text:
\section{Introduction}
Bose-Einstein condensation (BEC) is the transition process, in which a
macroscopic
fraction of bosons goes into the lowest energy state, as the temperature
is lowered below a certain critical
temperature $T_c$~\cite{Huang}. It was predicted by Einstein in 1925, based on
Bose's explanation of black body radiation. A great deal of activity, both theoretical
and experimental, has been seen in this field, since the experimental realization of
BEC in 1995. Although a number of static,
dynamic and thermodynamic properties have
been studied~\cite{Dalfovo,Pethick}, not much attention has been paid to the heat capacity of
attractive condensates. The main motivation of this
work is to fill this gap. \\

In laboratory experiments, the condensate is trapped by a confining potential,
usually a harmonic oscillator potential.
An attractive condensate ({\it e.g.} $^7$Li condensate)
has a negative value of the $s$-wave scattering length $a_s$ and collapses,
when the number of particles $N$ in the condensate exceeds a critical
number $N_{cr}$. On the other hand a repulsive condensate ({\it e.g.} $^{87}$Rb
condensate) corresponds to $a_s > 0$ and is stable for any $N$,
since repulsively interacting  bosons are contained in the
externally applied trap.
The situation is quite different for an attractive condensate: attractive
bosons tend to come to the center of the trap, which is balanced only by the
kinetic pressure, resulting in a metastable condensate. The total attraction
increases as the number of pairs $N(N-1)/2$, while the kinetic pressure increases as $N$.
Thus for $N$ larger than a critical value $N_{cr}$, the net attraction dominates
and a collapse occurs. \\

In this communication, we report the calculation of heat capacity of an
attractive condensate containing a fixed number of $^7$Li atoms, interacting
via the realistic van der Waals potential, appropriate for the experimental
scattering length.
The features are markedly different from those of repulsive condensates, only
which have so far been investigated. In a repulsive condensate, the heat
capacity $C_N(T)$
for a fixed number $N$ of bosons in the trap, as also the critical
temperature $T_c$, smoothly
approach a constant value as $N \rightarrow \infty$~\cite{Napolitano,Biswas1}. As a function
of $T$, the heat capacity for a given $N$ increases to a maximum $(C_N)_{max}$,
then falls rapidly to a saturation value $3Nk_B$ as $T$ increases ($k_B$
is the Boltzmann constant). These
features are qualitatively similar to those of a trapped non-interacting
condensate~\cite{Pethick, Napolitano}. However for an attractive condensate,
there are important changes in the nature. This is due to the fact that the
number of available energy levels of the system is limited, especially when
$N \rightarrow N_{cr}$, while for any $N$, there are infinitely many energy levels for the repulsive or non-interacting condensate. In the limit of high $T$, both the
repulsive and the non-interacting condensate behave as the corresponding trapped Bose-gas, resulting in a saturation in $C_N(T)$. On the other hand, an attractive condensate also shows similar behavior, only if it
is allowed to absorb energy internally through rotational motion involving
large orbital angular momenta. \\

We provide an understanding of this peculiar nature based on the many-body
picture. For the theoretical calculation,
we adopt the correlated potential harmonic (CPH)
method~\cite{Das1,Das2} to solve the many-body problem approximately. This
technique is based on the potential harmonics (PH) expansion method~\cite{Fabre}.
The laboratory BEC must be very dilute to preclude three-body collisions,
which lead to molecule formation and consequent depletion. Hence only
two-body correlations are relevant. The PH is a subset~\cite{Fabre} of the full hyperspherical
harmonics (HH) basis~\cite{Ballot}, that involves only two-body correlations. Hence
the PH basis is a good approximation for expanding the condensate wave function.
It reduces the bulk of the numerical procedure immensely, while retaining the most important
basic features of the condensate. However, the leading members of the PH
basis do not have the correct short separation behavior of the
interacting Faddeev component. This causes a very slow rate of convergence of the PH
expansion basis. To correct for this, we include a short-range correlation function
in the expansion basis. This correlation function
is obtained as the zero-energy solution of the two-body
Schr\"odinger equation~\cite{Das2}. It is a correct representation of the
short separation behavior and also incorporates the $s$-wave scattering length,
$a_s$, through its asymptotic behavior~\cite{Pethick}. The technique
has been shown to reproduce known results, both experimental and
theoretical~\cite{PHEM}. These include the following: ground state
properties (energy, wave function, condensate size, one-body density,
pair-correlation, etc.) as also multipolar moments of both repulsive and
attractive condensates, correct prediction of the critical number and
collapse scenario of attractive condensates,
thermodynamic properties of repulsive condensates, properties
of condensates in finite traps, etc.\\

We can understand the behavior of heat capacity of attractive condensates in terms of the energy levels of the system produced by the CPH method. This method generates an effective potential in which the condensate moves. For an attractive condensate, the effective potential has a metastable region (MSR), separated from a deep well on the inner side by an intermediate finite barrier. A finite number of energy levels are supported by the MSR. As the number $N$ of atoms increases, the MSR shrinks and the number of energy levels reduce drastically. As temperature increases, particles are distributed in higher energy levels, according to Bose distribution formula. Thus at low temperatures the internal energy and $C_N(T)$ increase with temperature. At higher temperatures, the bosons have fewer levels to occupy, causing $C_N(T)$ to differ from the repulsive case. There is also a dominant effect of the drastically reducing number of energy levels as $N \rightarrow N_{cr}$.\\

The paper is organized as follows. For easy readability and to introduce our
notations, we briefly review the
correlated potential harmonic method in Section~II. Section~III provides
our numerical procedure. Results and discussion are presented in
Section~IV. Finally we draw our conclusions in Section~V. \\

\section{Correlated potential harmonics (CPH) method}

We adopt the correlated potential harmonics method~\cite{Das1,Das2} to
solve the many-body problem of the BEC. We briefly recapitulate
the technique in the following. Interested readers can find details
in the cited references. \\

For the relative motion of a system of $N$ identical spinless bosons, we
introduce $(N-1)$ Jacobi vectors
\begin{equation}
 \vec{\zeta}_{i}=\sqrt{\frac{2i}{i+1}}\left( \vec{x}_{i+1} - \frac{1}{i}
\sum_{j=1}^{i} \vec{x}_{j}\right) , \hspace*{0.5cm} (i=1,...,N-1) ,
\end{equation}
where $\vec{x}_i$ is the position vector of the $i$-th particle. The
Schr\"odinger equation governing the relative
motion of the system trapped in a harmonic well, is
\begin{eqnarray}
\Big[&-&\frac{\hbar^{2}}{m} \sum_{i=1}^{\cal {N}} \nabla_{\vec{\zeta}_{i}}^{2}+
V_{trap}(\vec{\zeta}_1, ..., \vec{\zeta}_{\cal {N}}) +
\nonumber
\\
&&V(\vec{\zeta}_{1}, ..., \vec{\zeta}_{\cal{N}})-E_{R} \Big]
\psi(\vec{\zeta}_{1}, ..., \vec{\zeta}_{\cal{N}}) = 0 ,
\label{SE_rel_motion}
\end{eqnarray}
where ${\cal{N}}=N-1$ and the trapping potential $V_{trap}$ and
the interatomic interaction $V$ are
expressed in terms of the Jacobi vectors. The energy of
the relative motion is $E_R$. Next, we introduce hyperspherical
variables corresponding to the set of ${\cal N}$ Jacobi vectors.
First, a hyperradius is defined as
\begin{equation}
r=\left[\sum_{i=1}^{\cal N} \zeta_i^2\right]^{\frac{1}{2}}.
\end{equation}
The remaining set of $(3{\cal N}-1)$ `hyperangles' consists of $2{\cal N}$ polar angles
of ${\cal N}$
Jacobi vectors and $({\cal N}-1)$ angles defining their relative lengths~\cite{Ballot}.
In the hyperspherical harmonics expansion method
(HHEM) $\psi$ is expanded in the complete
set of hyperspherical harmonics (HH), which are the eigenfunctions of
the grand orbital operator [hyperangular part of
the $\cal{N}$ dimensional Laplace operator, given by the sum in the
first term of Eq. (\ref{SE_rel_motion})]~\cite{Ballot}. Substitution of this in
Eq. (\ref{SE_rel_motion}) and
projection on a particular HH result in a set of coupled differential
equations. Imposition of symmetry of the wave function and calculation
of the matrix elements become increasingly difficult and tedious as $N$
increases. In addition, the
degeneracy of the HH basis increases very rapidly~\cite{Ballot} with the increase in the
grand orbital quantum number $K$. Hence a convergent calculation using
HHEM with {\it the full} HH basis is extremely computer intensive
and unmanageable for $N > 3$. This is
the price one pays for keeping {\it all many-body correlations} in $\psi$. \\

