text:
\section{Introduction}
\label{sec:intro}

Now, as the creation of trapped Bose-Einstein condensates
\cite{ANDE95,BRAD95,DAVIS95} has nearly become a standard technique,
the interest in the field has turned to the manipulation of trapped
condensates. A major goal is the creation of coherent atomic beams
emerging from Bose condensates. Such a device, now called an atom
laser, was first realized in the MIT-group \cite{MEW97}. This
experiment created a rather small number of strong pulses of atoms.
Recently two groups were able to produce continuous
\cite{BLOCH99:1} or at least quasi-continuous \cite{HAGL99:1} coherent
atomic beams.

After the initial proposals of atom-laser models (see references in
\cite{PARK98:1}) the theoretical treatment of atom lasers has
focused on two major lines: the work in
\cite{BALL97,ZHAN98:1,ZHAN98:2,NARA97:2,STEC98:1,kneer98:_gener,%
HUTC99:1,JAPHA99:1,GRAH99:1,BAND99:1,EDWA99:1,SCHNEI99:1} starts
with the coupled Gross-Pitaevskii equations (GPE) (and generalizations
thereof like the Hartree-Fock-Bogoliubov theory) and analyzes the
corresponding solutions either numerically or analytically.

On the other hand, the studies in
\cite{HOPE97,MOY99:1,JACK99:1,HOPE99:1,hope99:_markov,BREU99:1}
concentrate on the characterization of atom lasers using master
equations analogous to the work on optical lasers and calculate
properties like the linewidth of atom lasers.

There are two different means of coherent outcoupling, {\em i.e}
getting atoms out of atom traps, which are investigated both
theoretically and experimentally. A radio frequency can be used to
flip the spin-state of magnetically trapped atoms to an untrapped
state; this so called radio-frequency outcoupling \cite{BALL97} has
been used in \cite{MEW97,BLOCH99:1}. An output coupler based on Raman
transitions was first described in \cite{MOY97} and implemented by the
NIST-group \cite{HAGL99:1}. In rf-outcoupling, the atomic beam just
falls downwards whereas two-photon Raman-outcoupling can be arranged
in such a way that the outcoupled atoms acquire momentum and the
resulting beam may thus be pointed in a specific direction.

Like in our previous work \cite{SCHNEI99:1} we concentrate on
rf-outcoupling describing the setup of the H\"ansch-group
\cite{BLOCH99:1} by a 1D-model based on coupled GPEs. In
\cite{SCHNEI99:1} we were able to characterize the experimental output
rate in a satisfactory way, differences were mainly due to the reduced
dimensionality of the model. Here, we want to investigate a slightly
different setup that was recently realized experimentally: instead of
only one rf-field Bloch {\em et al.} \cite{BLOCH99:2} used two radio
frequencies for outcoupling. Consequently, the coherently outcoupled
atoms have two different energies which leads to a pulsed, coherent
atomic beam. We will analyze the output properties of such a device
depending on the detunings of the radio frequencies and their
difference.

The paper has the following structure: In Sec.~\ref{sec:gpetheory} we
set the notation by introducing the basic facts about GPEs and rf-atom
lasers. In Sec.~\ref{sec:airy} we first show how stationary falling
waves can be described by appropriate combinations of Airy functions.
These are used to model the output of the two-mode atom laser and
to calculate its average output rate. The analytical results of this
section are then compared with numerical solutions of the coupled
GPEs (Sec.~\ref{sec:results}). It turns out that the visibility of the
pulse pattern of the beam can be related to the correlation function of
the trapped Bose gas (here at $T=0$, see also \cite{BLOCH99:2}). In
Sec.~\ref{sec:concl} we summarize our results.

\section{Coupled Gross-Pitaevskii equations with two radio frequencies}
\label{sec:gpetheory}

The properties of Bose condensates of atomic vapors at zero
temperature are very well described by the Gross-Pitaevskii equation
(GPE) (see \cite{DALF98:1} and references therein). It is a nonlinear
Schr\"odinger equation for the order parameter of the system, namely
the macroscopic wavefunction of the Bose condensate, and accounts also
for the coherence properties of the condensate. It may thus serve as a
starting point for considerations in coherent atom optics with Bose
condensates as it was done in \cite{BALL97}: the authors generalized
the GPE to a system of coupled equations that describe the physics of
the trapped and untrapped states of a Bose gas coupled via an rf-field
including the interaction due to collisions.

In the present article, we modify this approach to a situation where
the trapped atoms are exposed to two radio frequencies. Such a setup
has already been analyzed experimentally \cite{BLOCH99:2}. We focus on
a trap with Rb-87 atoms in the $F=1$ hyperfine-manifold. The three
Zeeman sublevels with $m \in \{-1,0,1\}$ are described by macroscopic
wavefunctions $\psi_m$; after applying the dipole approximation the
system of generalized GPEs reads
\begin{eqnarray}
  \label{eq:gpe3dbare}
  i \hbar \frac{\partial}{\partial t} \psi_m(\vec r, t) &=& \nonumber \\
  && \hspace{-1.4cm} \Bigg(-\frac{\hbar^2\nabla^2}{2M} + V_m(\vec r)
      + U ||\psi(\vec r, t)||^2 \Bigg) \psi_m(\vec r, t) \nonumber \\
  && \hspace{-1.4cm} + \sum_{m'} W_{m,m'} \psi_{m'}(\vec r, t)\;.
\end{eqnarray}
We assume that all Zeeman levels interact with the same s-wave
scattering length $a_0 = 110\, a_{\rm Bohr}$ so $U = 4\pi\hbar^2 a_0
N/M$. $||\psi(\vec r, t)||^2 = \sum_m |\psi_m(\vec r, t)|^2$ denotes
the total density in the trap divided by the number $N$ of particles.
The interaction between the atoms and the radio frequency fields with
frequencies $\omega_{\rm{rf},1}$ and $\omega_{\rm{rf},2}$ is described by
\begin{eqnarray}
  \label{eq:Wmm}
  W_{m,m'} &=& 2 \hbar\Omega
  \big(\cos(\omega_{\rm{rf},1} t)+\cos(\omega_{\rm{rf},2} t)\big) \nonumber\\
  && \qquad\quad\times\big(\delta_{m,m'+1} + \delta_{m,m'-1}\big)\;,
\end{eqnarray}
where $\Omega = g_F \mu_{\rm Bohr} B_{\rm rf}/(\sqrt{2}\hbar)$ ($g_F = 1/2$)
is the Rabi frequency corresponding to the magnetic field strength
$B_{\rm rf}$.

We now define $\bar{\omega}_{\rm{rf}} = (\omega_{\rm{rf},1}+\omega_{\rm{rf},2})/2$ to be the average
radio frequency and $\delta_{\rm{rf}} = \omega_{\rm{rf},1}-\omega_{\rm{rf},2}$ as the
difference between the two driving fields. In order to get rid of the high
frequencies, we apply the transformation $\psi_m(t) \rightarrow e^{-i
  m \bar{\omega}_{\rm{rf}} t} \psi_m(t)$ and skip all terms $\propto\exp{(-2 i m
  \bar{\omega}_{\rm{rf}} t)}$ (rotating wave approximation). This turns
Eq.~(\ref{eq:gpe3dbare}) into
\begin{eqnarray}
  \label{eq:gpe3drwa}
  i \hbar \frac{\partial}{\partial t} \psi_m(\vec r, t) &=&
        \Bigg(-\frac{\hbar^2\nabla^2}{2M} + V_m(\vec r)
        +m\hbar\bar{\omega}_{\rm{rf}} \nonumber\\
     && \quad + U ||\psi(\vec r, t)||^2 \Bigg) \psi_m(\vec r, t)
        \nonumber\\
     && + \sum_{m'} \tilde{W}_{m,m'}(t) \psi_{m'}(\vec r, t)
\end{eqnarray}
with
\begin{equation}
  \label{eq:Wmm2}
  \tilde{W}_{m,m'}(t) = 2 \hbar\Omega\cos\big(\delta_{\rm{rf}}t/2\big)
              \big(\delta_{m,m'+1} + \delta_{m,m'-1}\big)\;.
\end{equation}
Equation~(\ref{eq:gpe3drwa}) represents a set of equations in
three dimensions that has to be solved numerically. This is
computationally very demanding.  In earlier work
\cite{BALL97,NARA97:2,STEC98:1,SCHNEI99:1} a one-dimensional (1D)
approach has proven to be quite successful.  Usually, the traps used in
experiments are elongated in the horizontal plane. Like in
\cite{SCHNEI99:1} we choose coordinates where the $z$-axis points {\em
  downwards}, the long axis of the trap is denoted by $y$, the short
horizontal one by $x$. Taking gravity into account, the total
effective potentials in $z$-direction are then given by
\begin{eqnarray}
  \label{eq:veff}
  V_{m,{\rm eff}}(z,t) &=& -m\,M \omega_z^2 z^2/2
  + m \hbar \Delta \nonumber\\
                       && \hspace{2cm} - Mgz + g_{\rm 1D} ||\psi(z,t)||^2\;,
\end{eqnarray}
where $\Delta= \hbar\bar{\omega}_{\rm{rf}} - V_{\rm off}$ denotes the detuning from
the transitions at the trap center ($V_{\rm off} = -g_F \mu_{\rm Bohr}
B_{\rm off}$).  Due to gravity the output coupling proceeds mainly in
the vertical direction so it is natural to choose this direction as
the 1D axis for our model.

To obtain the effective interaction strength $g_{\rm 1D}$ in
Eq.~(\ref{eq:veff}) we require the chemical potential in Thomas-Fermi
approximation in the 1D model (for the trapped $m=-1$ state) to equal
the one of the full 3D situation. This leads to
\begin{equation}
  \label{eq:g1d}
  g_{\rm 1D} = \frac{2}{3} \left( \frac{\omega_y}{\omega_z} \right) ^{\frac{3}{5}}
  \left( \frac{15 N a_0}{a_z} \right) ^{\frac{3}{5}} \hbar\omega_z a_z
\end{equation}
with $a_z = \sqrt{\hbar/(M\omega_z)}$.

