own home, in your pajamas. Anything from groceries to prescriptions to dining room chairs can be purchased with the click of a mouse.
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There are lots of different varieties of dining chairs to choose from. There is a historic aspect to particular chairs and their design styles. The Chippendale style is intricate and bits of this kind of furniture are regarded as of great antique value. The Windsor design is more casual and famous for superior seating comfort. The Parsons style takes its name and style from the Parsons' school of Design.
Think about Thanksgiving dinner. The table is setthe feast is prepared, and famished voices are satisfying the dining room. The china is sparkling, the silver is shiny, and the linen is crisp. It is a classic image of Americana. After the picture-perfect dinner, the match is on, the children are playing with, and it is time to linger around the table. The time we spend here is frequently that which we recall when we all know about far-away family and friends.
Could it be time to create a change to the appearance of your dining area? Perhaps that table and seats have only had a few too many days serving a meal and are starting to show their age. Or maybe you simply don't like the look you had any more and therefore are thinking its time to get something fresh.
The dining table set you select can determine how inviting your dining room remains. You can really make a focal point in your home by picking interesting chairs for the dining room and coupling them with good lighting and colours. There are many styles now and you can have your distinctive design or design created specifically for you to create a unique customized dining room based on what you find to be most suitable. However, generally speaking, there are 3 factors which should matter when choosing the ideal chairs for your dining room.
Cherry dining room chairs include a lot of colour and design to y our room. Here are a couple suggestions to decorate and get this kind of furniture.
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If you are one of many men and women who possess the conventional glass dining table and also have regular, old, wooden seats, then you need to definitely consider giving your dining room a face lift with contemporary dining chairs. Though you have a glass dining table that's always in fashion, the seats that match your dining table can alter the overall look of the space dramatically.
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Whether your style demands heritage, contemporary appeal, or glitz and glamour, the ideal furniture is an important decision. This does not imply that chairs need be a costly improvement; there is seating to fit every budget, even for the"green" at heart. Dining room Furniture may be one of the most important parts of artifacts you might bring to your home. Here is a beginner's guide to all that you wish to learn about dining area furniture.
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Do you believe there is hope for the future? The world can be beautiful and open, if we want it. These children from around the world came together and discovered they are more alike than they ever imagined. In the film Dear mom and dad, we document what happens when 48 children from 12 different countries meet at a CISV camp funded by Momondo and run by CISV. We asked the children to write to their parents how they see the world in the beginning and the end of the camp. We are proud and honored to have been able to document the beautiful feelings and thoughts shared by the children. They don't come from the same culture, speak the same language or wear the same clothes, but none of that matters: jokes are shared, hearts are opened and friendships across borders are made. Momondo supports CISV International, a global non-profit organization dedicated to educating and inspiring action for peace. By educating the next generation, and through building intercultural friendships based on cooperation and understanding, CISV aims to help children and youth to develop the skills they need to become informed, responsible and active global citizens, able to make a positive difference in their communities and the world. Our collaboration with CISV and the Dear mom and dad campaign are part of Let's Open Our World; an invitation to cross boundaries, embrace our differences and open our world. Find out more about Let's Open Our World, our collaboration with CISV, and download free school kits at letsopenourworld.com.
Film advertisement created by &Co, Denmark for Momondo, within the category: Professional Services.


It's been at least 18 months since I made a knit Gabby Dress - not sure why I fell off the wagon as it's a pattern that has always worked for me (in a knit). When I bought this fabric from Tessuti earlier in the week (yes, I also have a Mandy Boat Tee in this fabric and I LOVE it) I had the Marianne Dress in mind. In the back of my mind though I thought it would also look great as a big, swingy tent dress. And that's exactly what I've made!
I've put on weight since my last Gabby Dress so I made the XL this time...with a slightly bigger seam allowance than I usually sew on the overlocker. I also added 5cm to the length as the dress is quite short. Not a problem when worn in winter with tights but for summer I like this at knee length.
If you look closely you'll see there's a seam down the centre back. I probably could've cut it on the fold as the fabric was 155cm wide but it was hot and I couldn't be bothered playing around with the fabric. The stripes line up well so I'm happy. I'm calling this a design feature.
The stripes on the side seam however - whoops! I thought I was laying out the fabric so that my side seams would match but clearly that is not what I was doing at all. I think it looks OK however as the dress is not a straight dress which would make the non-matching stripes very very obvious. I'm also calling this a design feature.
The fabric has good stretch in both directions so I was able to cut the neckband against the grain. I really love how this looks!