However all these complications can be avoided and a much simpler
computational procedure can be formulated for the laboratory BEC,
which is designed to be {\it extremely dilute} (typical number density
is $\sim 10^{15}$ cm$^{-3}$) in order to
avoid recombination through three-body collisions. Thus three-body
correlations and three-body forces are totally negligible.
We can then express $\psi$ as a sum of two-body Faddeev component
$\psi_{ij}$ for the $(ij)$-interacting pair~\cite{Fabre}
\begin{equation}
\psi=\sum_{i,j>i}^N\psi_{ij}(\vec{r}_{ij},r).
\end{equation}
Note that the assuption of two-body correlations only makes
$\psi_{ij}$ a function of the pair separation vector and the hyperradius only.
One can then expand $\psi_{ij}$ in a subset of HH, called the potential
harmonics (PH) subset, which is sufficient for the expansion of
the interaction potential $V(\vec{r}_{ij})$ as a function in the
hyperangular space for the $(ij)$-partition.
Since the labeling of the particles is arbitrary, we can choose
$\vec{r}_{ij}=\vec{\zeta}_{\cal N}$. Then the corresponding PH,
$\mathcal{P}_{2K+l}^{lm}(\Omega^{ij}_{\cal N})$ (the argument is
the full set of hyperangles for the $(ij)$-partition) is
independent of $\{\vec{\zeta}_1,\dots,\vec{\zeta}_{{\cal N}-1}\}$
and a simple analytic expression is possible~\cite{Fabre}.
Expansion of the Faddeev component in the PH basis reads
\begin{equation}
 \psi_{ij}(\vec{r}_{ij},r)=r^{-\frac{(3{\cal N}-1)}{2}}
\sum_{K}\mathcal{P}_{2K+l}^{lm}(\Omega^{ij}_{\cal N})u_{K}^{l}(r),
\label{PHexpn}
\end{equation}
where $\mathcal{P}_{2K+l}^{lm}(\Omega^{ij}_{\cal N})$ is a potential
harmonic~\cite{Fabre}.
The $r$-dependent factor in front is included to remove the first
derivative with respect to $r$. Substitution of this expansion in
the Faddeev equation for  the $(ij)$-partition
\begin{equation}
 (T+V_{trap}-E_{R})\psi_{ij}=-V(r_{ij})\sum_{k,l>k}^{N} \psi_{kl},
\label{Faddeveq}
\end{equation}
[where $T=-\frac{\hbar^{2}}{m}\sum_{i=1}^{\cal N} \nabla^{2}_{\vec{\zeta}_{i}}$]
and projection on the PH corresponding to the $(ij)$-partition
give a set of coupled differential equations in $r$. Note
that any realistic two-body potential, $V(\vec{r}_{ij})$ can be
used. A realistic interatomic potential has a very strong
repulsion (arising from the nucleus-nucleus repulsion) at
very short separations. Consequently, corresponding $\psi_{ij}$
must be vanishingly small for small values of $r_{ij}$.
But the leading PH (corresponding to $K=0$) in the expansion in Eq. (\ref{PHexpn})
is a constant and
does not have this behavior. Hence convergence of
the expansion in Eq. (\ref{PHexpn}) will be very slow. To improve
the rate of convergence, we include a short-range correlation function
$\eta(\vec{r}_{ij})$ in the expansion basis, so that Eq. (\ref{PHexpn})
is replaced by
\begin{equation}
 \psi_{ij}(\vec{r}_{ij},r)=r^{-\frac{(3{\cal N}-1)}{2}}
\sum_{K}\mathcal{P}_{2K+l}^{lm}(\Omega^{ij}_{\cal N})u_{K}^{l}(r)
\eta(\vec{r}_{ij}).
\label{CPHexpn}
\end{equation}
The short-range correlation function is chosen
to have the expected behavior of $\psi_{ij}(\vec{r}_{ij},r)$ for
small $r_{ij}$ in the following manner. The small $r_{ij}$
behavior of $\psi_{ij}$ will be that of a zero-energy pair
interacting via $V(\vec{r}_{ij})$,
since the energy of the interacting pair is practically zero.
We obtain $\eta(\vec{r}_{ij})$ by solving the zero-energy two-body
Schr\"odinger equation
\begin{equation}
-\frac{\hbar^2}{m}\frac{1}{r_{ij}^2}\frac{d}{dr_{ij}}\left(r_{ij}^2
\frac{d\eta(r_{ij})}{dr_{ij}}\right)+V(r_{ij})\eta(r_{ij})=0.
\label{2Beqn}
\end{equation}
Inclusion of the short-range correlation function $\eta(\vec{r}_{ij})$
enhances the rate of convergence greatly, which has been checked in our
numerical calculation. \\

The laboratory BEC is very dilute; hence the average separation of
the atoms is very large compared with the range of interatomic
interactions. Moreover, the atoms scatter with almost zero energy.
Hence the effective two-body interaction is represented by the
$s$-wave scattering length $a_s$. In our calculation, we take
$V(\vec{r}_{ij})$ to be the van der Waals potential with a hard
core: $V(\vec{r}_{ij})=-\frac{C_6}{{r_{ij}}^6}$ for $r_{ij} \geq r_c$ and
$=\infty$ for $r_{ij} < r_c$. The correlation function
obtained by solving Eq. (\ref{2Beqn}) quickly attains its
asymptotic form $C(1-\frac{a_{s}}{r_{ij}})$ for large $r_{ij}$.
The asymptotic normalization is chosen to make the wavefunction
positive at large $r_{ij}$. The hard core radius $r_c$ is
adjusted so that the calculated $a_s$ is the actual experimental
value of the scattering length~\cite{Pethick}. This procedure assures that the
realistic two-body interaction appropriate for the condensate
has been incorporated. \\

Substitution of the expansion, Eq.~(\ref{CPHexpn}) in
Eq.~(\ref{Faddeveq}) and projection on the PH corresponding to the
$(ij)$-partition result in
\begin{eqnarray}
\Big[&-&\dfrac{\hbar^{2}}{m} \dfrac{d^{2}}{dr^{2}} + \dfrac{\hbar^{2}}{mr^{2}}
\{ {\cal L}({\cal L}+1) + 4K(K+\alpha+\beta+1)\}
\nonumber
\\
&+& V_{trap}(r) - E_R  \Big] U_{Kl}(r) \nonumber \\
&+& \sum_{K^{\prime}}f_{Kl}V_{KK^{\prime}}(r)f_{K'l} U_{K^{\prime}l}(r) = 0,
\label{CDE}
\end{eqnarray}
where $U_{Kl}(r) = f_{Kl}u_{K}^{l}(r)$,  ${\cal L} =
l+\frac{3N-6}{2}$, $\alpha=\frac{3N-8}{2}$, $\beta=l+\frac{1}{2}$,
$l$ being the orbital angular momentum contributed by the
interacting pair.
$f_{Kl}^2$ is a constant representing the overlap of the PH for interacting
partition with the full set of all partitions, which can be
found in Ref.~\cite{Fabre}. The correlated potential matrix
element $V_{KK^{\prime}}(r)$ is given by~\cite{Das2}
\begin{eqnarray}
V_{KK^{\prime}}(r) &=& (h_{K}^{\alpha\beta}
h_{K^{\prime}}^{\alpha\beta})^{-\frac{1}{2}}
\int_{-1}^{+1} \Big\{
P_{K}^{\alpha
\beta}(z)
V\left(r\sqrt{\frac{1+z}{2}}\right)
\nonumber
\\
&&P_{K^{\prime}}^{\alpha \beta}(z)\eta\left(r\sqrt{\frac{1+z}{2}}\right)
W_{l}(z) \Big\} dz.
\label{corrPME}
\end{eqnarray}
Here $h_{K}^{\alpha\beta}$ and $W_{l}(z)$ are respectively the norm
and weight function~\cite{Abramowitz} of the Jacobi polynomial
$P_{K}^{\alpha \beta}(z)$.
Note that the inclusion of the short-range correlation function,
$\eta(r_{ij})$ makes the PH basis non-orthogonal. Numerical
solution of Eq. (\ref{2Beqn})  shows that
$\eta(r_{ij})$ differs from a constant value only in a small interval
of small $r_{ij}$ values. Hence the dependence of the overlap
$<{\mathcal P}^{lm}_{2K+l}(\Omega^{(ij)}_N)|
{\mathcal P}^{lm}_{2K+l}(\Omega^{(kl)}_N)\eta(r_{kl})>$ on the
hyperradius $r$ is quite small. Disregarding
derivatives of this overlap with respect to the hyperradius,
we approximately get Eq. (\ref{CDE}),
with $V_{KK^{\prime}}(r)$ given by Eq. (\ref{corrPME}). The effect
of the overlap being different from
unity is represented by the asymptotic constant $C$ of $\eta(r_{ij})$.
The emerging physical picture is: the effective interaction between pairs
of atoms at very low energy becomes $V(r_{ij})\eta(r_{ij})$. This is
justified, since at very low kinetic energy, the atoms have a very large
de Broglie wave length and do not approach each other close enough to
"see" the {\it actual} interatomic interaction. In the limit of
zero energy, the scattering cross section
becomes $4\pi|a_s|^2$ and the effective interaction is governed by
the $s$-wave scattering length $a_s$, through the asymptotic form of
$\eta(r_{ij})$. \\

Introduction of the PH basis and inclusion of the short-range
correlation function, referred to as the correlated potential
harmonic (CPH) method, simplifies the many-body problem dramatically.
A fairly fast computer code can solve Eq. (\ref{CDE}) with upto
15000 particles in the condensate. This technique has been
tested against known results, both experimental ones and theoretical
ones calculated by other authors,
for repulsive as well as attractive condensates~\cite{Das1,Das2,PHEM}.\\

\section{Numerical procedure}

\subsection{Solution of coupled equations}

Although Eq. (\ref{CDE}) can be solved by an exact numerical technique
using the Numerov method, we adopt the hyperspherical adiabatic approximation
(HAA)~\cite{das3}, which apart from simplifying the computations
greatly, provides an effective potential in the hyperradial
space, in which the condensate moves. This effective condensate
potential provides a physical picture for the internal mechanism
of the condensate.\\

In the HAA, one assumes that the hyperangular motion
is much faster than the hyperradial motion, since the latter corresponds to
the breathing mode. Therefore, one can
solve the former adiabatically for a fixed value of $r$ and
obtain the solution as an effective potential for the hyperradial
motion, as in Born-Oppenheimer approximation. The hyperangular motion is solved by diagonalizing the potential
matrix $V_{KK^{\prime}}(r)$ together with the hyper-centrifugal
potential [second term of Eq. (\ref{CDE})].
The lowest eigenvalue $\omega_0(r)$ [corresponding
eigen column vector being $\chi_{K0}(r)$], is the effective potential
for the hyperradial motion~\cite{das3}:
\begin{equation}
\Big[-\dfrac{\hbar^2}{m}\dfrac{d^2}{dr^2}+\omega_0(r)+
\sum_K|\dfrac{\chi_{K0}(r)}{dr}|^2-E_R\Big]\zeta_0(r)=0.
\label{HAAeq}
\end{equation}
The third term is an overbinding correction.
Eq. (\ref{HAAeq}) is solved by the Runga-Kutta method, subject
to appropriate boundary conditions to get $E_R$
and the hyperradial wave function $\zeta_0(r)$. The many-body wave
function can be constructed in terms of $\zeta_0(r)$ and
$\chi_{K0}(r)$~\cite{das3}. Total energy is obtained by adding the
center of mass energy ($1.5$ o.u.) to $E_R$. Energy levels, $E_{nl}$, are
characterized by the quantum numbers $(n,l)$, where $n$ represents
the excitation quantum number for a given orbital angular momentum
$l$. The HAA has been tested for nuclear, atomic and molecular systems
and shown to give better than 1\% accuracy, even for the long-range
Coulomb potential~\cite{HAAaccu}. In our case, the van der Waals
potential has a shorter range and HAA is expected to be better. Moreover,
in a BEC, the dominant confining harmonic oscillator potential is
smooth and the corresponding hyperradial equation is completely
decoupled. Hence in a BEC, the HAA is expected to be far better.
We tested this by solving the CDE, Eq.~(\ref{CDE}), with the interatomic potential for
the ground state by the renormalized Numerov method~\cite{Ghosh,Johnson},
which is an exact numerical algorithm for solving a set of coupled
differential equations. The calculated exact ground state energies
are (in o.u.) $948.6420, 1174.5284, 1277.8219, 1460.3706$ and $1596.2611$
respectively for $N=700, 900, 1000, 1200$ and $1400$. These compare very well
with the corresponding HAA results: $948.0986, 1173.9809, 1277.2040,
1459.6373$ and $1595.8163$ respectively. The error is less than
$0.06$\% in all cases. Thus we can safely use the HAA, which reduce
the numerical complications to a great extent. \\