The 1D approximation of Eq.~(\ref{eq:gpe3drwa}) then reads
\begin{eqnarray}
  \label{eq:gpe1d}
  i \hbar \frac{\partial}{\partial t} \psi_m(z, t) &=&
  \left( -\frac{\hbar^2}{2M}\frac{\partial^2}{\partial z^2}
       + V_{m,{\rm eff}}(z,t)\right) \psi_m(z, t) \nonumber \\
  && + \sum_{m'} \tilde{W}_{m,m'}(t) \psi_{m'} (z, t)\;.
\end{eqnarray}

In this work, we concentrate on the weak coupling regime of
Eq.~(\ref{eq:gpe1d}) which is characterized by $\Omega < \omega_z$
\cite{MEW97,STEC98:1,BAND99:1}. The condensate is hardly affected in
this regime, it merely changes its overall size due to the loss of
atoms by the outcoupling process \cite{STEC98:1}. In \cite{SCHNEI99:1}
we have pointed out that the coupling between the trapped and
untrapped states is concentrated spatially to the crossing points of
the effective potentials in Eq.~(\ref{eq:veff}). In the present case
where two radio frequencies are present, one expects two such points
of maximal coupling. They are located at
\begin{equation}
  \label{eq:zres}
  \zres = \sqrt{2(\Delta\pm\delta_{\rm rf}/2)
    / (\hbar\omega_z)}\, a_z\;,
\end{equation}
corresponding again to the crossing points of the effective potentials
for either the radio frequency $\omega_{\rm{rf},1}$ or $\omega_{\rm{rf},2}$ (see
Fig.~\ref{fig:pots}).  In Fig.~\ref{fig:densities2res} the densities
of the states $m=-1$ and $0$ ($F=1$) are shown for a specific
situation. The condensate is in the $m=-1$ state, the plot shows a
snapshot of the density distributions after $5\,\mbox{ms}$ of
outcoupling (for further computational details see
Sec.~\ref{sec:results}). The distribution for the $m = 0$ state
demonstrates clearly that the points $\zres$ are indeed the points of
maximum outcoupling; if one considers the two radio frequencies
separately, these points correspond to the classical turning points in
the effective potentials in Eq.~(\ref{eq:veff}) (see
\cite{SCHNEI99:1}).
\begin{figure}[htbp]
  \begin{center}
    \epsfxsize=0.47\textwidth
    \epsffile{fig1.eps}
    \caption{Plot of the densities for $m=-1,0$ ($F=1$) in the trap for
      weak outcoupling. The trapped $m=-1$ state (thick line, scaled
      down by a factor of 20) shows some small excitations on top of
      the ground state. The untrapped $m=0$ state (thin line) exhibits
      pulses for $z\gtrsim 23\,a_z$. The dashed lines denote the resonance
      points $\zres$ from Eq.~(\ref{eq:zres}), here we have
      $\omega_{{\rm rf}1,2} = 2\pi\times(21000 \pm 4500)\,\mbox{Hz}$.}
    \label{fig:densities2res}
  \end{center}
\end{figure}
In the weak coupling region we are considering here, the state $m=1$,
which is also untrapped, is hardly populated at all. For this reason,
its density distribution is not shown in Fig.~\ref{fig:densities2res}
and we will not discuss it further. Nevertheless, it is included in
all numerical calculations.

\section{Airy functions for falling atoms and output flux}
\label{sec:airy}

\subsection{Stationary, falling waves}
\label{sec:fallwav}

Outside the condensate region, the untrapped $m=0$ state feels only
the gravitational potential because the mean field contribution in
$V_{0,{\rm eff}}$ is practically zero there. Therefore, the
wavefunction for the falling particles is a linear combination of Airy
functions, which are the solutions of the Schr\"odinger equation for a
linear potential. The usual Airy function ${\rm Ai}(\xi)$ does not suffice
to describe a continuous, stationary beam of falling atoms. In analogy
to free planar waves, where both cosine and sine are used to form a
traveling wave $\propto\exp(ikx)$, we have to use a special complex
solution of the Schr\"odinger equation for a given energy $E$
\begin{eqnarray}
  \label{eq:psiE}
  \psi_E(z,t) &=& \big\{{\rm Ai}(-\xi_E(z)) -i{\rm Bi}(-\xi_E(z))\big\}
  \,e^{-iE t/\hbar}  \nonumber\\
  &=& {\cal M}(\xi_E(z))\,e^{-i[\Theta(\xi_E(z))+Et/\hbar]}\;.
\end{eqnarray}
The argument $\xi_E(z)$ simply shifts and rescales the $z$-axis
\begin{eqnarray}
  \label{eq:xi}
  \xi_E(z) &=& \frac{1}{l}\left( z + \frac{E}{Mg}\right), \qquad
  l = \left(\frac{\hbar^2}{2M^2g}\right)^{1/3}\;,
\end{eqnarray}
where l is a length scale (see e.g. \cite{FLUEGGE}). The wavefunction
$\psi_E(z,t)$, though being a solution of the Schr\"odinger equation
for a homogenous gravitational field, is not normalizable due to the
exponential growth of ${\rm Bi}(\xi_E(z))$ in the classical forbidden
region $z < -E/(Mg)$. This is to be expected, as it describes a
situation where particles are flowing steadily to $z\to\infty$ without
a source of particles at some finite $z$. Nevertheless, we are only
interested in the classically allowed region where the solution is
perfectly analogous to a freely falling wave.

We will later make use of the asymptotic forms ($z\to\infty$) of
${\cal M(\xi)}$ and $\Theta(\xi)$ \cite{ABRAMOWITZ}
\begin{eqnarray}
  \label{eq:asympt}
  {\cal M(\xi)} &\approx& \frac{1}{\sqrt{\pi}} \xi^{-1/4} \nonumber\\
  \Theta(\xi)   &\approx& \frac{\pi}{4} - \frac{2}{3} \xi^{3/2}
\end{eqnarray}
to obtain a nice interpretation for $|\psi_0(z,t)|^2$.

\subsection{Coherent superposition of two falling waves}
\label{sec:twowaves}

The two radio frequencies driving the condensate should lead to two
different energies in the resulting atomic beam (see
Fig.~\ref{fig:pots}).
\begin{figure}[htbp]
  \begin{center}
    \epsfxsize=0.45\textwidth
    \epsffile{fig2.eps}
    \caption{Effective potentials $V_{m,{\rm eff}}$ and energies
      $E_{1,2}$ of the outcoupled atoms for the two detunings $\Delta
      \pm \delta_{\rm rf}/2$. The two vertical lines denote the
      resonance points $\zres.$}
    \label{fig:pots}
  \end{center}
\end{figure}
The energy of the outcoupled beam for a detuning $\Delta$ is
given by
\begin{equation}
  \label{eq:energy}
  E = \mu - \frac{1}{2}\frac{Mg^2}{\omega_{\rm{z}}^2} - \hbar\Delta\;,
\end{equation}
where $\mu$ denotes the chemical potential.
If we consider the radio frequencies $\omega_{\rm{rf},1}$ and $\omega_{\rm{rf},2}$, we
have to use the two detunings $\Delta_{1,2} =
\hbar\omega_{\rm{rf},1,2} - V_{\rm off}$ to get the energies
$E_{1,2}$ indicated in Fig.~\ref{fig:pots}.

Assuming that the outcoupling process proceeds in a fully coherent
way, the total wavefunction of the outcoupled beam  is given by
\begin{equation}
  \label{eq:psi0}
  \psi_0(z,t) = {\cal N}\big( \psi_{E_1}(z,t) + s \psi_{E_2}(z,t) \big)\;,
\end{equation}
where $\cal N$ is an overall normalization constant and $s$ accounts
for the relative strength of the two contributing waves.  In
experiment, one usually measures the probability density
$|\psi_0(z,t)|^2$ via some imaging technique. If the two energies
$E_{1,2}$ are not too different from each other with respect to the
mean energy $\bar{E} = (E_1+E_2)/2$, {\em i.e.} $\hbar\delta_{\rm
  rf}/{\bar E} \ll 1$, then Eq.~(\ref{eq:psi0}) can be Taylor-expanded
around $\bar E$.  Taking the asymptotic forms in Eq.~(\ref{eq:asympt})
into account, we can write $|\psi_0(z,t)|^2$ as
\begin{eqnarray}
  \label{eq:psi02}
  |\psi_0(z,t)|^2 &=& \tilde{{\cal N}}^2 {\cal M}^2(\xi_{\bar E}(z))
  \nonumber\\
  && \times \big\{ 2 + 2 P \cos (\phi(z,t)-\alpha) \big\}
\end{eqnarray}
with the phase
\begin{equation}
  \label{eq:phizt}
  \phi(z,t) = \delta_{\rm rf}t - \frac{\hbar\delta_{\rm rf}}{Mgl}
    \sqrt{\xi_{\bar E}(z)}\;,
\end{equation}
the modified norm
\begin{equation}
  \label{eq:modnorm}
  \tilde{{\cal N}}^2 = {\cal N}^2 \frac{1+|s|^2}{2}\;,
\end{equation}
and
\begin{equation}
  \label{eq:Pvons}
  P = \frac{2 |s|}{1+|s|^2}\;.
\end{equation}
Apart from the ${\cal M}^2$-dependence, Eq.~(\ref{eq:psi02}) has the
typical form of an interference term with $P$ being the visibility.
The maxima of this term describe the falling of pulses emerging
from the trap. They are located at
\begin{equation}
  \label{eq:zmax}
  z_k = -\frac{\bar E}{Mg} +
       \frac{1}{2}g \bigg( t - \frac{2\pi k + \alpha}{\delta_{\rm
           rf}}\bigg)^2,
       \qquad k\in{\mathbb{N}}_0\;,
\end{equation}
corresponding to a pulse frequency $\nu_{\rm pulse} = \delta_{\rm
  rf}/(2\pi)$. This is exactly in analogy to ``mode-locking'' of two
modes in a laser.

The phase $\alpha$ of $s = |s|e^{\alpha}$ appearing in the above
equations is responsible for a shift of the interference pattern i.e.
the pulses. Eq.~(\ref{eq:psi0}) describes the output of the atom laser
only after it has reached a kind of stationary operation. We therefore
use $\alpha$ merely as a free parameter to shift the pulses in time.

\subsection{Rate of outcoupling}
\label{sec:rates}

To determine the normalization factor of the wavefunction $\cal N$ in
Eq.~(\ref{eq:psi0}) we use the fact that in 1D the flux density $j_z$
equals directly the rate of atoms going through a point. $j_z$ can be
written as
\begin{eqnarray}
  \label{eq:jzprinc}
  j_z(z,t) &=& |\psi_0(z,t)|^2 v_z(z), \\
  \label{eq:vz}
  v_z(z)   &=& -\frac{\hbar}{M}\frac{\partial\Theta}{\partial z} =
  \frac{\hbar}{Ml}\sqrt{\xi_{\bar E}(z)}\;,
\end{eqnarray}
$v_z$ being the velocity of atoms in z-direction. Eq.~(\ref{eq:vz}) is
obtained by considering only the leading terms in $\xi_E(z)$ for
$z\to\infty$.
Averaging over time in Eq.~(\ref{eq:jzprinc}) finally leads to
\begin{equation}
  \label{eq:jz}
  j_z = \frac{\hbar}{2\pi Ml} \tilde{{\cal N}}^2\;.
\end{equation}

In \cite{STEC98:1}, Steck {\em et al.} gave a formula for the outcoupling
rate of a three dimensional trap in the weak coupling limit.
Analogously, this result can be derived for the 1D situation we are
interested in (see \cite{STEC97:1}). The rate for one resonance point
$z_{\rm res}$ (resulting from a detuning $\Delta)$ is given by
\begin{equation}
  \label{eq:gamma1d}
  \Gamma^{\rm 1d}_{z_{\rm res}} =
  2\pi\bigg(\frac{\Omega}{\omega_{\rm{z}}}\bigg)^2
  \frac{|\psi_{-1}(z_{\rm res})|^2}{\sqrt{2\Delta/\omega_{\rm{z}}}}a_z\omega_{\rm{z}}\;.
\end{equation}
We now assume that the rates at the two resonance points $\zres$ add
up to the total outcoupling rate. This rate must be equal to $j_z$, so
finally with the help of Eq.~(\ref{eq:jz}) we arrive at an expression
for the normalization
\begin{equation}
  \label{eq:norm}
  \tilde{{\cal N}}^2 = \frac{\pi Ml}{2\hbar}
             \left( \Gamma^{\rm 1d}_{z_{\rm{rf},1}} + \Gamma^{\rm 1d}_{z_{\rm{rf},2}} \right)\;,
\end{equation}
where $\Gamma^{\rm 1d}_{\zres}$ is obtained from the detunings
$\Delta\pm \delta_{\rm{rf}} /2$.