Rest and relaxation in a beautiful beachfront setting is the big draw card for Macdonalds Beach Cottages. As soon as you arrive, this place just feels right...the perfect place to lie back and let the stress simply melt away.
Macdonalds isn't about adventure, it's not about packing in as many activities as you can every day, and it's not about party's every night. What it is about, is unwinding; lying back and enjoying a quiet and simple way of life for a few days. It's about turning off the cell phones, the internet, TV and deadlines, and recharging the soul.
If the legs need a little exercise take an hour and a half loop walk around the Western end of the Island at low tide. You will be amazed by the once a year holiday Cribs hidden away beneath the coconut trees. Or you can spend 4 hours walking around the whole island, although we didn't do this so can't vouch for the exact timing.
As for taking a swim in the tropical clear waters the best time is at full tide, but I must say the snorkelling was lacking in colourful fish and coral. You need to book a short boat ride out to the reef.
Arriving at Macdonalds Cottages, check out that beautiful clear water, can't wait to jump in!
Macdonalds have a selection of self contained cottages, each one set apart from the others to ensure privacy. The kitchen has gas powered cooking, with a large fridge/freezer and plenty of bench space. There is also a dorm, but why risk having to share when a cottage is so reasonably priced? There is the choice of a twin/double cottage or a 2 bed cottage. As tempting as it might be to share with friends in the 2 bed cottage, its only suitable for a family where you know everyone intimately - this is because the walls to the bathroom don't go all the way to the ceiling, anyone staying in the main bedroom (which also has short walls) will hear absolutely every last tinkle from the bathroom! Not so in the twin/double cottage where the walls go all the way to the top!
The generator comes on in the morning around 8.30am, takes a short break between 2pm to 5pm and runs until 10pm, so make sure you have recharged laptops cameras etc by then. The showers are cold water only... though it's more like lukewarm, so no real hardship. Beds are comfy, with good quality insect screens on the doors and windows. There are a few mosquitoes around, especially early morning and late evening, so do bring your insect repellent with you (it's expensive to buy on the island).
Cyclone Winston April 2016 hit Macdonalds Cottages really badly, you can see from the photo above that they lost their wharf, plans are in place to put it back. The dining and reception area got blown away too and is just about finished rebuilding (May 2016). Not too much damage to the cottages and they are all open now, just to Maxine's (the owner) own home, she has a bit of work still to do before she can move back.
Probably the fact that Nananu-i-ra requires a bit of effort to reach, is why it isn't overloaded with tourists the way that some Mamanuca and Yasawa islands are. It's certainly every bit as beautiful as those islands, and also better value for money. Travelling from Nadi, you need to get to Rakiraki (local or express buses run regularly). From there, a taxi to Ellington Wharf. The Macdonalds boat will be at the wharf to transport you to the lodge... about a 10 to 15 minute trip. For those travelling by car, there is secure storage for your vehicle at the wharf for a nominal fee (fj$10 a day).
All accommodation is self contained with kitchenettes and bathrooms. Rates valid to 31 March 2017.
Rates are inclusive of 25% taxes. Credit cards are accepted visa or m/card with a 3.5% service fee.
While Macdonalds do have self catering in all their accommodation, you might prefer to just bring tea coffee milk and snacks, and get all or some of your meals at the beachside restaurant. Prices aren't cheap, but meals are great (Filo is a fantastic cook!) and it saves a lot of hassle. You're probably not there to cook and clean up afterwards anyway, are you?


To whom this was written by, what are your examples?
I tried to run Loadiine GX2 I got the best games ever in this cable But APPERANTLY Wii U screw up everything and it give me error all the time.
Even when I was a kid I hated the controllers.
Nintendo only focuses on getting money from kids, not delivering good games to fans.
The wii u doesn't have such good exlusives, but their okay. Why no one buys a wii u? The wii u doesn't have good popoular games like Call of Duty bo3, Grand Theft Auto V, skyrim, and more good games who are available at xbox one and playstation4.
? The internet explorer doesn't let you scroll or zoom on some sites.
By now, if they release Zelda Wii U for Wii U, they should also release it for NX for higher sales. Apparently, it is the most expensive game they have ever made, so they probably want it to be profitable. But if they released it earlier this year, it could've saved the Wii U.
15 It took years to make actual good games for.
Super mario 3d world and donkey kong tropical freeze was released 2013 that was one year since the wii u got released not "several"
It's got Amazon Video, YouTube, Hulu Plus, and Netflix. That's it. No NFL Sunday ticket, no Crackle, no Crunchyroll (you have to go into Wii mode just to download it, and it only goes up to 480p), no Twitch (even though Nintendo has a good relationship with them, which feels like a betrayal), it can't even play DVDs or Blu Rays (which I could deal with that if they had more streaming options to make up for that). We're at a day and age where game consoles are more than just game consoles, and even modern computers now have streaming options (Microsoft store for Windows and Xbox, iTunes for iDevices), yet the Wii U insists on being only a game console. Nothing more.
I have heard stories that people have put a game in their Wii U and it didn't come out. Finally, when they take apart the console to get it out, it is all scratched up. Never happens with Wii.
Bought Minecraft Wii U Edition, (now got ps4) edition, then I got Madden NFL 13, and, after playing it, I insterted Minecraft disc. 'Invalid disc' 'The disc cannot be read, it might be dirty'. Bunch of liars, I cleaned it, and nothing. TERRIBLE CONSOLE.
Wii U. Wii, but with an U.