\subsection{Calculation of specific heat}

At a temperature $T>0$, bosons are distributed in available energy levels
$E_{nl}$ according to Bose distribution function
\begin{equation}
 f(E_{nl}) = \frac{1}{e^{\beta(E_{nl}-\mu)} -1}
\label{distribution}
\end{equation}
where $\beta = 1/{k_{B}}T$ and $\mu$ is the chemical potential. The latter
is determined
from the constraint that the total number of particles is $N$. Clearly, $\mu$
has a temperature dependence.
The total number of bosons in the trap is fixed and at any temperature
it can be written as
\begin{equation}
 N = \sum_{n=0}^{\infty} \sum_{l=0}^{\infty} (2l+1)f(E_{nl})
 \label{Nsum}
\end{equation}
At a particular temperature $T$, $\mu$ is determined from the
constraint Eq. (\ref{Nsum}).
The total energy of the system at $T$ is given by
\begin{equation}
 E(N,T)=\sum_{n=0}^{\infty} \sum_{l=0}^{\infty}(2l+1)f(E_{nl})E_{nl}
 \label{Esum}
\end{equation}
The specific heat at fixed particle number $N$ is calculated using
the relation
\begin{equation}
 C_{N}(T) = \frac{\partial E(N,T)}{\partial T}{\Big |}_{N}
\label{spheat}
\end{equation}
Using (\ref{distribution}), (\ref{Esum}), (\ref{spheat}) one can obtain the
heat capacity as
\begin{eqnarray}
C_{N}(T) = \beta\sum_{n=0}^{\infty}\sum_{l_n=0}^{\infty} \frac{(2l_n+1)E_{nl_n}\exp{(\beta(E_{nl_n}-\mu))}}{(\exp{(\beta(E_{nl_n}-\mu))}-1)^2} \nonumber \\
 \times {\Big[}\frac{E_{nl_n}-\mu}{T}+\frac{\partial \mu}{\partial T}{\Big]} \nonumber \\
\label{spheatform}
\end{eqnarray}
where
{\tiny{
\begin{eqnarray}
\frac{\partial \mu}{\partial T} = \hspace*{7cm}\nonumber \\
  - \frac{\sum_{m=0}^{\infty}\sum_{l_m=0}^{\infty}(2l_m+1)(E_{ml_m}-\mu)\exp{(\beta(E_{ml_m}-\mu))}
(f(E_{ml_m}))^2}{T\sum_{p=0}^{\infty}\sum_{l_p=0}^{\infty}(2l_p+1)\exp{(\beta(E_{pl_p}-\mu))}(f(E_{pl_p}))^2}
\end{eqnarray}
}}
For an ideal non-interacting bosonic gas containing $N$
bosons in a three-dimensional
isotropic harmonic well, the critical temperature
$T_{c}^0$ is well defined~\cite{Dalfovo}. $\mu$ remains equal to the
energy of the single particle ground state for
$T<T_c^0$ and start decreasing rapidly for $T>T_c^0$. In the
standard text book treatment~\cite{Huang} the sums in
eqs. (\ref{Nsum}-\ref{Esum}) are replaced in the semi-classical approximation
by integrals over energy, assuming a continuous energy spectrum. In a harmonic trap
the energy spectrum is discrete and this assumption is not valid, particularly
for small $N$ at low energies. A correct treatment~\cite{Napolitano} shows that $\mu$
{\it decreases slowly} from its maximum value (equal to the ground state energy)
as $T$ increases from zero, the rate of decrease becoming suddenly
rapid at some temperature close to the reference temperature $T_c^0$ corresponding
to the same value of $N$~\cite{Biswas1}. Thus, in this case the critical
temperature is not well defined. In the correct treatment, the
heat capacity also becomes a smooth function of $T$, attaining a maximum at
a temperature, at which $\mu$ suddenly becomes a rapidly
decreasing function of $T$. In the limit of large $N$, the behaviors of $\mu(T)$
and $C_N(T)$ curves approach those of the text book treatment.
The {\it transition temperature} $T_c$ for a finite interacting
system is defined as the temperature at which
$C_N(T)$ is a maximum~\cite{Napolitano}
\begin{equation}
\frac{\partial C_N(T)}{\partial T}{\Big|}_{T_c}=0
\label{defTc}
\end{equation}

For the numerical calculation for a chosen particle number
$N$, the CPH equations are solved for
a large number of energy levels -- typically $n$ running from
$0$ to $300$ and $l$ running from $0$ to $200$, subject to an
upper energy cutoff value, $E_{UL}$ (see below), so that
$E_{nl}<E_{UL}$. Using previously calculated values of
$E_{nl}$, Eq. (\ref{Nsum}) is solved for $\mu$, at a chosen
temperature $T$, by a
modified bisection method. Next $E_{UL}$ is increased and
the process repeated, until convergence in $\mu$ is achieved.
Using this upper energy cutoff, $C_N(T)$ is determined using
Eq.~(\ref{spheatform}). \\

\section{Results and discussions}

We consider the attractive condensate of $^7$Li atoms in the
trap used in the experiment at Rice University~\cite{Li-Bradley}. The
harmonic trap used was axially symmetric with
$\nu_x=\nu_y=163$ Hz and $\nu_z=117$ Hz. For
simplicity, we consider an isotropic trap with $\nu=
(\nu_x\nu_y\nu_z)^{\frac{1}{3}}$. The experimental
value of $a_s$ is $-27.3$ o.u. We use oscillator unit (o.u.)
of length ($\sqrt{\frac{\hbar}{m\omega}}$) and energy
($\hbar\omega$). As mentioned earlier, we choose van der Waals (vdW)
potential for the interatomic interaction, with
known value~\cite{Pethick} of
$C_6=1.715\times10^{-12}$ o.u. The value of $r_c$ is obtained by the procedure
discussed following
Eq. (\ref{2Beqn}), so that calculated $a_s$ has the experimental
value~\cite{Pethick}. Its numerical value is $5.338 \times 10^{-4}$ o.u.
The calculated effective potential, $\omega_0(r)$
is plotted as a function of $r$ in Fig. \ref{w0_r} for $N=1300$.
\begin{figure}[hbpt]
\vspace{-5pt}
\centerline{
\hspace{-3.3mm}
\rotatebox{270}{\epsfxsize=6.5cm\epsfbox{w0_r.eps}}}
\caption{(Color online)
Calculated effective potential $\omega_0(r)$ against $r$ in o.u.
for the attractive $^7$Li condensate with $N=1300$. The narrow
and deep well near origin is shown in the inset (note that different
scales are used).}
\label{w0_r}
\end{figure}
In the $r \rightarrow 0$ limit,
$\omega_0(r)$ becomes strongly repulsive, due to the repulsive core
of vdW potential and the hypercentrifugal repulsion of Eq. (\ref{CDE}).
As $r$ increases, there is a deep narrow well (DNW) arising from
the strong interatomic attraction at small values of $r$. This
attraction is proportional to the number of pairs and hence
increases rapidly as $N$ increases. For
still larger $r$, the effects of the kinetic pressure
(including the centrifugal repulsion), interatomic attraction and the
harmonic confinement together produce a metastable region (MSR). An
intermediate barrier (IB) appears between the DNW and MSR. The
DNW is very deep and narrow, hence it is shown as an inset in Fig. \ref{w0_r}
(note large changes in scale for both horizontal and
vertical axes).
\begin{figure}[hbpt]
\vspace{-5pt}
\centerline{
\rotatebox{0}{\epsfxsize=8.0cm\epsfbox{MSR_all.eps}}}
\caption{(Color online)
Plot of effective potential $\omega_0(r)$ against $r$ (both in
appropriate o.u.)
for the attractive $^7$Li condensate with $N=500$, $1300$,
$1400$, $1410$, $1420$ and $1426$ in panels (a) -- (f)
respectively, showing how the MSR shrinks in depth and width.
Note that different scales have been used in different panels,
to bring out the features of the MSR as $N \rightarrow N_{cr}$.}
\label{MSR}
\end{figure}
As
$N$ increases, the DNW becomes deeper, IB shallower and the minimum
of the MSR higher. At the critical value $N_{cr}$, the maximum of IB and
the minimum of MSR merge to form a point of inflexion and the MSR
disappears. At this point, the condensate falls into the DNW,
resulting in a collapse of the condensate and formation of clusters
within the DNW.
Our calculated value of $N_{cr}$ is 1430. In panels (a) -- (f) of
Fig. \ref{MSR}, we demonstrate how the MSR shrinks, with $N$ approaching
$N_{cr}$, for $N=500, 1300,1400,1410,1420,$ and $1426$ respectively.
From Fig. \ref{MSR}, one notices that both the depth and width of MSR
decrease as $N$ increases towards $N_{cr}$. Hence the number of
bound energy levels supported by the MSR decreases rapidly with
$N$ (see also Fig. \ref{en_levels}). \\