Inspection of Eq.~(\ref{eq:psi0}) shows that $|s|$ should
reflect the relative outcoupling rates at the two resonance points. We
define it via
\begin{equation}
  \label{eq:visib}
  |s|^2 = \frac{\Gamma^{\rm 1d}_{z_{\rm{rf},1}}}
               {\Gamma^{\rm 1d}_{z_{\rm{rf},2}}}\;,
\end{equation}
which leads to
\begin{equation}
  \label{eq:Pgamma}
  P = 2 \frac{\sqrt{\Gamma^{\rm 1d}_{z_{\rm{rf},1}} \Gamma^{\rm 1d}_{z_{\rm{rf},2}}}}
             {\Gamma^{\rm 1d}_{z_{\rm{rf},1}} + \Gamma^{\rm 1d}_{z_{\rm{rf},2}}}\;
\end{equation}
for the visibility.
The numerical results in the next section show that this is indeed
the correct expression. If the frequency difference $\delta_{\rm rf}$
is very small, one can also use
\begin{eqnarray}
  \label{eq:n2approx}
  \tilde{{\cal N}}^2 &=& \frac{\pi Ml}{\hbar}
  \Gamma^{\rm 1d}_{z_{{\rm res}}}\;,\\
  \label{eq:sapprox}
  |s|^2 &=& \frac{|\psi_{-1}(z_{\rm{rf},1})|^2}
               {|\psi_{-1}(z_{\rm{rf},2})|^2}\;,\\
  \label{eq:papprox}
  P &=& 2 \frac{|\psi_{-1}(z_{\rm{rf},1})| |\psi_{-1}(z_{\rm{rf},2})|}
               {|\psi_{-1}(z_{\rm{rf},1})| + |\psi_{-1}(z_{\rm{rf},2})|}\;,
\end{eqnarray}
which shows that $P$ is related to the correlation function of the
trapped Bose gas \cite{BLOCH99:2}.

\section{Numerical results}
\label{sec:results}

\subsection{Numerical method and observation of pulses}
\label{sec:method}

To solve the 1D GPEs in Eq.~(\ref{eq:gpe1d}) numerically we propagate
the wavefunctions with a usual split-operator algorithm using FFT on a
1D grid. As starting condition we always use the ground state of
the trapped $m=-1$ state, which we obtain by imaginary time
propagation.

The coupling of the Zeeman levels via the rf-field is implemented in a
very straightforward way: if the right hand side of
Eq.~(\ref{eq:gpe1d}) is written as $H\psi$, one can split up the
Hamiltonian $H$ in an obvious way $H=T+V(t)+W(t)$. The kinetic and
potential parts $T$ and $V(t)$ are taken care of by the
FFT-split-operator technique. It is sufficient to treat the coupling
part $W(t)$ separately in the most simple way by keeping only the
terms up to first order in the propagation time. The propagator from
time $t$ to $t+\Delta t$ then reads
\begin{equation}
  \label{eq:propa}
  U(t,t+\Delta t) = U_0(t,t+\Delta t)
                    \left( 1 - \frac{i}{\hbar}W(t)\Delta t \right)\;,
\end{equation}
where $U_0$ is the split-operator propagator for $T+V(t)$.

The trap parameters are basically taken from \cite{BLOCH99:1}, the
trapping frequency for the $m=1$ state is $\omega_z = 2\pi \times
127\,\mbox{Hz}$. We often use harmonic oscillator units, the length
unit is $a_z = 0.95\,\mbox{$\mu$m}$, time is measured in $1/\omega_z =
1.3\,\mbox{ms}$.

To investigate the output in our atom-laser model we have propagated
the initial wavefunction for up to $\approx 30\,\mbox{ms}$ with different
coupling parameters. We kept the coupling strength rather low to
ensure a clear separation of the time scales for Rabi oscillations and
for the pulses predicted in the previous section. We typically use a
magnetic field strength of $B_{\rm rf} = 0.1\,\mbox{mG}$ that is also
used in the latest experiments in the H\"ansch group \cite{BLOCH99:2}.
This amounts to a Rabi frequency of $\Omega = 2\pi \times
70\,\mbox{Hz}$, which is less than the trapping frequency $\omega_z$
and the pulse frequency $\delta_{\rm rf}$ (see below
Eq.~(\ref{eq:zmax})). All calculations were done with $N =
5\times10^5$ atoms in the trap.

In Fig.~(\ref{fig:twomode3d}) we show the density distribution of
the outcoupled state as a function of both space and time. The atomic
beam emerging from the condensate clearly exhibits the pulses predicted
in section \ref{sec:twowaves}.
\begin{figure}[!htbp]
  \begin{center}
    \epsfxsize=0.48\textwidth
    \epsffile{fig3.eps}
    \caption{Plot of the outcoupled density.
      The atoms in the free $m=0$ state emerge primarily at the two
      resonance points (cf. Fig.~\ref{fig:densities2res}) and then
      fall downwards (to the right in the plot). One can clearly see
      the pulse trains emerging from the condensate region that
      extends to $z \approx 22\,a_z$. The radio frequency detunings
      in this plot are $\Delta_{1,2} = 2\pi\times (19.5\pm
      3.0) \,\mbox{kHz}$.}
    \label{fig:twomode3d}
  \end{center}
\end{figure}
To prove that these pulses really follow the trajectories in
Eq.~(\ref{eq:zmax}), Fig.~\ref{fig:contour} shows a contour plot of
the data in Fig.~\ref{fig:twomode3d}.  As we mentioned in
Sec.~\ref{sec:twowaves}, we used the phase $\alpha$ in
Eq.~(\ref{eq:zmax}) to shift the trajectories in time. Apart from
this, the pulses show the correct behavior, they start between the two
resonance points at $-\bar E/(Mg)$ and appear with the right
frequency.
\begin{figure}[tbp]
  \begin{center}
    \epsfxsize=0.47\textwidth
    \epsffile{fig4.eps}
    \caption{Contour plot of the data in Fig.~\ref{fig:twomode3d}. The
      full lines are the contour lines for $|\psi_0(z,t)|^2 a_z =
      0.001,0.002,0.003$. The dashed lines denote the trajectories of the
      pulse maxima from Eq.~(\ref{eq:zmax}).}
    \label{fig:contour}
  \end{center}
\end{figure}

\subsection{Output rates and visibility}
\label{sec:visib}

In this section we want to compare the numerical results to the
analytic predictions of Sec.~\ref{sec:airy}. All results were obtained
by keeping the frequency $\omega_{\rm{rf},2}$ fixed such that the corresponding
resonance point is at the center of the condensate ($z_{\rm{rf},2} = z_{\rm
  sag} = g/\omega_{\rm{z}}^2, \Delta_2 = 2\pi\times 16.5\,\text{kHz}$).
$\Delta_1$ is then given by $\Delta_1 = \Delta_2 + \delta_{\rm
  rf}$; we consider only positive rf~differences $\delta_{\rm rf} = 0\ldots
2\pi\times 13\,\text{kHz}$.

The visibility in Fig.~\ref{fig:densities2res} is rather high, namely
$P = 0.90$. If one increases $\delta_{\rm{rf}}$, the visibility drops down, as
can be seen in Fig.~\ref{fig:visibdensity}. This is due to the fact
that it depends mainly on the quotient of the wavefunctions at the
resonance points (see
Eqs.~(\ref{eq:visib},\ref{eq:Pgamma},\ref{eq:gamma1d})), which
decreases if one pushes $z_{\rm{rf},1}$ further to the boundary of the
condensate.

One can now take
Eqs.~(\ref{eq:gamma1d},\ref{eq:Pgamma},\ref{eq:psi02}) to calculate
the visibility and the norm of the Airy functions from
Sec.~\ref{sec:airy} using the values of $|\psi_{-1}(\zres)|$ either
from the Thomas-Fermi (TF) approximation \cite{DALF98:1} or directly
from the numerical calculations. The dashed line in
Fig.~\ref{fig:visibdensity} is obtained in this way using the
numerical values, outside the condensate it fits the numerical
calculations quite well. The Thomas-Fermi result (not shown) is only
slightly different. The total output rate $\Gamma^{\rm 1d}_{z_{\rm{rf},1}} +
\Gamma^{\rm 1d}_{z_{\rm{rf},2}}$ can be calculated via Eq.~(\ref{eq:norm})
from $\tilde{\cal N}^2$; we compared it to the initial decay constant
of the condensate occupation and found good agreement.
\begin{figure}[!htbp]
  \begin{center}
    \epsfxsize=0.48\textwidth
    \epsffile{fig5.eps}
    \caption{Plot of the density distributions of the atom laser (see
      also Fig.~\ref{fig:densities2res}). This plot is made after
      $5\,\text{ms}$ of operation with $\delta_{\rm{rf}} = 2\pi\times
      12000\,\text{Hz}$. The right resonance point is in the wing of
      the condensate so the visibility drops to $P=0.61$.
      The dashed line is a plot of the function in
      Eq.~(\ref{eq:psi02}) with the normalization of
      Eq.~(\ref{eq:norm}). The density of the untrapped state goes
      down to zero around $z=40\,a_z$ due to absorbing boundary
      conditions used in the calculations.}
    \label{fig:visibdensity}
  \end{center}
\end{figure}

After having shown that the output can be characterized by the
wavefunction in Eq.~(\ref{eq:psi02}), we want to compare further the
semi-analytic results of Sec.~\ref{sec:airy} to the numerics. For
different $\delta_{\rm{rf}}$ one can plot the visibilities obtained either by
fitting the data or by calculating $P$ via (\ref{eq:Pgamma}) using the
TF-approximation or the values of $|\psi_{-1}(\zres)|$ from the
numerics.  Fig.~\ref{fig:visibility} demonstrates the result: the
TF-approximation (full line) fits the semi-analytic values (triangles)
quite well. Like in an experiment, we tried to fit the density
distribution (\ref{eq:psi02}) to our numerical data at a fixed time to
get values for $P$. As the figure shows, these values are in a
reasonable agreement with the other results.
\begin{figure}[!htbp]
  \begin{center}
    \epsfxsize=0.48\textwidth
    \epsffile{fig6.eps}
    \caption{Visibility versus radio frequency difference. The full
      line is obtained from the Thomas-Fermi approximation. The
      triangles are calculated from the numerical values of
      $\psi_{-1}(\zres)$ at a specific time. The points denoted by
      circles are obtained by fitting the density distribution
      (\ref{eq:psi02}) to the numerical data at fixed time (after
      $\approx 7.5\,\text{ms}$ of outcoupling). The error for these
      values is smaller than 5\% and was conservatively deduced from
      the fitting procedure.}
    \label{fig:visibility}
  \end{center}
\end{figure}
\begin{figure}[!htbp]
  \begin{center}
    \epsfxsize=0.48\textwidth
    \epsffile{fig7.eps}
    \caption{Density distribution of the untrapped state for $\delta_{\rm{rf}}
      = 2\pi\times 2000\,\text{Hz}$. The pulses have a substructure
      originating from roughly twice the difference frequency
      $\delta_{\rm{rf}}$.}
    \label{fig:pulses}
  \end{center}
\end{figure}
In Fig.~\ref{fig:visibility} we have not shown values for $\delta_{\rm{rf}} =
2\pi\times 2\,\mbox{kHz}$.  The reason for this is a resonance
phenomenon in this region that leads to a more complicated pulse
structure (Fig.~\ref{fig:pulses}) and prevents us from fitting
(\ref{eq:psi02}) to the data. The origin of this resonance is unclear
up to now, there are indications however that it is related to the
creation of small particle-like excitations in the condensate via a
process that is second order in the output coupling strength.