The Internet keeps countless recipes in neat, tidy digital files, so handwritten notecards are quickly becoming cherished keepsakes. Here's how to preserve your own.
"It's not under the Ps," I shout over the din of a pulsating dishwasher as I thumb through a small metal box filled with alphabetical dividers and yellowed notecards.
"Try F, for fudge," my grandmother shouts back.
It's not there either. It's also not in B (for butter, just in case), and it's not in the treasured As, which is actually the spot for the most-cooked recipe.
I'm standing in my grandparents' kitchen, looking for my grandfather's peanut butter fudge recipe. My grandfather, a larger-than-life figure who was renowned for his fudge in doctors' offices and hair salons across my small North Alabama hometown, had passed away three months earlier. He was the last one to use the fudge recipe card—no one else dare make it—so he's the one who knew his secret filing strategy.
"Oh, for dessert. That makes sense," my grandmother says.
It does not make sense, not in the least.
But here I stand, holding a recipe card with well-worn edges, their fray showing signs of use; the fading recipe, a testament to the number of times my Papaw had made this recipe. Some years ago, he marked out "Oleo" and wrote butter. The script number two beside teaspoons of vanilla was clearly once a one.
Now, the recipe card is mine, and it is as much a treasure as anything else I can ever receive. It holds memories of him, of holidays, of the times he tried to teach me how to make this beloved recipe. The recipe card is a gift.
In the age of digital recipes and limitless recipe "boxes," families are losing the tangible mementos of the recipes and foods that fed them for most of their lives. Gone are the metal boxes in the cupboard above the microwave. In their stead are Pinterest boards for every cuisine, craving, and curiosity.
That makes the recipe cards families do manage to find and retain all the more valuable.
It also makes saving and preserving those recipe cards big business.
Indeed, EverPresent, a company that can "expertly digitize and organize your home movies and photos," has seen the revenue from their recipe photo books grow from one percent to 20 to 30 percent in the last year, the Wall Street Journal reports.
EverPresent can scan those age-old cards, smudges and all, and preserve them in a printed keepsake book. They can print as many as you need, too, which means no family members need fight over cherished recipe cards.
Minted can turn recipe cards into foil-printed art, scanning every inch of written text and then printing it in a single framed piece. The cook's name can be added to the keepsake.
As more families scramble to find ways to preserve these cards, they're faced with some harsh realities, however.
Kitchens, it turns out, aren't great for delicate pieces of paper. The heat, humidity, splashes, and splatters can do a number on paper. For the purposes of cooking dinner, it may not matter. If you want to turn the recipe cards into art, it does.
Framing recipe cards can also present challenges. The recipe cards, hand-written long ago, are certainly not on acid-free paper. The natural patina of food and smoke provides characteristic charm, but the foods on the cards are likely filled with acids that will continue to deteriorate the paper.
Plus, there's the task of framing something that was inherently never meant to be framed.
If you or your family still cooks from the notecards, you'll have to decide whether they're treasured enough to write a new one in order to save the heirloom. If the joy of cooking a family recipe comes from using the card your ancestors used before you, by all means, keep cooking.
Just remember that the heat and moisture of a kitchen, combined with the exposure to food and water, can greatly deteriorate recipe cards. Consider moving them out of the kitchen entirely if you want to keep them safer.
Newspaper cutouts will quickly grow fragile. They should be placed in file folders, separate from other pieces of paper. The acid in the newsprint will quickly deteriorate other papers.
For long-term preservation, consider high-resolution scanning. You will still have the tangible copy to hold for many years to come, but you will also have an artifact—albeit, digital—for many generations to come.