However,
the effective potentials shown in Fig. \ref{w0_r} and Fig. \ref{MSR} are obtained for
$l=0$. For higher $l$, the effective potential has a higher IB, arising
from the $l$-dependent terms of the hyper-centrifugal repulsion
[see Eq. (\ref{CDE})]. Thus the position of the MSR rises higher in energy
as $l$ increases, as can be seen in Fig. \ref{w_all} for $l=0,1,2,3,4$ for a
condensate containing 1420 atoms.
\begin{figure}[hbpt]
\vspace{-5pt}
\centerline{
\hspace{-3mm}
\rotatebox{270}{\epsfxsize=6.5cm\epsfbox{w_all_l.eps}}}
\caption{(Color online)
Plot of effective potential $\omega^{l}(r)$ against $r$ (both in
appropriate o.u.)
for the attractive $^7$Li condensate with $N=1420$ atoms,
corresponding to $l=0,1,2,3,4$. The curves show how
the IB increases as $l$ increases.}
\label{w_all}
\end{figure}
Hence particles with $l>0$ can attain higher energy levels.
Inclusion of these levels will have a profound effect on the
heat capacity. If
such energy states were ignored ({\it i.e.}, only the energy levels
supported by the $l=0$ MSR considered), the heat capacity would reduce
drastically and $T_c$ would increase indefinitely as
$N \rightarrow N_{cr}$, since all the atoms would be forced into the
few remaining energy levels available for internal excitation. In our calculation, we have
retained all energy levels supported by a given $l$. A question
arises as to whether the metastable condensate can have large
$l$ values. Intuition indicates that, with increase of temperature,
the system can absorb energy only by increasing its rotational
kinetic energy, thereby increasing the stability of the metastable
system with enhanced centrifugal repulsion. Increase of kinetic
energy due to faster linear motion alone
would cause the system to fall in the DNW near the center of the
condensate. Compared with the
non-interacting or repulsive condensates, the attractive condensate
has a clear distinction, {\it viz.} while the number of hyperradial
excitations for a given $l$ in the former is not limited, it is
drastically limited in the latter. Thus for an attractive condensate,
there are fewer energy states, in which the system can reside.
This causes $(C_N)_{max}$ to increase initially for $N \ll N_{cr}$
(when energy levels are not greatly restricted), but as $N \rightarrow
N_{cr}$, it starts decreasing, after attaining a maximum. Fig. \ref{CN_N}
shows how $C_N(T)$ depends on $T$, for selected values of $N$.
It is seen that the transition temperature $T_c$ increases gradually
with $N$, but $(C_N)_{max}$ increases up to $N=1300$ and for larger
$N$, it starts decreasing.
When $N \ll N_{cr}$, the nature is similar to that of a repulsive
condensate~\cite{Biswas1}, since in this case, the number of available energy
levels are still large enough (the top most energy level -- including $l \neq 0$ -- in the MSR
has an energy much greater than $k_BT$),
so that the top most levels are still
\begin{figure}[hbpt]
\vspace{-5pt}
\centerline{
\hspace{1mm}
\rotatebox{270}{\epsfxsize=6.5cm\epsfbox{CN_N_all.eps}}}
\caption{(Color online)
Plot of heat capacity $C_N(T)/(Nk_B)$ (dimensionless) against
$T$ (in nK), for indicated number of $^7$Li atoms in
the metastable condensate.}
\label{CN_N}
\end{figure}
practically unoccupied and
there is scope for further internal excitation
as $T$ increases.
Consequently $T_c$ increases gradually with $N$,
as in the repulsive case. As $N$ approaches $N_{cr}$, the number of
energy levels supported by the MSR
decreases rapidly and there is less scope for absorbing energy
internally as $T$ increases. Hence $(C_N)_{max}$
decreases and $T_c$ increases faster, as $N$ increases
towards $N_{cr}$. At higher temperatures, higher $l$ states are excited,
which push atoms further outwards, increasing the average interatomic
separation. Consequently, the system behaves ultimately as a
non-interacting Bose gas. Thus the asymptotic value of $C_N(T)$
becomes $3Nk_B$.
In Fig. \ref{CN_N}, we plot the dimensionless quantity $C_N(T)/(Nk_B)$ against $T$ (in nK) for $^7$Li condensate
with $N=500, 1000, 1300, 1350$ and $1400$. The features discussed above are
clearly visible. One notices that the behavior for $N < 1300$ is
similar to that of a repulsive condensate, but
as $N$ exceeds $1300$, the curves become
\begin{figure}[hbpt]
\vspace{-10pt}
\centerline{
\hspace{-3.3mm}
\rotatebox{270}{\epsfxsize=6.5cm\epsfbox{Cvmax_N.eps}}}
\caption{(Color online)
Plot of the peak heat capacity, $(C_N)_{max}/(Nk_B)$ (dimensionless), against
the number $N$ of bosons in the attractive $^7$Li
condensate.}
\label{CNmax}
\end{figure}
flatter near their
maxima and the peak value of $C_N(T)/(Nk_B)$, namely,
$(C_N)_{max}/(Nk_B)$, decreases fairly rapidly, as $N \rightarrow N_{cr}$.
All the curves appear to converge to the Bose gas limit. But a closer
scrutiny shows that the curves for $N=1350$ and $1400$ show a slight downward trend. This is due to a limitation in the higher energy cut-off
used in our calculation.
In Fig. \ref{CNmax}, we plot calculated $(C_N)_{max}/(Nk_B)$ as a function of $N$.
It is seen that this quantity increases gradually up to $N=1300$.
Beyond this value, $(C_N)_{max}/(Nk_B)$ decreases fairly rapidly
as $N \rightarrow N_{cr}$.
\begin{figure}[hbpt]
\vspace{-1pt}
\centerline{
\hspace{-3.3mm}
\rotatebox{270}{\epsfxsize=6.5cm\epsfbox{Tc_N.eps}}}
\caption{(Color online)
Plot of transition temperature (in nK) versus $N$ for the attractive $^7$Li
condensate.}
\label{Tc}
\end{figure}
A plot of transition temperature $T_c$ (in nK) as a function of $N$
is shown in Fig. \ref{Tc}. Initially $T_c$ increases linearly for
$N < 1300$. As discussed above, this behavior is expected for small
$N$, as in the case of a repulsive condensate. But for $N > 1300$, $T_c$
increases rapidly. Both the decrease of $(C_N)_{max}$ and faster increase
of $T_c$ are due to reduction
\begin{figure}[hbpt]
\vspace{-5pt}
\centerline{
\hspace{-3.3mm}
\rotatebox{270}{\epsfxsize=6.5cm\epsfbox{number_en_levels.eps}}}
\caption{(Color online)
Plot of total number of available $l=0$ energy levels versus $N$,
close to $N_{cr}$ for the attractive $^7$Li
condensate.}
\label{en_levels}
\end{figure}
in the number of available energy levels as
$N$ approaches $N_{cr}$. We demonstrate this in Fig. \ref{en_levels} for the $l=0$
energy levels as $N$ increases from $1200$ to $N_{cr}$.
The decrease in the number of available energy levels forces a larger
fraction of the bosons to be in the ground state as T increases
[see Eq. (\ref{Nsum})]. This causes a decrease of $(C_N)_{max}$ and an increase of $T_c$, as $N \rightarrow N_{cr}$. \\

A possible scenario of the attractive condensate as its temperature
is gradually increased is the following. The standard definition of
critical number $N_{cr}$ referred to in the literature,
corresponds to the $l=0$ condensate at zero temperature.
As $T$ is gradually raised, the system absorbs energy by occupying higher
available energy levels upto the top of the MSR. However, there is a
finite life time of atoms in higher energy levels due to tunneling through
the IB into the DNW. Thus there will be a decrease in the number of atoms
in the MSR. The rate of loss of atoms will increase with the energy of
the level, as also with $N$ (increase of $N$ will lower the IB).
The usual definition of heat capacity,
$C_N(T)$, is the rate of change of internal energy with respect to $T$
[Eq. (\ref{spheat})],
{\it for a fixed number $N$ of atoms in the condensate}. This definition
is unambiguous for a repulsive or non-interacting condensate, since
in these cases there is no loss. However, since the loss is appreciable
for an attractive condensate for $N$ close to $N_{cr}$, or if $T$ is
such that $k_BT$ is comparable with the highest excitation energy
allowed by the IB, this definition
demands that atoms be pumped into the condensate at the same rate as the
loss rate from the condensate. Such an experimental procedure has not
been adopted yet. However, for $N \ll N_{cr}$ and $T \ll T_c$, the highest
appreciably occupied levels will have negligible tunneling probability
into the DNW. Under these conditions, the metastable attractive condensate
is fairly long lived and the standard definition of $C_N(T)$ is acceptable.
Hence standard experimental techniques can be adopted. Thus our results
presented in Figs.~4 -- 6 are experimentally verifiable in the small $N$,
small $T$ limit. We have presented, for theoretical completeness, results
for $N$ close to $N_{cr}$ and for $T$ beyond $T_c$. The question of how
the system can absorb energy internally for such values of $N$ and $T$ was
already discussed above.

\section{Conclusions}
In this work, we report a detailed calculation of the heat capacity
$C_N(T)$ of an attractive Bose-Einstein condensate containing $N$
atoms of $^7$Li.
The correlated potential harmonics method, which is appropriate for the
dilute BEC, has been used.
The effective potential, in general, supports a large number of energy levels.
At $T=0$, the lowest energy level accommodates all the bosons. As
temperature increases, particles are distributed in higher energy levels,
according to Bose distribution formula. Thus the internal energy of the
system increases. Heat capacity $C_N$ for a fixed number $N$ of particles
in the condensate is defined as the temperature derivative of the total
internal energy. For a repulsive condensate trapped by an ideal harmonic
oscillator, the effective potential has no upper cut off. Hence the energy
levels are not limited in energy. Consequently, total internal energy and
$C_N$ increase as temperature increases upto $T_c$. For $T > T_c$, the
ground state occupation becomes suddenly microscopic (negligible) and the
system behaves like a harmonically trapped Bose gas.
Hence $C_N$ decreases rapidly above $T_c$, reaching its asymptotic value
$3Nk_B$. Thus $C_N$ first increases, reaches a maximum value $(C_N)_{max}$
and then decreases  rapidly to its asymptotic value, as $T$ increases from zero. \\

For $N< N_{cr}$ bosons with mutual attraction, a metastable condensate is
formed in the metastable region (MSR) of the effective potential. On the
left of the MSR, an intermediate barrier (IB), followed by a deep narrow
well and finally a strongly repulsive core appear, as one approaches
the center of the condensate. For $N \ll N_{cr}$, the IB is very high  and
the minimum of the MSR is very low, so that the metastable well is
sufficiently deep compared with thermal excitation energy $k_BT_c$ at $T_c$,
and a large number of energy levels are supported. Hence for $T \leq T_c$,
even the most thermally excited particles do not feel the effect of the IB
and $C_N$ increases gradually, as in the repulsive case. \\

With increase of temperature, the system with a fixed $N$
absorbs energy internally by increasing the occupation probability of
higher energy levels supported by the metastable region of the
effective potential. Atoms in energy levels close to the top of the
intermediate barrier have appreciable probability to tunnel into
the deep narrow well, causing the condensate to loose atoms. But such
levels are not occupied with any appreciable probability if
$N \ll N_{cr}$ and $T \ll T_c$. Hence such a condensate is quasi-stable
and $C_N(T)$ calculated for a fixed $N$ is appropriate.
When the rate of atom loss from the condensate is appreciable,
standard definition of heat capacity at constant $N$ requires feeding the attractive
condensate with additional atoms at a rate such as to compensate
for the loss rate. Although this is not the usual experimental
technique, we investigate such cases for a complete theoretical
study. In such a situation,
there are drastic changes. The peak value of $C_N(T)$ (the
temperature at which this occurs is the transition temperature $T_c$)
initially increases gradually with $N$, then after reaching a
maximum, decreases fairly rapidly near $N_{cr}$. On the other hand, for
small $N$, $T_c$ increases almost linearly up to $N \sim 1300$.
For larger $N$, the transition temperature increases rapidly with
$N$. We provide an explanation of this
behavior, based on the microscopic mechanism of absorption
of internal energy, as $T$ increases. As $N$ increases
towards $N_{cr}$, the depth and width of the metastable well decrease
rapidly. As a result, the number of
energy levels supported by the metastable well decreases rapidly.
This tends to increase $T_c$, since fewer energy levels are available
for absorption of internal energy, and bosons are forced to be in lower
energy levels as $T$ increases. Rapid reduction of available
energy levels as $N \rightarrow N_{cr}$, causes quicker
saturation of internal energy of the condensate. Consequently,
the maximum of $C_N(T)$ decreases rapidly as $N \rightarrow N_{cr}$.