The small wiggles on top of the condensate density distribution in
Figs.~\ref{fig:densities2res} and \ref{fig:visibdensity} indicate the
presence of such excitations also for $\delta_{\rm{rf}}$ away from $2\pi\times
2\,\mbox{kHz}$. They are so small for these frequency differences that
the assumption made above Eq.~(\ref{eq:norm}) that the outcoupling
process proceeds as if the two radio frequencies were applied
separately is really satisfied, {\em i.e.} there are hardly any
processes of second order in the rf-coupling $\hbar\Omega$.

\section{Conclusion}
\label{sec:concl}

We have shown in this work that a rf-atom laser driven by two radio
frequencies --- a two-mode atom laser --- gives rise to a coherently
pulsing beam of atoms. We have given formulas for the output rate of
such a device and for the visibility of the pulse pattern of the
atomic beam. These analytic results are valid for atom lasers operated
at very low temperature (virtually $T=0$) and with weak output
coupling.

The main limitation of our results comes from dimensionality: we use a
1D model for our calculations instead of a full 3D treatment. In
\cite{SCHNEI99:1} we have shown that the output rate of a rf-atom
laser operated with one frequency can be calculated by the 1D model in
qualitative agreement with experiment. Accordingly, apart from
quantitative agreement of the output rates our model reproduces the
experimental features quite well \cite{BLOCH99:2}.

We did not address the problem of a pump for a true cw-atom laser.
Instead, we considered rather small couplings that ensure a continuous
and smooth operation for about $20-50\,\text{ms}$ but with slowly
decreasing output rates. After this time only very few atoms are left
in the atom trap. The output of a true cw-atom laser should
be very similar to that of our situation.

Coherently pulsing beams of atoms are certainly of interest for
applications in quantum and atom optics. The setup described in this
paper produces beams that always point downwards due to gravity. It
should be possible to use a similar setup with two different
two-photon Raman transitions to create a pulsed beam that can be
pointed in any direction by using the momentum kick from the
absorption-emission process.

Finally, if one uses more than two frequencies, one might create
pulsed beams with shorter pulses while keeping their repetition rate
fixed in analogy to a mode-locked optical laser \cite{ANDE98:1}.

\acknowledgements
We thank Immanuel Bloch and Tilman Esslinger for fruitful discussions.
Financial support by DFG under Grant Nr. SCHE~128/7-1 is
gratefully acknowledged.

redpajama_set_name: RedPajamaArXiv


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text:
What is midp in mobile computing?
January 22, 2021 By admin Tips
Mobile Information Device Profile (MIDP) is a specification for the use of Java technology for mobile devices. In the context of software development, MIDP sits on top of the Connected Limited Device Configuration (CLDC). Applications written with MIDP are normally designed for cell phones and PDAs.
Is Java available on mobile?
Java for mobile devices relies on the Java Platform, Micro Edition (Java ME), which provides a robust, flexible environment for applications running on mobile and other embedded devices: mobile phones, personal digital assistants (PDAs), TV set-top boxes, and printers.
What is Java support in mobile?
Java is deployed in personal computers; corporate servers; mobile devices, including cell phones; and other devices, including TV devices like TiVo. The Java Platform, Micro Edition, or Java ME, is specifically designed for embedded systems, including mobile devices like mobile phones.
How can I download Java on my phone?
Copy both APK files to the root directory of your Android device. Run the APK files to install them onto your device. Download JADGen on your computer, and then use it to create a JAD file for any JAR files you want to run….Find and download a Java emulator for Android.
phoneME.
JBED.
JBlend.
Netmite.
What does MIDP stand for?
Master Information Delivery Plan
The Master Information Delivery Plan (MIDP), is a primary plan which is used to manage the delivery of information during the project lifecycle.
Is mobile Java or bedrock?
The original version of Minecraft, purchasable through the Minecraft website, is dubbed the Java Edition. The version of Minecraft that you can grab on consoles, mobile devices, and through the Microsoft Store, is referred to as the Bedrock Edition.
Is bedrock on mobile?
Bedrock, or Bedrock Edition, is the version of Minecraft that brings together consoles, iOS/Android, and Windows 10.
Do Android phones use Java?
Current versions of Android use the latest Java language and its libraries (but not full graphical user interface (GUI) frameworks), not the Apache Harmony Java implementation, that older versions used. Java 8 source code that works in latest version of Android, can be made to work in older versions of Android.
How do I enable Java on my phone?
Click the menu button in the browser. Select "Settings" (located towards the bottom of the menu screen). Select "Advanced" from the Settings screen. Check the box next to "Enable Javascript" to turn the option on.
What artists were big in the 50s?
What antiemetic is given before chemotherapy?

redpajama_set_name: RedPajamaCommonCrawl


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Platform extensions to the Red and Blue lines will allow DART to upgrade to three-car trains during peak periods. In Part Four of our series Raising the Bar: Platform Extensions, we will be delving into how much this project will cost, and how it gets paid for.
Federal funding from the Federal Transit Administration's (FTA) Capital Investment Grants (CIG) program covers $60.8 million of the platform extensions project. The CIG is a discretionary grant program that funds transit capital investments, including heavy rail, commuter rail, light rail, streetcars, and bus rapid transit. DART received two grants: an initial CIG grant of $58.8 million, followed by a further $2 million grant in November 2018.
The state government's contribution to the platform extensions project amounts to $60 million and comes from a grant from the Texas Department of Transportation's Mobility Fund.
Local DART funding makes up the remaining $8 million in funding for the project, which comes from a 1% local sales tax dedicated to transit.
With the project fully funded, the next steps will be to award contracts, which DART expects will occur within the next few months. Construction work on the platform extension will be carried out in five phases, keeping trains running throughout.
To keep up to date with the progress of the platform extensions project, check out www.dart.org/about/expansion/platformextensions.asp and stay tuned for updates on DART Daily.


Burgos,at a height of 890m and with the Atlantic coast approximately 120km to the north, there will be no winter warming effect by the sea. There will be a chance of night time frost in the winter and a chance of snow.
Summertime average temperatures are amongst the lowest for Spanish cites though daytime temperatures are likely to be very good in the sunshine. The altitude effect will mean cooler temperatures when the sun is not shining.