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text:
See it Here, Save it There
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Joining forces with governmental agencies and organizations to inspire people to protect animals through personal, interactive and informative experiences.
Research is a key component of SeaWorld®'s larger commitment to conservation and animal welfare, and was established as a priority by our founders five decades ago. This commitment includes publishing our own research, sharing our parks and animals as controlled research environments, and funding and supporting projects around the world.
Our parks provide a unique environment that allows our team and outside researchers and scientists to better understand marine mammals. SeaWorld's animal health professionals contribute meaningful science learned through the care of these animals. Additionally, we are deeply integrated with universities and research organizations and provide access to our animals for scientists conducting humane studies on a variety of subjects. These studies complement and strengthen research efforts in the field.
We also provide direct support, both material and funding, to field researchers. This support is offered directly by SeaWorld, through grants from the SeaWorld® & Busch Gardens® Conservation Fund, and by research foundations associated with and supported by SeaWorld, including the Hubbs-SeaWorld Research Institute.
The animal health team and scientists of SeaWorld Parks & Entertainment™ have contributed to more than 1,000 published studies that advance the global scientific community's understanding of animals.
SeaWorld's contributions have led to advances in the care of animals in both zoological facilities and wild populations. Selected contributions to the greater scientific understanding include:
Sustainability For Marine Ornamental Fish—Coral reefs face numerous growing threats including ocean acidification, pollution and over-exploitation. Additionally, many colorful marine inhabitants are collected in ways that are not environmentally friendly and can impact the entire reef ecosystem. Rising Tide Conservation was initiated by SeaWorld Parks & Entertainment to protect reefs by developing techniques for rearing marine ornamental fish. The program promotes commercial production as an alternative to reef collection. Rising Tide has grown into a nationwide effort that is supported by corporate sponsors as well as the SeaWorld & Busch Gardens Conservation Fund. Its board of advisers includes environmentalists, professional aquarists and leaders in the aquarium industry. Many display aquariums throughout the country collect tiny fish eggs from their tanks to support this program and advance our understanding of reef fish reproductive biology. Since its inception in 2009, the program has developed captive rearing techniques for more than 18 marine fish species, including yellow and blue tang.
A ticket with a mission
Your visit to SeaWorld helps support animal rescue efforts, with over 35,000 and counting.
Marine & Ocean Conservation with the Humane Society of the United States
SeaWorld and the Humane Society of the United States (HSUS) have partnered to work together as advocates for the ocean and its animals. Together we will focus on ending commercial killing of whales, seals and other marine animals. Our mutual efforts include leveraging SeaWorld's world-class rescue, research and resources, protecting coral reefs, preventing over-exploitation of fish and protecting our oceans for future generations.
Shark Rescue & Conservation with Guy Harvey
World-renowned artist and marine conservationist Guy Harvey is actively working with SeaWorld to help raise awareness on protecting sharks and their natural habitats. The Guy Harvey Research Institute estimates that up to 73 million sharks per year are killed for the fin trade alone. SeaWorld has helped with his team's research on shark-tagging expeditions, as well as informing the public about shark conservation through storytelling within our Mako hyper-coaster queue and realm.
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SeaWorld and OCEARCH are focused on the global conservation of marine animals and the world's oceans. We're both purpose-driven organizations; we love the ocean and want to ensure an abundant resource for future generations. Together, we will focus on bringing everyday people closer to the water by sharing real-time data, content, and park experiences.
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Our company is committed to advancing knowledge and conservation. This bibliography lists the contributions to scientific literature we have made over the course of our history: more than 350 peer-reviewed articles, book chapters and books (authored in whole or part) by our team members, on a wide variety of marine and terrestrial animals in numerous arenas of investigation.
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These studies reflect the knowledge, skill, commitment and passion of our staff. Beyond these direct contributions, still more manuscripts were authored by outside researchers that utilized our animals and data. Those outside studies benefited from access to our animals in a controlled environment that is impossible to duplicate in the wild.
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COVID19: Lessons from Google Search Trends for brands
By Faysal Dalel, Commtractor and accomplished Performance Digital Marketing and Communications professional with 12 years of demonstrated success in developing and implementing strategies to drive market growth and bottom-line profitability. He is also the founder & director of Dynamic Digital.
Let's be honest, it's very grim out there. I'm feeling claustrophobic. Being cooped up indoors with loved ones is driving me mental. And to top it all off 'Rona' – aka COVID19 – is broadcast on every communication platform, hourly!
So, Rona has taken hold, wreaking havoc around the globe and we're all unsure how to deal with it. No more party invites, beach holidays, retail therapy, or coffee catchups – trips to Waitrose or Woolworths are now considered a highlight.
But what can advertisers and brands do? The answer is simple.
Help people find what truly matters to them at any moment and solve their needs, which is what we do as marketers – understand how customers are searching, what they're searching for, and why.
And there is no better source for that insight than Google Search Trends.
In 2020, marketers are facing new challenges across all sectors, and thus it's important to gain a deeper understanding of why people are searching, by exploring Search trends to create tailored experiences that are authentic.
With millions now working from home out of necessity, consumers' decisions about what time of day to shop, what to browse for, what to watch, read and listen to will change drastically as people establish new norms and form new habits.
Immediate shifts
In the earlier days of the pandemic, we are seeing that the priority for people was to create a comfortable working space in their homes. They valued messaging containing accurate information and worried less about the speed of service or the quality of products.
In South Africa for example, there was increased search interest for 'essential services' ('essential services'), and in Turkey for ('is it open').
Google Trends insights reveal the searches people make to fill COVID19 information gaps. Their questions sought immediate answers and solutions, reflecting the uncertainties of their new situation.
New day-to-day emerging behaviours
Even though the COVID19 situation was evolving very quickly, consumers proved equally fast to adapt, researching ways to fit life around changing circumstances.
There has been an increase in search interest for ('board games') and ('puzzles'), in Italy, Spain, and Denmark and an increase in ('professional development') in Saudi Arabia as people try to keep themselves busy and their minds active, while self-isolating.
People were also finding new ways to maintain social connections and recreating communities online as shown by an increase in searches for play with friends' ('play with friends') in the UAE and for 'party app' ('party app') in Nigeria. (1)
As people adapted to their new circumstances, there has been an increase in ways to connect with the outside world virtually as shown by an increase in search interest in VR ('virtual reality headset') in Sweden.
Whereas in Spain, the U.K., and Italy, there has been an increase in interest for technology that can help people spend their time in interesting ways at home with increased searches for 'smart TV' ('smart tv'). (1)
In the midst of all these growing searches that help people adapt to their new ways of living, there has also been considerations for the wider community, by celebrating the efforts of health workers and helping people in need.
In the U.K. ('clap for') saw an increase in searches, as people applauded health workers as well as an increase in ('how to volunteer for'), while we saw an in increase in interest to help farmers find people workers in France ('des bras pour ton assiette'). (1)
During these unusual times, brands need to be especially transparent in their communications, showing an ability to address the real challenges facing people's lives. Fortunately, some businesses were doing so – being helpful and talking directly with people – showing a level of corporate responsibility.
As consumers re-evaluate what's important to their lives in a pandemic – what is of real value and what is the best way to navigate new ways of working, shopping, and connecting – brands and advertisers, too, must re-evaluate their understanding of consumer behaviour.
Ultimately, brands need to make themselves helpful to consumers, meeting their needs as they adapt to the "new norm". Brands must process these changes to people's personal and professional lives.
Communications must be authentic and compassionate to reflect the palpable sense of solidarity – the 'we are in this together' that is so visible and vital and in everyday life right now.
Email Marketing Best Practices Navigating Federal and State Government Messaging Confusion During a Pandem...