\section {Acknowledgement}
We would like to thank Dr. Parongama Sen for useful discussions.
SG acknowledges CSIR (India) for a Junior
Research Fellowship [Grant no. 09/028(0762)/2010-EMR-I],
TKD acknowledges UGC (India) for the Emeritus
Fellowship [Grant no. F.6-51(SC)/2009(SA-II)] and AB acknowledges CSIR (India) for a Senior
Research Fellowship[Grant no. 09/028(0773)/2010-EMR-I].

redpajama_set_name: RedPajamaArXiv


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text:
Q: NSUndoManager: disable "redo" for destructive action I'd like to add undo/redo functionality to my Mac app. The app works with notes and I'd like to add an "undo" action for when the user deletes a note.
This works just fine, the "Undo Delete Note" menu becomes active after the user deleted a note, but after using the "Undo Delete Note" command, there is a "Redo Delete Note" menu that becomes active.
Currently nothing happens when I click "Redo Delete Note", because I didn't register an action. I don't want the user to be able to delete a note accidentally through the undo/redo stack.
Is it possible to add an "undo" action without a "redo" action?

A: Not in the common case. And to do so would be to violate the implicit contract of the platform-standard undo/redo mechanism. You want the things you register to be symmetric. If a user deletes a note, then the available undo action should bring the note back. If the user elects to undo, then the redo action would be to "delete the note" again. It shouldn't matter if a user "accidentally" deletes a note by virtue of undo or redo, because they should always be able to get it back by doing the inverse action, right?
Don't overthink this.

redpajama_set_name: RedPajamaStackExchange


text:
Can Bees Be Trained to Sniff Out Cancer?
December 13, 2013 Some insects, such as bees, have a sense of smell so acutely sensitive that they can locate the faintest of odors in a room, even if it consists of only a few molecules. But scientists are particularly intrigued by the fact that these bugs can even be...
Roboticists Create Rover To Move And Drill On The Moon
Engineers and robiticists created a robot to explore the moon. Running on the same amount of power as a 100-watt light bulb the rover uses heat from radiation to support its sensors, movement, and drill. It can move about five inches a second and work in harsh conditions to analyze the...
Producing Electricity On the Moon at Night
Scientists from the Polytechnic University of Catalonia and other international collaborators have proposed a system of mirrors, processed lunar soil and a heat engine to provide energy to vehicles and crew during the lunar night. This would preclude the need for batteries and nuclear power sources...
New Data Compression Method Reduces Big-Data Bottleneck; Outperforms, Enhances JPEG
In creating an entirely new way to compress data, a team of researchers from the UCLA Henry Samueli School of Engineering and Applied Science has drawn inspiration from physics and the arts. The result is a new data compression method that outperforms existing techniques, such as JPEG for images,...
Companion's Comets the Key to Curious Exoplanet System?
The nearby star Fomalhaut A hosts the most famous planetary system outside our own Solar System, containing both an exoplanet and a spectacular ring of comets. Today, an international team of astronomers announced a new discovery with the Herschel Space Observatory that has made this system even...
Graphene-Based Field-Effect Transistor With Semiconducting Nature Opens Up Practical Use in Electronics
UNIST announced a method for the mass production of boron/nitrogen co-doped graphene nanoplatelets, which led to the fabrication of a graphene-based field-effect transistor (FET) with semiconducting nature. This opens up opportunities for practical use in electronic devices. A...

redpajama_set_name: RedPajamaCommonCrawl


text:
Statement of the Permanent Conference of Ukrainian Orthodox Bishops Beyond the Borders of Ukraine
April 25, 2018 ~ Fr Gregory
Source: (UOC-USA)
To the Venerable Clergy, Clergy, Monastics and Faithful of our Holy Ukrainian Orthodox Church in Diaspora:
CHRIST IS RISEN! INDEED HE IS RISEN!
We write to you all having been informed about recent events in Ukraine surrounding the life of the Ukrainian Orthodox Church. If you have not yet heard or read anything about these events, which are filling the social websites and media in and beyond Ukraine, we hereby inform you that the President of Ukraine met in a day-long audience with His All-Holiness, the Ecumenical Patriarch of Constantinople, Bartholomew I, on Bright Monday – 9 April 2018. The result of this meeting was the beginning of the Patriarchate's long-awaited consideration of Autocephaly for the Ukrainian Orthodox Church of Ukraine.
Upon his return to Ukraine, President Poroshenko immediately began the process of rallying the hierarchs of the Ukrainian Orthodox jurisdictions in Ukraine and the Verkhovna Rada (Ukrainian Parliament). All the hierarchs of two of the three jurisdictions and the vast majority of the Rada responded to the President's emotional appeal to support the process of asking His All-Holiness Patriarch Bartholomew and the Holy Synod of Constantinople to move forward with the process of granting a Tomos of Autocephaly to the Church in Ukraine, which has for 1030 years been the canonical territory of the Patriarchate of Constantinople, since 988 when our nation was baptized and confirmed into the Holy Orthodox Faith.
Not even under 332 years of non-canonical and often tortuous subjugation to a foreign Orthodox patriarchate could the faithful of Ukraine be convinced that they did not belong to the authority of the Ecumenical Patriarchate. This is simple history, as documented by generations of Patriarchs and Synods of Constantinople, which never abandoned its canonical rights and privileges in Ukraine.
The Ecumenical Patriarchate, through releases on its own website and through the media has confirmed that the process of considering the Autocephalous status of the Church of Ukraine has begun, which will continue through the next meeting of the Holy Synod to be held in May.
President Poroshenko in all his public appearances and statements about these current events has been incredibly enthusiastic about the possibility of the Ukrainian Orthodox Church of Ukraine being granted even by the 1030thanniversary in July 2018 of the Baptism of Ukraine into the Orthodox Faith in 988 by Equal-to-the-Apostles, Great Prince Volodymyr.
The Permanent Conference of Ukrainian Orthodox Bishops Beyond the Borders of Ukraine has written a strong letter of support for the actions being taken by His All-Holiness and the Holy Synod of Constantinople regarding the possible granting of a Tomos of Autocephaly to the Ukrainian Church. We have assured His All-Holiness of the unceasing prayers of not only the hierarchs, but also the millions of Ukrainian Orthodox clergy and faithful in and beyond the borders of Ukraine, for him personally during this process.
We invite our faithful to join us in this prayer:
Prayer for the Unification of the Ukrainian Orthodox Church
O Lord our God, You can see, as the invisible and visible enemies divided the Ukrainian Orthodox Church, and with it all Ukrainian people. Help us to promote the unification of Ukrainian Orthodoxy into a single Church, putting the cornerstone of apostolic rule that orders us to know that every nation, and among them the Ukrainian people, must have its first hierarch.
O Lord, inspire our separated brethren, so that they will unite around the Throne of Kyiv into a single Church and that Christian love would prevail among all of us, because You said: "By this everyone will know that you are my disciples, if you love one another".
Look upon us, Lord the Lover of all mankind, and do not punish us for our iniquities, voluntary and involuntary, committed in knowledge and in ignorance. Let us have a true love amongst us, forgive us our trespasses and do not remember our transgressions.
Great Merciful Master, protect and preserve Ukraine from those who encroach on its independence and wants to divide it, as you have always protect the Christian countries. Let a single Ukrainian Orthodox Church be a strong spiritual foundation for the indivisible Ukraine and the unity of our people, let it enemies be scattered and let peace, harmony and unity prevail in us.
O Lord, You said: "For without me you can do nothing." Hear, o God, prayer of your faithful and bless the begun matter of the unity of the Orthodox in a single Church of Ukraine to lead to a successful conclusion. To His All-Holiness Patriarch Bartholomew, the Ukrainian Orthodox Hierarchs, the President, the Verkhovna Rada, and all those who work for this, send wisdom and inspiration of Your Holy Spirit, and in the good cause of the recognition of the Ukrainian Church to bring everyone to close conclusion. For Yours it is to have mercy on and save us, our God and we glorify You, Father, Son and Holy Spirit, now and ever and to the ages of ages. Amen.
With Archpastoral Blessings,
+YURIJ, Metropolitan of the Ukrainian Orthodox Church of Canada
+ANTONY, Metropolitan of the Ukrainian Orthodox Church of the USA and Diaspora
+JEREMIAH, Archbishop of the Ukrainian Orthodox Eparchies of Brasil and South America
+DANIEL, Archbishop of the Ukrainian Orthodox Church of the USA and Western Europe
+ILARION, Bishop of the Ukrainian Orthodox Church of Canada
+ANDRIY, Bishop of the Ukrainian Orthodox Church of Canada
Posted in Encyclical, Ukrainian History, Uncategorized, UOC
Published by Fr Gregory
View all posts by Fr Gregory
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Andre Kostelanetz was a famous Musician from Russia, who lived between December 22, 1901 and January 13, 1980. He/she became 78 years old.
Our collection contains 3 quotes who is written / told by Andre.
"The conductor has the advantage of not seeing the audience"
"Everybody should have his personal sounds to listen for - sounds that will make him exhilarated and alive or quiet and calm"
"One of the greatest sounds of them all - and to me it is a sound - is utter, complete silence"