text:
Boris' Buzzer-Beater
Renovations begin to turn former KKK meeting spot into racial harmony site (ABC)
Newark police: No officer fired a single shot in 2020, thanks to de-escalation program (News 12 NJ)
"Action may not always bring happiness, but there is no happiness without action" —Benjamin Disraeli
"The unique ability to take decisive action while maintaining focus on the ultimate mission is what defines a true leader." — Robert Kiyosaki
Boris' Buzzer Beater: A Last-Minute Lockdown Decision
(Christopher Furlong via Getty Image)
A fast-spreading variant of COVID-19 is sweeping through the UK, threatening to overwhelm hospitals already hard-pressed. On Sunday, Scotland's first minister Nicola Sturgeon, noted for having taken decisive action last year to try staying ahead of the pandemic, announced another full-scale lockdown for her country.
Britain's prime minister Boris Johnson acknowledged current controls on daily life in England were insufficient, then waited a day to impose a similar shutdown. He declared a strict new nationwide lockdown late Monday, and ordered schools and colleges to shutter their campuses and return to remote learning. The restrictions will remain in effect at least until the middle of February.
Johnson has been fiercely criticized for his handling of the pandemic, and can't seem to catch a break. Two vaccines seen as the way out of the formidable, ten-month-long health crisis just arrived on the scene. But that good news was overshadowed by the frightening escalation in new coronavirus cases. In London and southeast England the numbers of new infections spiked close to 60,000 a day, putting hospitals under acute pressure.
For Johnson's critics, Monday's developments illustrate his tendency to postpone important decisions until the last minute. Supporters said he was simply trying to balance public health issues with the devastating impact on the economy. But pressure was growing even within Johnson's own Conservative Party. Earlier Monday, senior lawmaker and former health secretary Jeremy Hunt tweeted that it was "time to act" and "to close schools, borders, and ban all household mixing right away." The head of the global public health program at Scotland's University of Edinburgh concurred: "He's already late. The situation is dire with the new variant. They have to manage borders, pause schools, and stop mixing between households."
In the end, Johnson's decision was inevitable. "It's clear that we need to do more together to bring this new variant under control while our vaccines are rolled out," he said in a televised address.
On Tuesday, Sturgeon said Scotland's lockdown, which includes a ban on non-essential travel, applied to President Trump, putting an end to rumors that Trump would visit his Turnberry golf resort on January 20 during President-elect Joe Biden's inauguration.
Norway Sells The Most EVs. Shocking, Isn't It?
(Sean Gallup via Getty Images)
Norway is the first country where electric car sales have overtaken sales of those powered by any other means.
Battery electric vehicles (BEVs) made up 54.3% of all new cars sold in Norway in 2020. That's a global record, up from 42.4% in 2019 and from a mere 1% of the overall market a decade ago.
Volkswagen's Audi brand topped the 2020 leaderboard with its e-tron sports utility and sportsback vehicles as the most sold new passenger cars in Norway last year, while Tesla's mid-sized Model 3, the 2019 winner, was relegated to second place.
Despite being an oil-producer, Norway exempts fully electric vehicles from taxes imposed on those relying on fossil fuels. The policy has turned the country's car market into a laboratory for carmakers seeking a path to a future without internal combustion engines. (Guardian)
On Delisting Chinese Comms Companies, NYSE Can't Seem To Make A Call
Last November, President Trump signed an executive order banning American firms and individuals from owning stock in 31 Chinese companies previously listed as having ties to the Chinese military. The order was set to take effect on January 11 and gave investors until November 2021 to divest.
The administration stepped up its hard-line stance against China in December when the US Commerce department added dozens of Chinese companies to a trade blacklist, accusing Beijing of using its firms to harness civilian technologies for military purposes.
On January 2, the New York Stock Exchange (NYSE) began delisting three Chinese telecom firms: China Mobile, China Unicom, and China Telecom. China announced it would be taking "necessary measures" to safeguard the interests of its companies.
Then, late Monday, the NYSE announced that "in light of further consultation … [it] no longer intends to move forward with the delisting action." A spokesperson for the exchange declined further comment. (MSN, Axios)
China blocks entry to WHO team studying COVID's origins (Guardian)
Trump administration targets Iran steel sector with new sanctions (Aljazeera)
Facial Recognition And Beyond: Journalist Ventures Inside China's 'Surveillance State' (NPR)
The scope of China's use of forced labor in Xinjiang is bigger than we knew (Axios)
Qatar crisis: Gulf states vow 'solidarity' as Saudis end embargo (BBC)
UK Lockdown: Schools, Colleges to Close as Coronavirus Variant Rages (NYT, $)
Death of Chinese tech worker fuels anger over brutal hours (WaPo, $)
Analysis: What to make of Iran's half-measures (CNN)
How the Gulf crisis spurred Qatar to expand its military (Aljazeera)
Singapore says COVID-19 contact-tracing data can be requested by police (NPR)
Hong Kong Police Arrest Dozens of Pro-Democracy Leaders (NYT, $)
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Georgia Goes Down To The Wire
It was a very late night for those watching Georgia's two runoff elections, with the lead changing at head-spinning turns. Between the two Democrats, Reverend Raphael Warnock had received more votes than fellow Democrat Jon Ossoff, perhaps because Warnock is a Georgia native and pastor of the renowned Ebenezer Baptist Church.
Warnock was leading his incumbent Republican opponent, Kelly Loeffler, by 34,000 votes at 11:17 pm ET when he was projected as the winner by Buzzfeed. Loeffler was appointed and had not distinguished herself in any way other than to tout her support of President Trump. Unless something changes, Warnock will become the state's first African American Senator, and only one of three African Americans in the Senate when his term begins.
Ossoff's race against David Perdue was still too close to call. Perdue is the first cousin of the former governor of Georgia, Sonny Perdue, who is currently President Trump's Secretary of Agriculture. (Buzzfeed)
Trump Administration Takes On House Cats For Title Of Birds' Greatest Enemy
The Trump administration keeps busting up the furniture and setting fire to the drapes on its way out the door. This week the Department of the Interior (DOI) and what's left of the Environmental Protection Agency (EPA) delivered parting gifts to fossil fuel companies and other major polluting industries. On Monday, the hollowed-out EPA finalized a measure effectively barring some scientific studies from consideration when the agency is drafting public policies.
And on Tuesday, the DOI gutted protections for migratory birds, meaning companies won't be held liable for "unintentionally" killing any feathered flyers, whether by toxic oil spills, waste in ponds, electrocution on power lines, or even by illegally spraying banned pesticides.
These two so-called "midnight regulations" are among the last major environmental rollbacks expected from the Trump administration, and they'll present an immediate challenge to the incoming Biden administration which has pledged to suspend and reverse many of these last-minute "conflagration" regulations.
And while industry leaders and administration officials say they expect businesses to continue to 'voluntarily' protect bird habitats, environmentalists called the decision just plain cruel. "It's horrendous," said the director of litigation at the Center for Biological Diversity. "It will just have a really overwhelming negative effect on our already dwindling bird populations." (NYT)
Senate GOP opposition grows to Electoral College challenge (Politico)
Top US business leaders call on Congress to certify election results (Guardian)
Facebook will resume political ad ban in Georgia after polls close (Axios)
Justice Dept. Seeks to Pare Back Civil Rights Protections for Minorities (NYT, $)
Biden to tap more Obama vets to fill key national security roles (Politico)
Prosecutor Announces No Charges Will Be Filed Against Officer Who Shot Jacob Blake (NPR)
Delay, dismantle, resist: DeVos leaves a legacy like no other Education secretary (Politico)
Proud Boys leader released, must leave DC before Trump rally (Aljazeera)
FBI, NSA say ongoing hacks at US federal agencies 'likely Russian in origin' (TechCrunch)
Pennsylvania GOP Refuses To Swear In Democratic Incumbent After His Victory (NPR)
'Lazy,' 'Money-Oriented,' 'Single Mother': How Union-Busting Firms Compile Dossiers on Employees (Vice)
What Comes After Veganuary? Fe-brew-ary?
Raise your hand if you're among the record number of people who signed up to turn January into "Veganuary" by eating only plant-based foods for the entire month. (If you're in Texas, Nebraska, or Kansas you can skip this part.)
Veganuary is a global campaign that challenges people to give up eating animals for a month in favor of the alternatives out there. 500,000 people signed up, double the number who pledged to go vegan for January 2019. Of this year's half-million contestants, 150,000 are in Latin America, 125,000 in the UK, 50,000 in Germany, and 80,000 in the US.
OK, so it's not a huge percentage of the global population, but it's a start. There are plenty of good reasons to cut down on the amount of animal foods in our diets, from reducing animal suffering to lessening the environmental damage caused by food production, not to mention improving our own health.
The World Health Organization declared processed red meat to be a carcinogen in 2015, and unprocessed red meat such as steaks and chops to be a probable carcinogen. Yet people in rich nations still eat more than the recommended amount of red meat, which is also linked to heart disease, strokes, and diabetes. Plus, scientists say cutting out meat is the single best way individuals can tackle climate and wildlife crises.
The biggest reason people give for not trying plant-based meat is that they don't think it will taste good. They'd have to eat those words if they tried an Impossible Whopper from Burger King. (Guardian)
Brazil Is Famous for Its Meat. But Vegetarianism Is Soaring. (NYT, $)
Scientists Are Hunting for a Mysteriously Missing Supermassive Black Hole (Vice)
The race to save an Indigenous Brazilian language from extinction (Aljazeera)
Court says Uber can't hold users to terms they probably didn't read (ArsTechnica)
These spiders may sew leaves into fake shelters to lure frogs to their doom (Science News)
Agriculture Industry Bets on Carbon as a New Cash Crop (WSJ)
One in three US rivers have changed color since 1984. Here's what this means (Salon)
Inclusive design pioneer August de los Reyes dies of COVID-19 complications (Fast Company)
More Birds Bring More Happiness, According to Science (Audubon)
Renewables produce more power than fossil fuels in Germany for first time (Clean Energy Wire)
Finally, a story that's very close to our hearts: The absolute best way to make peanut butter (Salon)


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text:
Tamera Mowry Explains Why She 'Cried Multiple Times' During The Masked Singer
Celebrity By TooFab Staff | 4/22/2021 1:54 PM PT
Getty/Fox
"It was such an amazing journey and I am a different person because of it. I'm stronger."
Tamera Mowry-Housley is opening up about her experience competing on "The Masked Singer."
In an interview with People, the actress-singer reflected on her stint on the Fox reality competition series, revealing she even "cried multiple times." For those who missed it, Tamera, 42, was eliminated on Wednesday night's episode of "The Masked Singer" and was revealed to be the Seashell.
Masked Singer Double-Elimination Unmasks Two Teen Idols -- From Different Worlds of Entertainment
"For me, it was about facing the fear, not hiding anymore, tapping into something that I have loved to do for years and just going for it, taking that big leap of faith," Tamera said. "I was shaking in my boots, literally -- Seashell had boots."
"I cried multiple times because there were moments I wanted to run the opposite way, because I hadn't performed in over 20 years," she continued. "And you are brought into this whirlwind. It was me up against the girl that was afraid to sing, afraid of what people would say, afraid of the critiques, afraid of even succeeding. Every single time I made it to the next round, I was like, 'I'm going to do this all over again!' But it was such an amazing journey, and I am a different person because of it. I'm stronger. I had the best time."
While the "Sister, Sister" star admitted that she hoped she went farther in the competition, she said she's "so grateful" to have made it to the Super 8.
"I knew what I was up against. You can hear the voices," Tamera told People. "And I am so grateful I made it as far as I did. Yes, would I have liked to have won? Abso-freaking-lutely. But I feel like every person has their own personal journey."
"I faced that fear every single day and I gave it my all," she added. "And that's all you can do is do your best. And my best was good enough for me. I got to do four songs. I'm good."
During her time in the competition, Tamera performed four songs: "Listen to Your Heart" by Roxette, "Confident" by Demi Lovato, "Tell Me Something Good" by Rufus featuring Chaka Khan and "I Think We're Alone Now" by Tiffany Darwish.
On Wednesday's double elimination, the former co-host of "The Talk" and Bobby Brown -- who was revealed to be Crab -- were both axed from the show.
However, none of the panelists including Robin Thicke, Jenny McCarthy, Ken Jeong and Nicole Scherzinger suggested Tamera could be Seashell until Wednesday's episode when Scherzinger guessed correctly.
While speaking with People, Tamera explained why her Seashell costume was "a great representation" of who she is.
"One of my favorite places to be ever is Hawaii. I was raised there," she said. "My mom's side is from the Bahamas, Eleuthera Bahamas, and Eleuthera Bahamas is probably one of the most beautiful beaches that I've ever seen. I feel like it's home. The beach is home to me and it just made sense [to be Seashell]."
The Masked Singer Recap: Final Wild Card Has Us Asking -- Where Are All the Ladies?
Meanwhile, Tamera also revealed why she decided to join "The Masked Singer" in the first place.
"It's always been a dream of mine to sing again," Tamera said. "I started my Hollywood career in a theater group, actually. I was acting and singing at the same time. It was called Voices and I was 14. And at that same time, I was doing a pilot called 'Sister, Sister.' So I had to focus more on acting, but I always wondered what it would have been if I went that route."
"I had sang on 'Sister, Sister,' I sing in the shower all the time," she continued. "The last performance in front of an audience was with my sister. We sang at the Malibu triathlon and it was awesome, but it was a long time ago, so I wanted to revisit it."
When asked if she plans on pursuing music now, Tamera said, "Absolutely. I want to do a gospel album, a musical, a Disney film. That would be fun."
#TameraMowry #TheMaskedSinger