The topics for argumentative essay are usual and easily available. Once you get the viable topic in possession the essay writing becomes easy. You can write the essay in the straight forward manner. There are no twists and turns in the course of writing. Once you attempt the paper you should do the needful. You should make things interesting for the reader in the kind of situation to make them think more on the right track. The more you think the more the argument becomes clear. The subject of the essay is worth learning. You should take interest in the topic and learn things accordingly.
In the kind of essay writing it is necessary that you discuss the argument in details. The problem or the controversy should be stated with the best of clarity. The sides of the debate should be properly explained in the essay. The debate is perfect and you need to concentrate on the points with the best of clarity. In the argumentative essay you should take time in explaining your side. This will help people have an idea what you are stating exactly. You should try to convince people that your side is the right one, and that you should defend things appositely.
The objections that you present in the course of essay writing should be clear and perfect. You should be presenting the objections in the relevant way without letting the reader to refute things. You should compel the reader adopt your point of view. You should make them believe in you. As they read on they should start thinking in your way. The argumentative essay deals with the hot topics of the time. This makes the essay interesting and lucid while you read on. If you are already familiar with the incident, you can take on the course and try to support the topic of the essay.
The introduction part of the argumentative essay should be catchy. In the introduction you should explain the subject well. Here, the controversy should be presented along with the thesis. Here are the best of tips to follow. One should make use of the title to present with the exact viewpoint. You can present the title in form of a question. This will sound quite interesting. In the form of essay writing you need to think about the audience. You should think about the part of the issue or the aspect that is sure to convince or interest the audience.
At the time of writing the introduction part you should think of creative ways to present the paper with the effectiveness. You should come up with the clear thesis, and this will help in answering the questions appositely. The thesis will help in marking the position, and the last sentence of the introduction should be completed with a stunt. Argumentative essay is different from the rest. In the kind of essay writing you have clear introductions and conclusions. Reading the same you can understand the main line of argument.
In the body portion of the argumentative essay you should mention the points in the manner to make the audience agree with the thesis. The body should be structured in the manner to help in refuting the objections and the other points of view. You should adopt the reasons and the supporting points when going through the kind of essay writing. You need to have three or more reasons in order to accept the point of the reader, and this will help in defending the position in the essay.
In the argumentative essay you have the kind of direct link with the reader. You write things in the manner to make them believe in you. You should be having three or more reasons in order to make the reader accept your position. This should be stated in the topic sentence of essay writing. All the reasons mentioned in the essay should be supported with arguments. To support your point you can even make use of statistics, examples, anecdotes and authorities. These will make the reason seem plausible. Things should be connected back to back by making use of if and then.
In the form of argumentative essay one must anticipate the opposing objections and positions. You should have in mind the objections of the readers. These objections should be best answered with the arguments and the evidences. You should know about the other positions taken by people based on the subject. You should show reasons in rejecting the positions. In the end of the essay writing, there is the conclusion part. You should prepare a final point which will tell the reader regarding what he should do or think. There should be reasons stating why the reader should adopt your point of view. One should also make use of the anticipating objections in the framing of the conclusion.
One can make use of the best strategies in the framing of the argumentative essay. There are three kinds of argumentative strategies. You have the Classical, the Rogerian and the Toulmin. You can best choose from one of the strategies in the combining and creating of the argument paper. You should make use of the correct strategy in making the argument strong. This is when you get the chance to make the audience agree with you in the course of the essay writing.
In the kind of essay writing you should have clear conception about the parts. In the argumentative essay you should well deal with the sections like narration, partition, argument, refutation and the conclusion. In the narration you should speak about the background and the context. You should also include other things like the statement of the problem or the definition. In the partition one can state the thesis or the claim and can properly outline the arguments.