text:
Vintage Pulp May 27 2020
I'm not worried. I know something you don't. I'm the star of an entire series.
Above, a 1959 cover painted by James Meese for John Ross MacDonald's 1950 thriller The Drowning Pool. We looked at a 1951 cover for this a while back, but rather than talk about the story made some dumb jokes and called it a day. So about the book. The novel features franchise detective Lew Archer trying to solve a drowning murder while dealing with a family torn apart over an inheritance. Liking the book is a matter of liking the character. Archer is cynical, quippy, and pretty rude most of the time—in short, a typical mid-century fictional detective. And therein lies the issue. He's standard, which means the mystery needs to be unique, but instead it's a drop-off from the series debut The Moving Target. It's not bad, though, and consensus is the eighteen Archer adventures improve as they progress. We'll see, because we plan to keep reading them. Hopefully Archer will make us glad he survived this gun to his head.
Pocket BooksJohn Ross MacDonaldRoss MacDonaldJames Meesecover artliterature
Vintage Pulp Dec 1 2018
L.A. stands for Lew Archer in John MacDonald's tinseltown thriller.
We love this cover art by Harvey Kidder for John MacDonald's, aka Ross MacDonald's first Lew Archer novel The Moving Target. The way the figures are placed at such a remove from the viewer and the text is stretched across the underside of the pier is strikingly different. The book was originally published in 1949 with this Pocket Books paperback coming in 1950, and it stars MacDonald's franchise detective trying to locate a philandering millionaire who's gone missing. The man's wife is more concerned about the possibility of her spouse being on a bender and sharing the family money than she is about foul play, but Archer soon decides that the situation is a kidnapping.
We'd been meaning to read MacDonald for a while. We'd heard that his prose has a Dashiell Hammett vibe and that certainly turned out to be true. Set in and around Los Angeles, it weaves summer heat, wacky mysticism, outsize ambition, and broken dreams together into a tale with great Southern California flavor. And Archer is appropriately road worn: "I believed that evil was a quality some people were born with, like a harelip. But it isn't that simple. Everybody has it in him, and whether it comes out in his actions depends on a number of things. Environment, opportunity, economic pressure, a piece of bad luck, a wrong friend."
In this world that he's accepted as more complex than he'd like it to be, he navigates using a solid personal code and a very hard skull—both severely tested multiple times. We gather the story is considered unremarkable compared to later Archer novels, but for us it was entirely satisfactory. It satisfied Hollywood too, which made it into a star vehicle for Paul Newman called Harper. Why the name of the detective was changed we can't even begin to guess, but we saw the movie a couple of years ago and it was enjoyable. Below you see a 1959 Pocket Books edition of The Moving Target with Jerry Allison art. More from MacDonald later.
John MacDonaldRoss MacDonaldJohn Ross MacDonaldKenneth MillarHarvey KidderJerry Allisoncover artliterature
Vintage Pulp Jun 1 2015
Give a girl a light? You'll have to lean down here, though. If I come up there I'll start flopping around something awful.
We love this Ray App cover for John Ross MacDonald's, aka Kenneth Millar's mystery The Drowning Pool because it's incredibly bizarre. Plot of the book aside (it's the second Lew Archer novel), there can be only two reasons for the female figure to be positioned as she is—she's either standing in a rowboat, presumably for the pure pleasure of it, or she's trying to conceal her mermaid half. She shouldn't worry about hiding, though—generally guys don't hang around the docks unless they're at least a little interested in seafood. 1950 original copyright, and 1951 on the paperback.
Pocket BooksThe Drowning PoolJohn Ross MacDonaldRoss MacDonaldKenneth MillarRay Appcover artliterature
SEARCH PULP INTERNATIONAL
The headlines that mattered yesteryear.
1950—Alger Hiss Is Convicted of Perjury
American lawyer Alger Hiss is convicted of perjury in connection with an investigation by the House unAmerican Activities Committee (HUAC), at which he was questioned about being a Soviet spy. Hiss served forty-four months in prison. Hiss maintained his innocence and fought his perjury conviction until his death in 1996 at age 92.
1977—Carter Pardons War Fugitives
U.S. President Jimmy Carter pardons nearly all of the country's Vietnam War draft evaders, many of whom had emigrated to Canada. He had made the pardon pledge during his election campaign, and he fulfilled his promise the day after he took office.
1915—Claude Patents Neon Tube
French inventor Georges Claude patents the neon discharge tube, in which an inert gas is made to glow various colors through the introduction of an electrical current. His invention is immediately seized upon as a way to create eye catching advertising, and the neon sign comes into existence to forever change the visual landscape of cities.
1937—Hughes Sets Air Record
Millionaire industrialist, film producer and aviator Howard Hughes sets a new air record by flying from Los Angeles, California to New York City in 7 hours, 28 minutes, 25 seconds. During his life he set multiple world air-speed records, for which he won many awards, including America's Congressional Gold Medal.
It's easy. We have an uploader that makes it a snap. Use it to submit your art, text, header, and subhead. Your post can be funny, serious, or anything in between, as long as it's vintage pulp. You'll get a byline and experience the fleeting pride of free authorship. We'll edit your post for typos, but the rest is up to you. Click here to give us your best shot.
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Things you'd love to buy but can't anymore


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Girls your hangover tips were a godsend! I now have Berocca ready to go in the office at all times and a litre of water beside my bed – JUST IN CASE! You never know when Christmas drinks will be sprung on you.
Amelia won the competition with her hilarious stories of dressing for work the next morning while still under the influence: a killer ensemble of satin jeans and pink stilettos! I now get Fran to sign off outfit choices as I go through the door. As with shopping, sartorial decisions made when drunk are never the strongest.
Another day, another work related battle. Today it's the database. I've been trying to tidy up all our client details and addresses so they're ready for producing our Christmas card labels next week. I know, sounds dry right? Should be incredibly straight forward, but not when you have a technophobe in charge of the database.
I've just managed to email the entire database asking the clients to confirm that our address details are correct rather than theirs! Too embarrassing! You can just imagine the responses, can't you: 'I would have thought you were better placed to confirm that than me, Lucy?' Good point, well made. So now I've got to follow up with a second grovelling email correcting my first. Next I'll be fielding all their complaints about being spammed with all my emails.
You guys are absolute lifesavers!! I have been putting your hangover tips to good use all week and arriving at work considerably bonnier and brighter than I think I would have otherwise. I owe you one!
1) I managed to pitch my dress just right (for once!) – I wore a black lace number with pretty long sleeves: not too long, not too short, not too slutty, not too frumps. Success – compliments all round.
2) Even though the wine was free flowing (and in bottomless supply!) I managed to pace myself. Those lunchtime pasta pots are really paying off in the drinking stamina stakes (Lord knows what they're doing to my waistline, but it's the lesser of two evils. I'll just have to deal with that in the gym in January).
3) I have full recollection of the entire evening, and apart from being ever so slightly nervous for the first half hour I don't think I behaved remotely inappropriately.
As I jumped into a cab at the end of the night I was reflecting happily to myself on how I must be growing up at last. But as I slammed the taxi door shut and climbed the stairs at the front of my building it all suddenly unravelled: I had the horrific realisation that I had forgotten my house keys! In my hurry to get ready in the office, and to grab my essentials to cram into my impossibly teeny clutch bag, I had completely forgotten to scoop up my keys!
As Fran and I live on the 2nd floor at the back of a Victorian terrace, as our doorbell is broken and as Fran sleeps like the dead this was a terrible state of affairs! I was locked out, at 2am, on a cold rainy December night, wearing only a little black dress and a leather jacket! I was terrified, I was alone in the world with nowhere to sleep, what could I do??
I span round, but the taxi was long gone. I knew Charlie was out of the country on a stag do and I obviously tried to call Fran – I think around 10 times before I accepted defeat. Next, I worked my way through my contacts list of school and uni friends who might possibly have their phone on loud and who might be able to take me in. I was on the verge of tears and in complete desperation when I finally got through to someone – a guy who lived miles away in Angel, but beggars can't be choosers so I jumped into my second epic taxi journey of the night and arrived with him about 3 in the morning. Thank god for mobile phones and old friends.
The worst part of all of this, however, was having to do the walk of shame the next morning: after waking up in a house of boys I had to go to work in exactly the same party dress and heels I had said goodbye to everyone in just hours before. You can imagine the comments can't you? And no one believed my story about the keys. Argh can I leave for Christmas now please?
Last day of term kids! If we were at school we'd be wearing paper crowns about now, scooping up fist fulls of Quality Street and wheeling in the TV set for a video morning. Depending on how much sherry Mr Waring had over lunch it could end up as a video afternoon as well. Eeeee I love Christmas, and I used to love those lazy school days in the lead up!
To be honest, things are not much more productive over here in Mayfair – the meetings have completely dried up, there are no calls and for at least the past 2 days everyone's been in a sluggish egg-nog haze. We've got an incredible spread of mince pies, boozey panettones and chocolates spilling out of the kitchen and I'm hoping a few corks might pop this afternoon… I usually hate it when it's this quiet, but it's absolute heaven at the moment because it's beginning to look so much like Christmas.
What's brilliant as well is that Priscilla's definitely in the same headspace as me, so the pressure has eased off until the New Year. She's having a lovely old time of it, she's raided Claire's Accessories and is now the proud owner of the most horrendous collection of novelty Christmas earrings – I so wish you could see them! My favourite are today's giant dangly felt Rudolfs that clash spectacularly with her hot pink cardi. I've never seen her looking so excited it is pretty adorable! I have warned her though not to lean over any candles at dinner with those polyester babies on, what with her generous application of hair spray it could be catastrophic!
Just dashing off to Oxford Street for the last few pressies now, so wish me luck! Nothing like a tug of war with a stranger over the last tasteful scarf in the store to get you in the Christmas spirit!


The Ladies Thursday Club meets on the last Thursday of the month except in August when there is no meeting. We have a variety of speakers, demonstrations, and some outdoor events. We welcome any new members who will find a friendly greeting. We start at 7.30pm.