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A series of discourses on the principles of religious belief as ..., Volume 2
they could not tell of whom the Prophet spake, they would yet be comforted with the sublime thought that one was to come, who should" raise up the tribes " of Jacob, and restore the preserved of " Israel," who was to be given " as a " light even to the Gentiles, and who " should carry salvation unto the ends of
the earth!" " Your father Abraham " himself," says our Saviour to the Jews,
rejoiced to see my day, and he saw it and " was glad."
There is yet a third observation, which may shew the importance of Prophecy in animating the hopes of the pious even since the introduction of the Gospel. From the fulfilment of those prophecies which refer to that great event, it is reasonable for us to conclude, that all connected prophecies will be fulfilled, and, even under the radiance of the Sun of Righteousness himself, the clouds which sit upon human affairs are sufficiently deep and portentous to make us rejoice in that additional light which Prophecy has kindled. Powerful as are the hopes and consolations of the Gospel, the faith of the righteous is yet, at times, in danger of being shaken by the disorderly appearances around them; and when they behold the triumph of successful crime, and nations themselves subjected to the caprices of individual ambition, they are apt to forego their trust in a superintending providence, and to fear that some dark fatality governs the world. .
The book of Prophecy, my brethren, dispels these gloomy apprehensions. Amidst the storms of the moral world, we there behold the hand which restrains and guides them. We see an omnipotent Lord, under whose direction, even the crimes of men are converted into the means of accomplishing greater ultimate
good. We perceive, indeed, the rage and the tumult of human power; but we are, at the same, time made acquainted with ONE who " knoweth its
going out, and its coming in, whose " bridle is in its lips, and who can turn " it back by the way by which it came :" and, as the final issue of human affairs, we are presented with those pictures of infinite beauty which describe the universal triumph of the Gospel, when "the 66 earth shall be full of the knowledge of " the Lord, as the waters cover the sea;" when " violence shall no more be heard " in the land, wasting nor destruction 56 within its borders;" when " the people " also shall be all righteous :" and when, "as the earth bringing forth her bud, and 56 the garden causeth the things that are " sown in it to spring forth, so the Lord $ God will cause righteousness and praise " to spring forth before all nations." ...,
Notwithstanding the imperfection of these observations, I trust it will yet appear
from them, that, without examining closely the coincidence between particular predictions and events, we may draw an indirect inference in favour of Christianity, from contemplating the grandeur of that scheme of Prophecy upon which it is founded; the benevolence with which this dispensation supplied the defects of those religious systems which preceded the Gospel ; and the animating hopes which it still awakens, amidst the inevitable darkness and disorders of the world. We shall thus discover, in many interesting points of view, the connection between the Prophetical and the Christian dispensations--that they form indeed but one system, extending from the beginning to the end of time, and corresponding in its progress, with admirable wisdom and benevolence, to all the varying circumstances in the condition of human nature.
In opposition to the direct argument from Prophecy, the most plausible objection that can be urged, probably, is, that the people among whom the predictions of the Prophets were made, and who, therefore, may be supposed most able to interpret them, have never admitted the soundness of that interpretation which we have given them. But it may be remarked in reply—that at least the genuineness of the predictions themselves is undoubted, from their existing in the hands of those who are the greatest enemies to the Gospel,--that the prejudices of that people have, for obvious reasons, ever been peculiarly strong against the Christian interpretation of their prophecies--and what, perhaps, is-a more striking fact still, that none of the prophecies are more clear and explicit


Since I started using The Five Minute Journal, I realized how much I am in control of how my day unfolds. It is so easy to feel powerless and to feel like things happen to you; that you are a victim. Of course, things do happen that are out of our control but it is amazing how being aware of our thoughts can change our perception of reality.
For example, The Five Minute Journal asks me to begin my day listing three things for which I am grateful. I used to do this without the journal. I would wake up, and as I crawled out of bed, I would say something I was grateful for with each step. Waking up with gratitude helps me to focus on what I have, and not what I am lacking. Starting the day off this way caused me to appreciate other things during the next 24 hours that I may have looked past if I woke up "on the wrong side of the bed".
When you are in a negative state, and you feel powerless, you aren't a problem solver and obstacles feel insurmountable. "I'll be stuck in this job unhappy forever." Well, why? Is there a way to solve this issue? What steps can you take to create a reality you love?
If you don't feel as though you can control your future, you are less likely to take action to make changes. You'll feel as though all your efforts will be for not and you are doomed to remain _____ forever. (You can fill in the blank with whatever adjective you feel suits your current situation if it is less than desirable). Your fate is in your hands.
I used to hate my legs. I was very skinny and felt boyish. Typically, I would just whine about it. I'd obsess over it. I would enviously look at other women and wish I looked that way. I wanted some shape, and according to me, I was given a genetic death sentence when it came to feminine curves.
One day, someone very close to me made a negative comment about my legs. A switch flipped. I decided TO DO something about it. If I didn't like it, I was going to change it as much as I could. And what I couldn't change, THEN I would accept. This complaining, self-loathing, and constant cloud of negative energy was really for the birds. It was bringing me down. I thought about what I didn't like about myself way too much when I could be thinking about how wonderful my life is and enjoying my days.
I focused on eating for my goals and training. I started making my health a priority and also just "being". Being happy, being content. Refusing to compare. Meditating. My lower body changed (slowly), and while I was working on changing what I could change, I also stopped the negative self-talk.
After Nolan had gone to Kindergarten, I went back to work full time. I was a school nurse (still sub- I do love it) full time, behind a desk. I am not a desk person. I was unhappy missing Nolan's school functions during my workday, and I was miserable at a desk. I decided, against everyone else's opinion, to begin my own business. My husband was supportive (naturally, since he is my business partner) and I slowly started to believe in myself. "Change what I can". Now, I do not work at a desk, still sub, and have created my reality. I could have remained at my desk job complaining for years to come.
Think about how much negative energy we can accidentally put out in the universe if we aren't careful. That energy can be used to transform your reality. It is just sitting there, waiting for you to scoop it up, decide it won't be spent that way, and transfer it to better your life.
Realize you are powerful, not powerless. You are in control. You can change your life. Be a problem solver. If something is making you miserable, consider how you can change it. There is always a way. Make a conscious decision to do what it takes. Don't make excuses, don't talk down to yourself, be aware of your self-sabotage.
What if I told you that you could have anything you want in life? I honestly believe you can; now you need to believe you can, too.


text:
About Me♥
About SITARA
Author Writer, Researcher, Teacher.
This entry was posted in About Me♥, Mind,Body, Health Articles and tagged divine, healing, holistic, Pleiades, sitara, Spirituality by admin. Bookmark the permalink.
24 thoughts on "About Me♥"
Ahmad on March 26, 2013 at 6:20 am said:
Well done Sitara
Arjuna on March 27, 2013 at 11:26 am said:
Miss you lately Shining Star lol
Jase on March 29, 2013 at 3:29 am said:
Stellar in every sense, Star. Beautiful photos and body of work.
Tiffany on March 29, 2013 at 3:47 am said:
This is usually a really great site content, im delighted I came across it. Ill be back off the track to look at
Barron on March 29, 2013 at 6:25 am said:
Hi Sitara. Lovely site, thank you for sharing your light! Bright Blessings from New Zealand! ~ Barron
Gun-Britt on March 29, 2013 at 10:45 am said:
Thank you so much!! Lovely site and your message is what the world need right now! Love Gun-Brit
Sitara on March 29, 2013 at 7:40 pm said:
Thank you all for your lovely, kind comments!
Kelly Lightchalice on March 29, 2013 at 7:00 pm said:
Oh lovely one, I am sooo happy for you! We are blessed for your presence and I am blissed out that so many starseeds are finding their origins and missions, what a lovely time it is
Sending love for you and yours and your efforts, you are an example of what we can do.
Irina on March 30, 2013 at 12:46 pm said:
Aggree!!!!!!!!!!
Hugging you, my Angel!
Lots of love & thank you ♥♥♥
Lord Enlil on March 30, 2013 at 11:10 pm said:
You remember Me ?
Well you know me i am Alfred…
Yes i go from Ashtar because i have other things to be done but that not mean i do not SEE you all..
Sitara on March 30, 2013 at 11:39 pm said:
Yes i remember you… thank you for stopping by Alfred
eva on April 1, 2013 at 9:37 pm said:
sista !!! i am just in awe !! feeling home in your beautiful star space bravo !! much love thank you from bottom of heart blessings ………………..
infinite love sharing ………… <3 <3 <3
Enlil on April 4, 2013 at 5:07 am said:
i Change All Things..because I Can Create..
what you will find there it will Change your life and your way of thinking..
You know i always like you Star.
Well to be honest i like kitties …
Yumi yumi…
Jan on April 5, 2013 at 11:02 am said:
Thanks fоr sharing superb informations. Your site iѕ sо cool.
verySirius on April 15, 2013 at 5:27 am said:
Pro !
Allahu Akbar !
Love n Light . Onward !
Kim Caldwell on June 1, 2013 at 6:23 am said:
OMG this site is gorgeous
just like uuuuuuuuuuu
Austin on June 24, 2013 at 5:21 am said:
Hi S! truly awesome YouTube videos, its my luck to pay a quick visit this website and finding these cool YouTube videos made by you
Kamil. on October 23, 2013 at 11:13 pm said:
Alright, IM IN, BE MY QUEEN ~
Moe on March 25, 2014 at 11:43 am said:
Hi Sitara
Many thanks for your help. I am really glad to come across your page. It seems like being pulled by the nature to come and visit your homepage and see the video.
Much love from Port Moresby, PNG.
Nicola on April 18, 2014 at 8:32 pm said:
U fill people with love and hope.
U show us all that, there are people in the world
who feel the same way.
U are amazing!
And i thank u for all that u are
David on June 1, 2014 at 3:39 pm said:
Hi Sitara,
Being in the Joy of the Light
from the 5th dimension !
David Power
Leave a Reply to Nicola Cancel reply


Citation NOTHOSCORDUM BIVALVE (Linnaeus) Britton, in Britton & A. Brown, Ill. Fl. N. U.S. 1: 415. 1896.
Basionym: Ornithogalum bilvalve Linnaeus 1753.
Allium bivalve Allium bivalve (Linnaeus) Kuntze, Revis. Gen. Pl. 3(2): 312. 1898. BASIONYM: Ornithogalum bivalve Linnaeus 1753.
Geboscon bivalve Geboscon bivalve (Linnaeus) House, New York State Mus. Bull. 233/234: 66. 1922. BASIONYM: Ornithogalum bivalve Linnaeus 1753.
Nothoscordum striatum Nothoscordum striatum (Jacquin) Kunth, Enum. Pl. 4: 459. 1843. BASIONYM: Allium striatum Jacquin 1797.
Ornithogalum bivalve Ornithogalum bivalve Linnaeus, Sp. Pl. 306. 1753.
USA Louisiana Avoyelles Par. 16 Mar 1973 P. St. Romain s.n.
USA Georgia Oglethorpe Co. 07 Apr 1965 F. Montgomery s.n.
Mexico Oaxaca Jun 1995 Livorio 95-62 Mixtec name: ita ndo'oyó.
Mexico Oaxaca 29 Jun 1994 Sabastian 94-6-124 Mixtec name: ita asusena yucú.
USA Vermont 12 May 1877 L. F. Ward s.n.


Sally is nervous for her pretrial hearing and decides to call one of the witnesses on Imran's list. Paula warns her she could get in serious trouble but Sally refuses to listen and sacks her. Later, Sally sets off for court with no solicitor and a very worried Tim and Gina. Imran is amused that she is representing herself and wastes no time telling the judge that she has harassed a witness.
Meanwhile, Imran finds a list of pros and cons about him made by Leanne and Toyah and sacks Leanne. Soon, Adam insists that he reinstate her as the filing system is in a mess.
Elsewhere, Peter tells Vicky that she can keep her job but she needs to tell Tyler to call off his mates; Audrey is upset when Maria reveals that Claudia plans to open her new salon in Victoria Street; and Geoff and Brian's gardening war hots up.
Ross is rattled as Gaz arrives with more drugs and later, he spirals out of control.
Ste makes a heartfelt video pleading for Tony's return and posts it on social media. Before long he gets a message from someone claiming to be Tony.
Meanwhile, Dee Dee doesn't recognise Tegan due to her condition, devastating Tegan. The doctor suggests they treat her with a type of chemotherapy.
Elsewhere, Yazz is terrified of Imran, but decides not tell Misbah that he punched her.
When Mrs Tembe finds out that Mrs Smail is recruiting new staff and that the Mill is losing patients to Sutton Vale, she recruits Sid to go undercover as an interested candidate.
Meanwhile, things are still frosty between Daniel and Zara and she can't help notice when Melissa, a glamorous new client arrives to see him at the Granger Clinic. Zara shares her woes with Emma who suggests they go for a drink after work.
At the end of the day Zara and Emma head off together while at the Icon Bar, Melissa reveals that she wants to hire Daniel and his Michel 7 products for the TXR Shopping Channel.