text:
function [A]=getLaplacian1(I,consts,epsilon,win_size)

  if (~exist('epsilon','var'))
    epsilon=0.0000001;
  end
  if (isempty(epsilon))
    epsilon=0.0000001;
  end
  if (~exist('win_size','var'))
    win_size=1;
  end
  if (isempty(win_size))
    win_size=1;
  end

  neb_size=(win_size*2+1)^2; % neighbour size
  [h,w,c]=size(I);
  img_size=w*h;
  consts=imerode(consts,ones(win_size*2+1)); % erode scribbles

  indsM=reshape((1:img_size),h,w); % create indices for all pixels in image, column first.

  tlen=sum(sum(1-consts(win_size+1:end-win_size,win_size+1:end-win_size)))*(neb_size^2); % calculate how many unknown pixels should be estimated.

  row_inds=zeros(tlen ,1);
  col_inds=zeros(tlen,1);
  vals=zeros(tlen,1);
  len=0;
  for j=1+win_size:w-win_size
    for i=win_size+1:h-win_size
      if (consts(i,j))
        continue % ignore any pixels under scribble regions.
      end
      win_inds=indsM(i-win_size:i+win_size,j-win_size:j+win_size); % get neighbour pixel indices of pixel(i,j).
      win_inds=win_inds(:);
      winI=I(i-win_size:i+win_size,j-win_size:j+win_size,:); % get neighbour pixel matrix from original image
      winI=reshape(winI,neb_size,c); % reshape neighbour pixel matrix into a neb_size*c matrix, each column represents a color channel.
      win_mu=mean(winI,1)'; % get mean value of each channel.
      win_var=inv(winI'*winI/neb_size-win_mu*win_mu' +epsilon/neb_size*eye(c)); % see equation 12.

      winI=winI-repmat(win_mu',neb_size,1); % see equation 12.
      tvals=(1+winI*win_var*winI')/neb_size; % see equation 12.

      row_inds(1+len:neb_size^2+len)=reshape(repmat(win_inds,1,neb_size),...
                                             neb_size^2,1);
      col_inds(1+len:neb_size^2+len)=reshape(repmat(win_inds',neb_size,1),...
                                             neb_size^2,1);
      vals(1+len:neb_size^2+len)=tvals(:);
      len=len+neb_size^2;
    end
  end

  vals=vals(1:len); % cut unused space.
  row_inds=row_inds(1:len); % cut unused space.
  col_inds=col_inds(1:len); % cut unused space.
  A=sparse(row_inds,col_inds,vals,img_size,img_size); % Create the laplacian matrix, holding the sum of second part of equation 12. Note that the row,colomn pairs may have repeated position, so all elements of vals that have duplicate row and column'indices are added together, see the help.

  sumA=sum(A,2);
  A=spdiags(sumA(:),0,img_size,img_size)-A; % Sum of ach row of Laplacian matrix is zero.

return

redpajama_set_name: RedPajamaGithub


Founder and President of the Media Research Center, Mr. Bozell runs the largest media watchdog organization in America. Since its launch in 1987, the MRC has developed the largest video archive in the world; the popular NewsBusters.org blog site; the CNSNews.com internet news service; MRC Business; MRC Culture; and in April of 2014 launched MRC Latino. The MRC has over 800,000 members nationwide, with over 9 million fans on Facebook.
In 2010, Mr. Bozell founded ForAmerica, an organization committed to restoring America to its founding principles. ForAmerica has grown to over 7 million Facebook followers making it the largest social media organization in the conservative movement. It has also registered twice as Facebook's most engaged group on its platform. In 1998, Mr. Bozell founded and was the first president of the Parents Television Council, the largest group in America dedicated to a restoring responsibility to Hollywood. He founded the Conservative Victory Committee PAC in 1987. Before founding the MRC, Mr. Bozell was the finance director and later the president of the National Conservative Political Action Committee.
He has been a guest on numerous television programs, including the O'Reilly Factor, Nightline, The Today Show and Good Morning America. He appeared weekly on the "Media Mash" segment of Hannity, on the Fox News Channel, as well as regular appearances on The Kelly File, Your World with Neil Cavuto and Varney & Co.
Mr. Bozell received his B.A. in History from the University of Dallas, where he was named the 1998 Alumnus of the Year. In 2015 he received an honorary PhD after delivering the commencement address there. He is married, with five children and ten grandchildren.