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The Most Inappropriate Outfits Worn By Madonna
Stephen Lovekin/Getty Images
By Raegan Davies/Sept. 3, 2021 11:58 am EST
If there is one person who the word "icon" should be reserved for, it's Madonna. Since she exploded onto the music scene in the '80s, she has kept audiences on their toes and managed to stay relevant over three decades since the beginning of her career. So just how has the "Queen of Pop" stayed confidently perched atop the pinnacle of pop culture? It depends on who you ask. Some would say that her timeless music is the reason. Others would answer that her controversies keep her relevant — from the outrage sparked over her 1989 "Like a Prayer" video to her 2006 tiff with church groups over her cross imagery during her Confessions tour (via Biography).
The answer you may get the most, though? Her style. Madonna has consistently shocked — and often offended — audiences with her overtly sexual and revealing clothing choices. Keep reading to see some of the most inappropriate outfits worn by the pop icon throughout the years.
Madonna shocks with the cone bra
Gie Knaeps/Getty Images
Of all of Madonna's signature looks throughout her career, this is definitely the most widely recognized. Just the two words "cone bra" summon up images of the pop star — no photo necessary. This bra made its most iconic appearance on her Blond Ambition Tour in 1990 (via CNN). The pink, belted, satin corset worn over black tights was designed by Jean Paul Gaultier, who had been working on similar conical designs for his runway shows in the 1980s.
The cone bra didn't only serve the purpose of shock value — it also made a statement of the singer's unwillingness to bend to criticism in her career. The Blond Ambition Tour started off the heels of intense heat for Madonna over her risqué "Like a Prayer" — which even had Pope John Paul II calling for people to boycott the pop star. Just before the "Like a Prayer" album's release, Madonna told The New York Times, "art should be controversial, and that's all there is to it" — and what a way for her to double down on that!
Madonna's sheer bra on the MDNA tour
Dave J Hogan/Getty Images
Per Harper's Bazaar, in 2012, Madonna kicked off her MDNA tour. In true-to-her fashion, her concert outfits were just as outrageous (and sometimes inappropriate) as her red carpet style. Case in point: the sheer bra she sported onstage which left very little to the imagination. She didn't stop there, however, as she also revived the infamous cone bra of decades past. But her concert outfits were a fantastic way to promote not only her music but also her lingerie line, fittingly named Truth or Dare by Madonna (via The Cut).
WWD reported at the time that she sported outfit pieces from high-end designers such as Jean Paul Gaultier, Prada, Alexander Wang, and Miu Miu, among others. She also sang a somber version of the typically boppy "Like a Virgin" while wearing an Agent Provocateur bra. This is one of those looks that very few can pull of, but suffice to say, Madonna made it look easy.
Another see-through look at the 2016 Met Gala
Ovidiu Hrubaru/Shutterstock
If you thought Madonna's controversial looks started and ended in her early career, you'd be dead wrong. The pop star has continued to shock the public into her early 60s, and it's part of what's kept everybody talking. She turned heads — and raised eyebrows — at the 2016 Met Gala when she arrived in black leather thigh-high boots, black arm wraps, and a black lace getup that exposed her butt and her breasts, with only two strips of black tape covering her nipples (via Elle).
Not one to shy away from criticism, Madonna responded to the backlash with this caption on her Instagram: "We have fought and continue to fight for civil rights and gay rights around the world. When it comes to Women's rights we are still in the dark ages. My dress at the Met Ball was a political statement as well as a fashion statement. The fact that people actually believe a woman is not allowed to express her sexuality and be adventurous past a certain age is proof that we still live in an age-ist and sexist society. I have never thought in a limited way and I'm not going to start."


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Lab specialist invests in Rochdale office
Boulting Environmental Services, a design and construction firm specialising in cleanrooms and laboratories, has moved into new premises at Rochdale's Sandbrook Park, a relocation that has seen it double its floorspace to 10,000 sq ft.
Boulting was previously based in Middleton on the Greengate Industrial Estate.
The company acquired two adjacent 4,000 sq ft offices, Maple House and Rowan House, and has invested £500,000 in adding an extension to connect the two buildings.
Steve Marsh, managing director, said: "In the last two years, BES has experienced exceptional growth; it has trebled its turnover and increased its staff numbers to match. The major investment in our impressive new office space means that our facility now matches the ambition of the business. The move to Sandbrook Park will also give our team room to grow again and we expect to further strengthen our team again in 2017.
"The collaborative workspace will improve the output and efficiency of our engineers. Our people are our greatest asset and the new facility will enable our project teams to work together on design and construction projects in an open and vibrant environment."


Denmark has dominated the global happiness indices for many years, showing the world that it can strike the perfect balance between being the nanny state and letting its citizens develop on their own terms. Hygge, the Danish philosophy of living, can now be found in almost every hipster's home and Danish design has reminded people all over the world that less is often more.
Maybe the same can be said about Denmark's leading roasters. Of the four or five that spring to mind, almost all of them use white packaging, work only with a handful of selected coffees, most of them traded directly, and carefully handpick the partners they want to work with. That makes them both desirable and slightly elusive, something that clearly works in their favour. Here at The Coffeevine, we can count ourselves fortunate to have worked with most of Denmark's leading roasters and this month will see us joining forces with April Coffee Roasters from the capital Copenhagen for the second time.
April Coffee Roasters is still a relatively young outfit founded by Swedish expat Patrik Rolf after learning his skills at both Da Matteo in Gothenburg, his hometown, and Five Elephant in Berlin. He previously told me that he chose Copenhagen as his base because to him, the city is an endless source of inspiration. A place that continues to innovate, that champions the quality of life of its citizens and where chefs, brewers and roasters are always looking for ways to change the rules of the game. Noma, Mikkeler and Coffee Collective immediately spring to mind when thinking of well-known examples.
Today, April Coffee Roasters is a team of two consisting of Patrik and Joseph Fisher and April has gained a solid reputation not just for its outstanding coffees but also for being unafraid to try different formats. April is one of the few European specialty coffee roasters who offers some of its coffees in Nespresso compatible capsules and Patrik has even launched his own podcast series featuring interviews with some of the industry's most respected names.
Naturally, it is a great honour to have Patrik and Joseph back in one of our boxes and this month, they are completing the exquisite lineup of our forthcoming October '18 coffee box that also includes Calendar Coffee from Galway and Nømad Coffee from Barcelona. The coffee that we chose for our box is an outstanding Kenyan coffee from the Mount Elgon region. It hails from the Kapsokisio wet mill and is one of our personal favourites from previous years.
We don't feature Kenyan coffees too often but when we do, we want them to be the most delicious we can get. The Kapsokisio mill is one of the country's most reputable factories and has been in operation since 1971. Today, it works with more than 850 smallholder farmers from that region and it employes well-developed quality standards to make sure only the ripest cherries are processed. That has lead to its unique flavour profile that is often hailed as the quintessential Kenyan coffee.
Don't want to miss out on our forthcoming October '18 coffee box that will also feature coffees from Calendar Coffee and Nømad Coffee?


Linux Howtos: News Archive -> 100000th hit on Newsticker file.
Today the newsfeed counter hit the 100.000 mark.
Those newsfeeds had led to 627 visits.
Keep on reading. During the next weeks, there will be some improvements on this site. They will be anounced here.


Hello, I suppose the big news is I am Halton Sports Person of the Year 2014. It was for the double gold and silver I won at the European Transplant Games in Lithuania and the bronze medal I won at the British Transplant Games as well as the silver hard bat doubles awards locally.
I attended a lovely ceremony with my friend Claire at The Select Security Stadium. And we got a roast dinner before the awards. I wasn't driving, so utilised the bar!


This photograph was taken very close to where I used to live – a small town called Meltham in West Yorkshire. I do a lot of night photography and have found that one of the best times to do this is when there has been a fresh fall of snow, as there are no cars on the road and the snow clings to everything. It was exactly like this the night I took this photograph.
I set out with a Yashica Mat-124G using Ilford HP5 film, which gives 12 exposures. As it turned out, 12 exposures were all I had, as the air was too wet to allow me to change the film. I think this restriction really focuses your mind and helps to ensure that you make every single image count.
It seemed as though there was a great picture everywhere I looked that night – it was so eerie and magical. I got quite a few good shots as a result, but this was the strongest.
To take the photo, I positioned myself in the woodland looking out through the trees towards a small wall, behind which was a road. I saw the spot as I was walking up the road. I spotted the trees first and thought how interesting the shapes were, and it got me thinking about how the scene in front of me would look from their perspective. So I jumped over the wall into the woods and found that the view was amazing. I took one shot and knew it would be the best of the night.
The light source in the photograph is a street light. When shooting at night in the snow, every bit of light is magnified through reflections. If there had been no snow that night, the street light would have given me only a pocket of light, but because of the snow on the ground and the snow still falling from the sky, the light bounced everywhere, lighting up the sky and my surroundings.
I used no additional lighting to take the photograph other than what was provided by the street light. I used a tripod and the exposure would have been in the region of 11⁄2mins. The aperture was f/11.
In terms of framing, it is vital to remember that night photography is about dramatic lighting. I therefore place the silhouetted trees in the foreground, to give really strong shapes with a real sense of drama.
That said, I had to be quite careful about where I positioned the street light. With night photography you do not want a glaring highlight, and if I had shot directly into the light this is what would have happened. What you want to do is hide the light behind something so you get the effect of the light without the direct intensity of the light itself. In this photo, the street light is hidden behind a branch. However, the light was still very intense on the branches in the centre of the picture and that gave me some problems when printing due to the strong changes in contrast.
high-contrast film mask to control the contrast. The trick is to make the burning-in look natural, not clumsy, and that takes practice. I am an Ilford Master Printer so I know what I am doing, but it still took a lot of testing and trying out of techniques. I think the print had around ten different stages of darkroom process to get it to the point you can see here. It is not something you can rattle off quickly – it was around five hours of really hard work to get the print right. You do get a bit sick of it after that long, and you don't go near it for a while afterwards!
I much prefer to use the darkroom than the scanner and editing software, as it gives me much more satisfying control over the image. Likewise, film is much better at compressing tonality than digital imaging. You would not be able to shoot this image digitally, as the highlights would blow out. You would have to do a number of exposures and overlay them, but then you have the difficulty of branches moving.
I think the definition is also a really strong element of the photograph, and while that is down predominantly to the Yashinon 80mm f/3.5 lens on the camera, I also think you can't beat medium-format film for the sharpness of the image.
Overall, it was magical scene that evening and I was really pleased to capture it – despite getting a bit cold!


text:
6819 McGarvey eller 1983 LL är en asteroid i huvudbältet som upptäcktes den 14 juni 1983 av den amerikanska astronomen Suzanne Smrekar vid Kiso-observatoriet. Den är uppkallad efter upptäckarens mor, Flora McGarvey Smrekar.

Asteroiden har en diameter på ungefär 5 kilometer.

Referenser

Huvudbältesasteroider
Småplaneter namngivna efter personer
Astronomiska upptäckter av Suzanne Smrekar
Astronomiska upptäckter 1983

redpajama_set_name: RedPajamaWikipedia


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La Lega Nazionale A 2022 è le 36ª edizione del campionato di football americano di primo livello, organizzato dalla SAFV.