Nestled in the foothills of Scottsdale Mountain, Villa Falcone will sell to the highest bidder regardless of price on May 18th.
Villa Falcone is a romantic Santa Barbara Tuscan style home perched in the gated community of Shadestone within Scottsdale Mountain. This jewel of the desert will be sold at a luxury no reserve auction on May 18th, 2017 by Supreme Auctions in cooperation with Keller Williams Realty Sonoran Living.
Designed over a two-year period, the home was built by Tom LaBlonde Development while the sellers' supervised construction themselves. Each of the quality materials were meticulously selected, such as the Omni Block for the homes construction. The design elements throughout the home even reflect the sellers' travels throughout Italy and Spain with authentic materials being imported from as far away as Morocco. The result is a singularly exquisite home that was built to last forever.
Villa Falcone features a castle-like great room with natural stone walls, a fluted tortoise-shell chandelier, and a carved limestone mantel and fireplace. Four elegant Juliette balconies overlook the extensive sitting area beneath the soaring tongue and groove wood ceiling with 20-inch hand-hewed beams. French doors lead out to the main patio and pool deck. Two stunning pools offer formal or fun swimming, a jetted spa, a waterslide, a water wall feature, and even a hidden grotto behind a waterfall. Combined with the swim-up barstools and lush grounds, this oasis in the desert is perfect for entertaining.
The homes balconies provide access for residents and guests alike to soak up the sun and the soft breezes while viewing stunning mountain, desert, and city lights views. The spacious master en-suite is its own retreat complete with a sitting area. His and her Onyx vanities and walk-in closets boast custom built-in cabinetry, while a crystal chandelier suspended from a domed ceiling offers elegance for a luxurious soak in the master tub. Guests can enjoy their own separate guest quarters, complete with their own bedroom, bathroom, living room, kitchen, and 2-car garage.
Additional rooms in the home include a refined library, home gym, office, as well as a music, family, and game room. Casual and formal dining spaces offer opportunities to enjoy the finest delicacies and conversation, while an observation tower allows residents to feast on 360-degree views.
While Villa Falcone enjoys peaceful and tranquil surroundings, just minutes away are highly acclaimed Basis charter schools, nationally recognized premier event venue West World, and the world-renowned Mayo Clinic. Scottsdale Quarter offers shopping and fine dining experiences, while the largest employment region in the Phoenix Metropolitan area boasts Fortune 500 headquarters. Sky Harbor International Airport, Talking Stick Arena, and Chase Field in Phoenix are just 40 minutes away.
Villa Falcone will be sold at a luxury no reserve auction on May 18th, 2017. Interested parties are invited to contact Supreme Auctions directly at (866) 929-2243 or visit www.supreme-auctions.com.


AFTERBUZZ TV -- WWE's SmackDown edition, is a weekly "after show" for fans of WWE's SmackDown. In this episode host Ric Drasin breaks down the episode for the week of April 13th, 2012 in which Wrestle Mania no.1 contenders collide as Chris Jericho takes on the "Great White", Sheamus. There to help Ric are co-hosts Allison Danger, Patricia Summerland, and Ryan Clum. It's the week of April 13th, 2012 Smackdown podcast!


Winners of the Best in Sector – Floor Plans award three years running, and runners up in the Supplier of the Year category in 2016 and 2017, Metropix are hoping to go one better in 2018.
The ESTAS sponsored by Zoopla determines the best estate & letting agents, mortgage advisors and suppliers in the UK through research carried out amongst customers who are asked a series of questions about the service they have received from their agent or supplier. This year saw record entries making the competition the toughest yet and one of the biggest surveys in the UK property industry with just over 36,000 customers completing one of the online questionnaires.
The supplier categories are sponsored by Estate Agent Today and Letting Agent Today. CEO Nat Daniels said "These record figures show just how far the ESTAS have come, they also demonstrate how keen clients are to provide feedback. Client feedback provides agents and suppliers with a useful way of measuring up to their competitors as well as highlighting how they can improve their service in the future. We're very excited for this year's biggest ever event."
Eighteen supplier firms have made this year's shortlist across various product sectors. The shortlist is determined purely on the feedback received from thousands of agents who use each supplier's services.
Metropix Customer Services Manager Steve Sanashee adds "the competition seems to get tougher every year and to be shortlisted again is real testament to the efforts of the team.
The winner of our £75 Amazon voucher was Andy Weller of Church and Hawes in Essex. Thank you to all those who voted.


Following is an example of the PHP used to make a connection to a database in Microsoft SQL Server.
This is the Server name that displays when making a connection using SQL Server Managment studio. In this screen shot, the Server name is Computer1\\Instance1. In this example, Computer1 is the name of the computer, and Instance1 is the name of the SQL Server instance.
This is the database listed after a successful connection is made using SQL Server Management Studio.
This is the Login name that displays when making a connection using SQL Server Managment studio. In this screen shot, the Login is user1.
This is the password that displays when making a connection using SQL Server Managment studio. In this screen shot, the password is ******** (when not hidden, the password is "password").


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Home » Business » Ben Chin, Morneau's chief of staff, to join PMO on Friday as senior adviser
Ben Chin
Ben Chin, Morneau's chief of staff, to join PMO on Friday as senior adviser
OTTAWA- Finance Minister Bill Morneau's former chief of staff Ben Chin will start a new job as a senior adviser to Prime Minister Justin Trudeau this week.
Morneau's office in fall 2017, the veteran political aide worked for former British Columbia premier Christy Clark and former Ontario premier Dalton McGuinty.
Chin, a former TV journalist, will be reporting to Trudeau's chief of staff Katie Telford starting Friday.
He has spent much of his political career out of the headlines, but over the winter his name came up during testimony by former justice minister Jody Wilson-Raybould about the SNC-Lavalin affair.
Wilson-Raybould asserted that Chin warned her staff about the political impact of potential job losses during a Quebec provincial election if the embattled Montreal-based engineering firm was unable to secure a plea-bargain-type deal with prosecutors over alleged corruption in Libya.
Morneau has insisted Chin didn't do anything inappropriate in discussing the SNC-Lavalin case with Wilson-Raybould's staff.
The company is facing a possible 10-year ban from lucrative federal government contracts because of 2015 bribery and fraud charges.


FDA laboratory regulations based webinars, in-person seminars, standards and best practices. Learn from renowned experts about FDA regulations for laboratories and compliance requirements - Good laboratory practices (GLP), ISO 17025, Lab accreditation, CLIA inspection guidelines, etc.
Research laboratories conducting regulatory studies must comply with GLP requirements to ensure the quality, traceability and validity of test results. GLP compliance training can facilitate the process by helping employees better understand regulatory requirements for lab practices and learn how to implement these regulations within an organization. For laboratory professionals involved in the planning, executing, monitoring, reporting of non- clinical studies, GLP training can deliver best practices and guidance for complying with industry mandates and regulations.
Introduced in 1972, GLPs (Good Laboratory Practice) were first practiced in New Zealand and Denmark. Today, GLPs represent a global standard applicable to non-clinical studies conducted for the assessment of the efficiency and safety of laboratory practices within the manufacturing industry. GLPs form a principled framework within which lab studies are planned, performed, monitored, recorded, reported and archived. GLP not only regulates the non-clinical laboratory studies of the drug products but also applies to testing of food and color additives, biological products and medical devices.
GMP Compliance: Why is it Important?
Non-compliance with the GLP regulations can lead to FDA warning letters or the equivalent of it from other regulatory authorities. In addition, they can also result in the disqualification of a study or even denial of the investigational drug application (IND). GLP compliance and training have thus become an integral part of an organization's preparedness to meet and exceed regulatory requirements.
GLP compliance can be multi-faceted and complex depending on your operations. An effective training program will consider current trends and requirements, bringing you the latest updates from experienced instructors. ComplianceOnline offers GLP compliance training programs in various formats, including: live webinars, training recordings, in-person seminars, and customised organization-level in-person seminars. Led by recognized experts and industry veterans with decades of experience in regulatory affairs and compliance, our training programs will offer staff and management an interactive platform to understand and discuss current industry standards.


text:
Q: circle graph showing bearings and distance I'm trying to show the bearings that individuals travelled away from a site and the distance travelled within 1 day, as well as the numbers of individuals travelling at different bearings.
Presently, I can make those basic plots in ggplot2:
# distance & bearing
ggplot(data=df,
       aes(bear, dist)) +
  geom_point() +
  scale_y_log10()

# no. individuals & bearing
ggplot(data=df.postDepDT,
       aes(bear)) +
  geom_histogram(bins = 36)

#my data looks like the following
bear <- c(-172, -175, -160, -155, -150, -10, 23, 87, 122, 179)
dist <- c(5, 101, 326, 47, 23, 55, 6, 7, 44, 162)
df <- data.frame(bear, dist)

I would like my final plot to have two panels. The first is a circle with points at different lengths (indicating distance) radiating away from the circle in the direction of the bearing.  These points would be connected to the circle along the bearing.  The second is a histogram around the circle, showing numbers of individuals moving away from a circle along each bearing.
In these figures 0o (or North) would be at the top at -180o/180o (South) would be at the bottom, with -90o and 90o (west and east) on the left and right, respectively.
UPDATE:
Adding coord_polar() to the figures helps make a circular figure, however, I'm still unable to get the 0o value (for North) at the top of the figure (start=0 puts the 0o value at the bottom). Also, I'm still looking for a solution to connect the points in the first plot to the centre point.

A: Are you looking for something like this?

ggplot(data=df,
       aes(bear, dist)) +
  geom_segment(aes(xend = bear, yend = 0.1)) +
  geom_point() +
  scale_x_continuous(limits = c(-180, 180),
                     breaks =  seq(-180, 180, 90)) +
  # scale_y_log10() +
  coord_polar(start = pi) +
  theme_bw()

Explanations:

*

*geom_segment() expects aesthetics for x, y, xend, & yend. The "pre-coord_polar" version of a circular chart with lines radiating from the centre would have been a chart in Cartesian coordinates with lines that drop down vertically to intersect the x-axis, so we'd want each xend value to be the same as the x value, and each yend value to be the smallest possible (which would be 0 for distance, but since you are interested in the log scale for the y-axis, I've added a small positive value):

ggplot(data=df,
       aes(bear, dist)) +
  geom_segment(aes(xend = bear, yend = 0.1)) +
  geom_point() +
  scale_x_continuous(limits = c(-180, 180),
                     breaks =  seq(-180, 180, 90)) +
  # scale_y_log10() +
  # coord_polar(start = pi) +
  theme_bw()

*coord_polar() expects the following for its start argument (emphasis added):

offset of starting point from 12 o'clock in radians

Since your bearing's actual values are in the c(-175, 179) range, I expect your scale to be c(-180, 180). The default start = 0 would thus place -180/180 at the 12 o'clock position. To place 0 at the 12 o'clock position, set start = pi, which is 180 degrees in radians.