text:
Hit Makers Troy Sneed & Alvin Darling Team Up For "All Is Well" Tour
Oretha Winston, Lead Editor
Gospel Artists, Troy Sneed and Alvin Darling have teamed up for the "All is Well" Tour 2013, which will kick off, March 14th in Georgia. Earlier this year, Gospel Hit-Maker Troy Sneed promised fans that he would continue touring and promoting his current project "All is Well" and the time has now come.
The "All Is Well" Tour 2013 is geared to encourage hearts that no matter what the circumstance or how you may feel, remember that with God "All Is Well".
Troy Sneed and Alvin Darling have both made a huge impact on the Gospel Music Industry with their chart topping radio hits and projects.
Read: "All Day Jesus"- Canton Jones [WORLD PREMIERE]
Alvin Darling is best known for his Top 5 hit song, "All Night", Top 10 hit "Nobody But the Lord" and Top 20 hit song, "You Can Make It". Sneed is also no stranger to radio success and his hit song repertoire includes, "My Heart Says Yes", "All Is Well", "Lay It Down" and current single "I Know You Hear Me". The first stops of the "All is Well" Tour will begin in St. Mary's GA on Thursday, March 14th at the Young Zion Baptist Church 4500 GA 40 E, St.
The first tour date will be a special Benefit Concert featuring both Sneed and Darling and other artists from the local area.
Immediately following the Georgia date, the tour will continue on Saturday, March 16th in Mobile, AL at Ark of Safety-2700 First Ave and on Sunday, March 17th in Pensacola, FL at the Deliverance Tabernacle Christian-1780 W Detroit Blvd. Fans and supporters can look forward to more dates in several markets across the country. The "All Is Well" Tour will be an exciting time in God as Troy Sneed and Alvin Darling share their heart, testimonies and music.
Like Elev8 On Facebook To Enrich Your Mind, Body & Soul!
Hit Makers Troy Sneed & Alvin Darling Team Up For "All Is Well" Tour was originally published on elev8.com
Alvin Darling	, troy sneed


text:
Pivovar Velke Popovice celebrates its 131st anniversary. It is now the third largest brewery in the Czech Republic
To celebrate its 131st anniversary, Pivovar Velke Popovice gradually handed out gifts, both to itself and other people. During 2005 it reinforced its position as the third largest brewery in the Czech Republic. It is one of the major breweries whose output increases in double-digit figures and today it is approaching the 1.5 million hectolitre mark. Velkopopovicky Kozel beer dominated in many domestic and international competitions of quality. The brewery opened a new visitor route and renewed the historic brewery courtyard. The Velkopopovicky Kozel brand launched a new product – 11° Medium – and after Russia and Slovakia also started up licensed production in Hungary. The history of the brewery and its plans for the future were the subject of discussion at the celebrations of the 131st anniversary of the first brew in the Velke Popovice brewery, which took place at the weekend.
"We are glad that our brewery is able to add another successful link to a long and rich tradition. This motivates us to work even harder, and during the year the brewery succeeded in implementing several important measures. We expanded the Velkopopovicky Kozel portfolio to include the 11° Medium. Output continues to rise – during 2005 this increased by more than 17 % and we are getting near the historic mark of 1.5 million hectolitres of beer a year. In the Czech Republic we continue to strengthen our position as the third-largest Czech brewery, behind Pilsen and Radegast. Our beer is also very successful abroad: due to ever growing exports and above all licensed production, Velkopopovicky Kozel is now the best-selling Czech beer outside the Czech Republic. The confidence of experts and consumers in the beer's quality is confirmed among other things by the titles of Czech beer of the year, Dark beer of the year and the prizes that Velkopopovicky Kozel has won at the international competition Monde Selection in Brussels," said Pavel Semik, manager of the Velke Popovice brewery.
"We are gradually reconstructing and modifying the brewery. In the summer, for example, we reconstructed the historic brewery courtyard according to the original plans and opened the new visitor route, which could be viewed by people attending the traditional June Kozel Day. We are conscious of the connection between the brewery and the region, and as a result are investing not only in developing technology and quality but also in environmental projects, for example water treatment plants, in which we have invested CZK 50 million alone. We also provide significant support to publicly beneficial activities for the Velke Popovice municipality," added Pavel Semik.
Alexej Bechtin, press officer Plzensky Prazdroj, tel.: 257 287 209, 724 617 219
Radim Kovacs, AMI Communications, tel.: 234 124 112, 724 012 617
Plzensky Prazdroj, a. s., is the Czech market leader and, with exports to 50 countries worldwide is also the biggest exporter of Czech beer. Plzensky Prazdroj is part of the international brewing company SABMiller plc, one of the largest in the world, with a presence in 40 countries on four continents.
Velkopopovicky Kozel is a brand that holds an irreplaceable position in the Plzensky Prazdroj portfolio. It is one of the brands with the most dynamic growth, both on the Czech and international markets. Velkopopovicky Kozel dark beer is also the market larder for dark beers in the Czech Republic. Last year, Pivovar Velke Popovice celebrated the 130th anniversary of its foundation in 1874.
You can find up-to-date information on projects supported by the Velkopopovicky Kozel brand at www.kozel.cz.
Velke Popovice
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PLENTY OF ROOM IN ANY SIZE.
X-Large - for heights between 5'11" - 6'1".
*Small, Medium and Large fit 0-14 US sizes, while X-Large fits up to 18 US size.
BUY WITH CONFIDENCE! We are sure about high quality of our products. That's why we offer 30 day money back guarantee and the lifetime warranty on all our products. If you don't like the onesie for any reason, return it within 30 days and get a full refund.


text:
Q: Two way binding on angular material slide toggle not working as expected (Angular 4) I have implemented the angular material slide-toggle that all seems to work except for some reason it isn't binding the value to the relevant variable for some reason?
// other irrevelant imports above..
import {MatDialog, MatDialogRef, MAT_DIALOG_DATA} from '@angular/material';