*Lastly, I urge you to think through why you want to use the log scale to represent distance. On a technical level, the choice of an arbitrarily small positive value for yend can result in the same point appearing to be at different distances from the centre. (see illustration below for some yend values) On a more theoretical level, I understand log scale to be appropriate when we are comparing a large range of quantities, which isn't really the case here.

p <- ggplot(data=df,
       aes(bear, dist)) +
  geom_point() +
  scale_x_continuous(limits = c(-180, 180),
                     breaks =  seq(-180, 180, 90)) +
  scale_y_log10() +
  coord_polar(start = pi) +
  theme_bw()

gridExtra::grid.arrange(
  p + geom_segment(aes(xend = bear, yend = 1)) + ggtitle("yend = 1"),
  p + geom_segment(aes(xend = bear, yend = 0.1)) + ggtitle("yend = 0.1"),
  p + geom_segment(aes(xend = bear, yend = 0.01)) + ggtitle("yend = 0.01"),
  p + geom_segment(aes(xend = bear, yend = 0.001)) + ggtitle("yend = 0.001"),
  nrow = 2
)

redpajama_set_name: RedPajamaStackExchange


Sasha Banks and Rey Mysterio are the newest WWE Superstars to get WWE Network Collections, highlighting a few of the most essential matches and promos of their careers. WWE Network Information had the unique reveals of each the titles and content material of each collections.
Bounce off the highest rope into the high-flying, fast-paced world of Rey Mysterio with this action-packed WWE Network Assortment. Witness the Grasp of the 619's unlikely journey via ECW, WCW, and WWE the place he proved measurement doesn't matter. Alongside the best way, The Largest Little Man created unforgettable moments as he battled the likes of Shawn Michaels, Kurt Angle, John Cena, and the late, nice Eddie Guerrero. The Man Behind the Masks is revealed on this extraordinary Assortment. Booyaka! Booyaka!
Two wrestling legacies collide when Rey Mysterio Jr. challenges Dean Malenko for the Cruiserweight Championship.
Rey Mysterio Jr. makes a reputation for himself by battling Jushin 'Thunder' Liger on this thrilling and action-packed contest.
In an epic battle between two legendary luchadores, Rey Mysterio Jr. and Ultimo Dragon meet head-to-head.
Together with his sacred masks on the road, Rey Mysterio Jr. challenges Eddie Guerrero for the WCW Cruiserweight Championship.
Rey Mysterio Jr.'s points with the LWO intensify after dealing with Juventud Guerrera and Kidman for the WCW Cruiserwieght Title.
Rey Mysterio makes an epic WWE Pay-Per-View debut on this thrilling match towards Kurt Angle.
Rey Mysterio appears for his style of gold in WWE by difficult Matt Hardy for the Cruiserweight Championship.
Rey Mysterio and Kidman problem The World's Biggest Tag Group for the WWE Tag Staff Championships.
Eddie Guerrero and Rey Mysterio unite to battle The Basham Brothers for the WWE Tag Group Titles.
The friendship between Rey Mysterio and Eddie Guerrero is strained when each males battle one another on this bout.
Secrets and techniques and lies run rampant throughout this private confrontation between Rey Mysterio and Eddie Guerrero.
The extreme and private rivalry between Rey Mysterio and Eddie Guerrero escalates over Mysterio's son, Dominick.
With custody of his son on the road, Rey Mysterio takes to the ring battle Eddie Guerrero in a Ladder Match.
Rey Mysterio seems to be to endure and overcome an onslaught of Superstars on this record-breaking Royal Rumble Match.
After being out of motion for almost a yr resulting from damage, Rey Mysterio returns to settle a rating with Chavo Guerrero.
With a RAW future forward of him, Rey Mysterio takes to the ring to bid farewell to the SmackDown viewers.
Rey Mysterio defends the coveted Intercontinental Championship towards Dolph Ziggler on this thrilling contest.
Rey Mysterio finds himself locked in a metal cage with an animal when he battles Batista for a World Heavyweight Title shot.
Rey Mysterio's issues with The Straight Edge Society get bushy on this basic battle towards CM Punk.
Tensions between Rey Mysterio and the aristocratic Alberto Del Rio explode on this confrontation.
Rey Mysterio and Alberto Del Rio face off with their respective groups in a Survivor Collection Elimination Match.
Rey Mysterio finds himself dealing with one other masked opponent within the type of 'Dashing' Cody Rhodes.
Lower than two hours after capturing the WWE Championship, Rey Mysterio places his newly gained title on the road towards John Cena.
In what can be his final match in WWE for a number of years, Rey Mysterio goes one-on-one with Dangerous Information Barrett.
Countdown: Superior Entrances – Who's That Leaping Out the Sky?
Rey Mysterio's breathtaking entrance is examined by WWE Superstars and Legends.
WWE Superstars and Legends talk about the unimaginable in-ring talents of Rey Mysterio.
After years of absence, Rey Mysterio makes a shocking return within the 2018 Royal Rumble Match.
WWE's latest Network Assortment is legit! Be a part of Sasha Banks for an unique sit-down interview and relive her epic journey from groundbreaking days in NXT to creating an impactful assertion on WWE's principal roster. Whether or not main-eventing within the first ever ladies's Hell in a Cell Match, or toppling obstacles in Abu Dhabi, Sasha continues to show the sky's the restrict. Watch as The Legit Boss battles her fiercest rivals in a Assortment you could take straight to the financial institution!
Sasha Banks displays on the early days of her profession previous to creating an efficient in-ring persona.
Sasha Banks unveils her expertise to the WWE Universe in her TV debut towards Paige.
The seeds of the storied rivalry between Sasha Banks and Charlotte are planted on this memorable first encounter.
Sasha Banks' frustrations following a match towards Paige leads her to embrace one other aspect of herself.
Sasha Banks' newly adopted angle makes her a fierce competitor on this one-on-one bout towards the harmless Bayley.
Sasha Banks appears to finish Charlotte's reign as NXT Ladies's Champion by difficult her for the gold.
The 4 Horsewomen of NXT battle one another in a Deadly Four-Means Match for the NXT Ladies's Championship.
Sasha Banks finds herself falling sufferer to the underhanded techniques of Alexa Bliss throughout this controversial bout.
Sasha Banks takes to the ring on the lookout for a measure of retribution towards the sly and artful Alexa Bliss.
Issues take a violent flip when Becky Lynch and Sasha Banks meet to signal the contract for his or her NXT Ladies's Championship match.
Sasha Banks places the NXT Ladies's Championship on the road towards Becky Lynch on this unforgettable match.
After recalling her epic battle with Becky Lynch, Sasha Banks feedback on what led to her arrival on WWE's most important roster.
In her most important roster debut, Sasha Banks exhibits the WWE Universe her unimaginable in-ring expertise by battling Charlotte.
The Ladies's Revolution is ignited when Sasha Banks and her NXT comrades arrive on the primary roster to shake issues up.
With the NXT Ladies's Championship on the road, Sasha Banks and Charlotte meet of their final match collectively in NXT.
Bayley seems to be to silence her critics by difficult Sasha Banks for the NXT Ladies's Championship on this basic.
Sasha Banks and Bayley show they will go the space on this historic Iron Lady Match for NXT Ladies's Title.
Sasha Banks recounts her matches with Bayley, and how the street she adopted introduced a Legit Boss to The Grandest Stage of Them All.
Becky Lynch, Sasha Banks, and Charlotte shed their 'divas' picture by battling for the reborn WWE Ladies's Championship.
Sasha Banks companions with Bayley to tackle the duo of Charlotte Aptitude and Dana Brooke in a Tag Group Match.
Sasha Banks exhibits everybody why she is a Legit Boss by difficult Charlotte Aptitude for the WWE Ladies's Championship.
Sasha Banks is confronted with a dear state of affairs when she defends the WWE Ladies's Championship towards Charlotte Aptitude.
Sasha Banks tries to place the RAW Ladies's Title round her waist by difficult Charlotte Aptitude for the gold in the primary occasion.
For the primary time, two ladies meet within the cell when Charlotte Aptitude challenges Sasha Banks for the RAW Ladies's Title.
When Sasha Banks's rivalry with Charlotte Aptitude proves to be too intense, they battle for gold in a Falls Rely Anyplace Match.
Sasha Banks and Charlotte Aptitude's rivalry reaches a brand new degree in an Iron Lady Match for the RAW Ladies's Title.
Sasha Banks shares her ideas on how she tailored to totally different opponents in effort to cope with the likes of Nia Jax and Alexa Bliss.
Sasha Banks manages to make use of her legit expertise to get the higher of Nia Jax on this one-sided battle.
Sasha Banks battles Bayley, Nia Jax, and Charlotte Aptitude in a Deadly Four-Approach Match for the coveted RAW Ladies's Championship.
Sasha Banks is confronted with an unlimited problem when she competes a Gauntlet Match for a shot on the RAW Ladies's Championship.
Alexa Bliss appears to get the higher of Sasha Banks as soon as once more on this bout for the RAW Ladies's Championship.
In one other probability to regain the RAW Ladies's Championship, Sasha Banks pushes Alexa Bliss to the restrict.
Sasha Banks finds herself with the chances towards her in a Deadly 5-Approach Match for the RAW Ladies's Championship.
Sasha Banks speaks on competing within the first Ladies's Match to happen in Abu Dhabi, sharing her reminiscences of this historic milestone.
WWE Reside 12/07/2017 – A First for Every thing [Duration 11:35] Sasha Banks and Alexa Bliss make historical past by assembly one another within the first ever Ladies's Match to happen in Abu Dhabi.
Sasha Banks seems to be to make historical past as soon as once more when the ladies of WWE compete within the inaugural Ladies's Royal Rumble Match.
Sasha Banks tries to finish the storied undefeated streak of Asuka on this unimaginable bout towards The Empress.
Sasha Banks continues to cement her place in historical past by competing the primary Ladies's Elimination Chamber Match.
Sasha Banks appears to climb the ladder of success by competing in her first Cash within the Financial institution Ladder Match.
The Boss 'n' Hug Connection of Bayley and Sasha Banks takes to the ring to battle The Riott Squad in a Tag Staff Match.
Sasha Banks companions with Natalya and Bayley to tackle Ruby Riott and her Riott Squad in a Six-Lady Tag Staff Match.
With a continuing want to pave the best way for future feminine Superstars, Sasha Banks seems to be past to see what's subsequent for WWE's Legit Boss!
Each collections can be found to observe on the WWE Network immediately.
The publish Sasha Banks and Rey Mysterio Get WWE Network Collections appeared first on Bleeding Cool Information And Rumors.