@Component({
  selector: 'app-calendar',
  templateUrl: './calendar.component.html',
  styleUrls: ['./calendar.component.scss'],
    host: {
     '(document:click)': 'handleClickEvent($event)',
  }
})

export class CalendarComponent implements OnInit {

  filteringSchedule: boolean = false;
  filteringSent: boolean = false;
  filteringFailed: boolean = false;
}

// component
<mat-slide-toggle
    class="calendar-filter-types"
    [ngModel]="(filteringSchedule)"
    [color]=""
    [checked]="">
    Scheduled : {{ filteringSchedule }}
</mat-slide-toggle>

Once I check or uncheck the toggle I would expect the filteringSchedule value to change to true or false accordingly? However within the component it always stays as false for some unknown reason - can anyone suggest why is this?
I am Angular 4

A: [ngModel]="(filteringSchedule)"

Change this to:
[(ngModel)]="filteringSchedule"

A: This works on Angular8+
[(ngModel)]="filteringSchedule"

And make sure you already imported FormsModule
import {FormsModule} from '@angular/forms';

A: Just update your html to
[(ngModel)]="filteringSchedule"

redpajama_set_name: RedPajamaStackExchange


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The wide area around the hamlet offers a unique play ground for kids. Caves, rocks and trees invite the children to play and discover the beauty of nature. Besides, Barranconi offers lots of beautiful places where one can find peace, silence and recovery for oneself.
In the Garden we grow vegetables and in the in the cellar we store jars filled with apricot jam. The fresh products are available for purchase by the guests settled at the hamlet.
For bikers we have prepared small tours which allow the exploration of the place. Hiking trails go through the coast and the hills.


Ah Bordeaux keeps popping up everywhere I look and I'm taking it as a sign that I need to book!
How delicious! I love fresh baked goods in the morning - makes waking up worthwhile.
Absolutely, Claire - after I came back to the cold and crumbly croissants at Sainsbury's, I vowed to book tickets back to Bordeaux (or anywhere in France, for that matter) ASAP!
I'm astonished at just how much eating you packed in! But astonished in a good way.
Haha! Well, we did need 3 meals per day ... plus snacks, of course. ;) It's a foodie's paradise!
I am dying to go here! For the food and the amazing wine tasting. Your posts are giving me a serious case of wanderlust. Beautiful pictures as well.
Oh, I am very hungry now! I've head such lovely things about Bordeaux, and this only confirms that I need to get there SOON.
The food looks so good. I must check out Bordeaux next time I go to France!
It's definitely worth staying for a day or two - I loved our week there and would readily go back again!
You've certainly convinced me to go to Bordeaux!
Me too! I'm definitely going to plan this into to my Summer list!
Haha, you and me both, Lins! Thanks so much for reading. You must be looking forward to New York! It will be magical at that time of year. If you get a chance, brunch at The Standard Grill (part of the Standard Hotel) just under the Highline. I'm sure they'll have gluten-free options and it's just a beautiful place (full of beautiful people) to enjoy. Then you can stroll along the Highline afterwards!
The food in bordeaux sounds divine!! I love my steak rare and miss a good French steak so much!


The Southland Arts Festival is delighted to present Kiss The Sky, supported by The Southern Institute of Technology.
The New Zealand Dance Company (NZDC) forges its stellar national and international reputation for powerful contemporary dance with Kiss The Sky, a diverse magical experience that grabs your attention from start to finish (DANZ).
Kiss The Sky combines the high-octane physicality of Korean choreographer and composer KIM Jae Duk in his work Sigan with the vibrant aesthetic of New Zealand's Victoria Columbus in her world premiere work The Fibonacci for an evening of sensory indulgence (Theatreview).
The Fibonacci is co-commissioned by the Festival of Colour and NZDC. In a tribute to the memory of Susan Paterson, the commission is also generously supported by Jane Vesty, Greg Fahey and Brian Sweeney of SweeneyVesty.
NZDC dancers' versatility, virtuosity and artistry combined with the excellence of the design and production teams (NZ Herald) will leave you dreaming for more.


The Peruvian autumn inspires this pullover sweater or chompa for men designed by Alfredo Falcón. He selects soft baby alpaca wool, the season's first sheer, in warm shades of brown: espresso, chestnut, and camel. This crew neck, long sleeve alpaca sweater would be considered an item of elegant clothing for men intended for important ceremonies, according to longstanding Andean traditions that have historically valued this material.


I'm no doctor, but the quad injury DeMarcus Cousins suffered less than four minutes into Game 2 of the Warriors-Clippers first-round playoff series looked horrifying. A sad scene for a guy who just returned to action in mid-January after missing a full year of ball when he suffered an Achilles injury with the Pelicans.
Cousins is expected to have an MRI Tuesday morning to determine his fate, but reports indicate that it could be a torn quad, an injury that ended Charles Barkley's career back in 1999. The best case scenario would be a strained quad, but this close-up snapshot of Cousins' quad on his walk to the locker room does not look natural.
Hopefully the MRI shows something different than a near certainty of a quad tear.