Squadre partecipanti

Stagione regolare

Calendario

1ª giornata

2ª giornata

3ª giornata

4ª giornata

5ª giornata

6ª giornata

7ª giornata

Recuperi 1

8ª giornata

9ª giornata

10ª giornata

11ª giornata

12ª giornata

13ª giornata

Classifica
La classifica della regular season è la seguente:

PCT = percentuale di vittorie, G = partite giocate, V = partite vinte, P = partite perse, PF = punti fatti, PS = punti subiti
La qualificazione ai playoff è indicata in verde
L'ultima classificata sfida la vincente della Lega B per la partecipazione alla LNA 2023 (giallo)

Playoff

Tabellone

Semifinali

XXXVI Swiss Bowl

XXXVI Swiss Bowl

Spareggio relegazione

Verdetti
   Campioni di Svizzera 2022
  non relegati in Lega B 2023

Note

Voci correlate
Lega B 2022 (football americano)
Lega C 2022 (football americano)
Campionato svizzero di football americano

Collegamenti esterni

 2022 A


This Part of the Northern Territory Law Journal includes the following articles based on papers originally presented at the Criminal Lawyers Association of the Northern Territory (CLANT) Conference, "Victims of the System" in Bali (June 2013): "Unnecessary suffering: Violence against Aboriginal women in the Northern Territory – A discussion of contemporary issues and possible ways forward" – Justice Jenny Blokland; "Boat people as victims of the system: Mandatory sentencing of 'people smugglers' – Politics or justice?" – Dina Yehia SC; "Vulnerability, risk and justice for children and young people in the Northern Territory" – Howard Bath; as well as a look at 2015 legislative reforms to summary procedure in "Recent legislative reforms to summary procedure in the Northern Territory" – Leonique Swart.
The June 2011 issue of Family Law Review contains several interesting pieces about various aspects of family law, including Professional Insights, Recent Cases and International Family Law. There is also an article about collaborative law in Australia, with particular reference to family lawyers in the ACT.


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I am still learning from his case. This spring and summer, a co-worker and I crisscrossed Robeson and Cumberland counties, finding jurors who unwittingly sentenced an innocent man to death. The jurors served at McCollum's original trial in 1983, and his retrial in 1991, held in Fayetteville. Both juries voted unanimously for death.
We hoped they could shed light on how our system got it so terribly wrong. But as I knocked on strangers' doors, I worried they would be defensive or angry. Instead, they welcomed us into their homes.
Some seemed relieved to finally talk through the trauma of the trial, though none would let us use their names. Many were ashamed of their role, afraid of what their neighbors would think. Some feared God's wrath, and wondered if they would go to hell for McCollum's wrongful conviction. Some shed tears at the mention of his name and said the experience was too painful to revisit. They remembered McCollum at the defense table, silent and unresponsive, like a confused and broken child.
All were denied the information they needed to reach a fair verdict. They were shown gruesome crime photos and McCollum's confession, written by the police. Even McCollum's defense attorneys admitted his guilt, believing the jury would spare him if he accepted responsibility.
No one told the jury that another, almost identical crime was committed just a month after the girl's murder — and that the culprit was not McCollum, but a man who lived by the field where her body was found. The jury didn't know fingerprints were found at the scene, and that none of them were McCollum's. They didn't know the case against McCollum started with a rumor from a teenage girl, who later admitted she made it up.
One juror said his biggest regret is that he trusted prosecutors to tell the truth. If McCollum was on trial, he believed, he'd probably done it.
Like everyone we talked to, his most vivid memories were the photos. At the time, he had a daughter the same age as the victim. When the verdict was announced in the courtroom, he looked at her father. The juror had done what the prosecutor said was right, and he hoped it would ease another father's pain.
"I've been trying to figure out, where did we go wrong?" he said. "I feel like we got duped by the system."
I was in the courtroom for McCollum's exoneration four years ago. I will never forget the sight of him standing in a cage — the court probably calls it a holding cell — during a break. He stared silently at the floor, powerless against a system that had chained and caged him for his entire adult life.
Now, there is another image that stays with me. A woman sitting in the dim light of her living room, hardly strong enough to rise from her chair, wondering what those 30 years were like for Henry McCollum. Wondering whether God has heard her pleas for forgiveness.
Kristin Collins is the associate director of public information at the Center for Death Penalty Litigation, a non-profit law firm that represents prisoners on death row.
Henry McCollum sits stunned as applause rings out in a Robeson County courtroom in Lumberton, N.C. Tuesday, September 2, 2014 after a judge has declared McCollum and his brother Leon Brown innocent of a brutal rape murder for which they have spent 30 years in prison. The brothers were convicted of the 1983 rape and murder of an 11-year-old girl whose body was found in a soybean field near the tiny town of Red Springs. Behind him is I. Beverly Lake, Jr. founder of the Innocence Commission who were vital in the process to free the two men. Chuck Liddy cliddy@newsobserver.com
Take a look back at the work of cartoonist Dwane Powell
Can ACC basketball live up to the glory of former years?
7/18 Letters: Explain to me how the N&O came to the conclusion that Trump is racist
7/17 Letters: Why aren't Republicans speaking up about Trump's comments about elected officials?
Trump outwitted the media to turn his census citizenship 'concession' into a win


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Summit Announces Release Date for 'Cold Light of Day'
written by Luciana V.V
Finally, Cold Light of Day got a release date! It has an opening of May 06, 2012.
Cold Light of Day, directed by Mabrouk El Mechri, follows on a man (Cavill) whose family is kidnapped while on vacation in Spain. In a race against time to rescue them, the ma uncovers some family secrets that form a mysterious connection to their disappearance, as well as a government conspiracy as maze-like as Madrid's ancient streets.
May 05 2011 The Cold Light of Day
Shooting starts on Bruce Willis film in Alicante News from the movie, but I think this magazine got the wrong summary. Am I wrong? Willis is the father and Henry is...
Henry to Star in Kidnapping Thriller Henry Cavill, one of the stars of "The Tudors," will topline "The Cold Light of Day", a kidnapping thriller from Intrepid Pictures and...
"The Cold Light of Day": Henry Interview The site Flicks & Bits has an interview done with Henry, not sure when done but published this week. Check it: In 24...
The Witcher follows the story of Geralt of Rivia, a solitary monster hunter, who struggles to find his place in a world where people often prove more wicked than monsters and beasts. But when destiny hurtles him toward a powerful sorceress, and a young princess with a special gift, the three must learn to navigate independently the increasingly volatile Continent. UpdatesPhotosIMDb
Zack Snyder's Justice League
Clark Kent / Superman
Zack Snyder's director's cut of the 2017 film, Justice League. UpdatesPhotosIMDb
When Enola Holmes-Sherlock's teen sister-discovers her mother missing, she sets off to find her, becoming a super-sleuth in her own right as she outwits her famous brother and unravels a dangerous conspiracy around a mysterious young Lord. UpdatesIMDb
galgadot
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The National Carnival Commission (NCC), will control all financial income via the gates of all national carnival shows. NCC Chairman, Kenny de Silva said yesterday: "We are coming out with a joint statement tomorrow, indicating that the NCC will be handling the gates for the carnival shows and we'll be doing an audit after, and the Special Interest Groups (SIG's) will manage their shows." He added: "We are dealing with all revenue aspects of the Panorama and all payments pertaining to that show. Pan Trinbago would be paid a management fee to be decided upon in terms for what they need for Panorama, and a similar situation exists with TUCO (Trinbago Unified Calypsonians Organisation), and we already have the Mas." Told there was talk of pan, Mas and kaiso being put back together on Dimanche Gras night de Silva said: "That has not been settled.
That composition hasn't been worked out as yet." And when asked who is producing Dimanche Gras and what will be the format? De Silva responded that in collaboration with TUCO, the NCC will be producing Dimanche Gras but stated that the format is still evolving. Calls to TUCO president Lutalo Massimba and acting Pan Trinbago president Richard Forteau all went unanswered.
However a reliable source from TUCO said at last week Saturday's General Membership Meeting to discuss Carnival 2017, the majority of members voted for 16 finalists singing one song each. The source added that the only way that will change is if the NCC took control of Dimanche Gras and go for eight finalists including the reigning monarch, each rendering two songs.


Presented with Kim Doogan at the National Case Management Network of Canada Conference.
This paper is directed primarily at younger lawyers without significant trial experience who, by virtue of their facility with technology, are perhaps best equipped to use it creatively in the litigation process.
Darcy R. Merkur & L. Craig Brown, Use and Abuse of Technology at Pre-trial and Trial, presented at the OTLA 2012 Spring Conference "Torts & Trials: The Tips You Need to Know & Use" on June 7-8, 2012.
On September 1, 2010, the interpretation of "incurred expense" will change and will create new challenges for the families of innocent accident victims. Paper: Incurred Expenses – A New Challenge for Accident Victims Navigating the New SABS: Finding Solutions to Key Challenges – Incurred Expenses from Thomson Rogers on Vimeo.
Is Mary Carter dead – or just wounded?
Mary Carter – Friend or Foe?


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text:
Dichaetomyia comorensis este o specie de muște din genul Dichaetomyia, familia Muscidae, descrisă de Adrian C. Pont în anul 1978. Conform Catalogue of Life specia Dichaetomyia comorensis nu are subspecii cunoscute.

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Dichaetomyia


Sorry, I totally forgot about this game. Now reading the post.
Now I'm caught up. Voting.
moody7277 is hereby elected Chancellor.
From Lawrenelot, I received one liberal and one fascist policy.
Correct. I had 2 fascist policies and a liberal policy.
Should I nominate Carlington as chancellor? I know they sent me a liberal policy, so I trust them slightly more than mpolo right now.
Gopher of Pern wrote: Should I nominate Carlington as chancellor? I know they sent me a liberal policy, so I trust them slightly more than mpolo right now.
I expect that you and he doing the Putin-Medvedev thing would be the highest probability of another liberal policy enacted.
Carlington is hereby elected Chancellor.
So, I was sent one liberal and one fascist policy. Assuming all the claims thus far have been true, six fascist policies have been discarded. That leaves five in the deck, which isn't enough for the fascists to win?
I guess probably the discarded policies are just shuffled and used again. Still, we have ideas on how many of each policy are left, and we can assign probabilities to different claimed three-card draws.
No, I dropped a liberal policy. I was dealt two liberal and one fascist policy. Where did you get the idea that we discarded two fascist policies?
In other news, I plan to nominate Lawrencelot for Chancellor. To give time for any other discussion, I'll wait until Monday morning CST to make it official.
Re: where I got the idea, I just got ahead of myself and assumed, sorry about that.
Losing track of this a whole lot… I will be travelling over the week, but hopefully can check in.
Lawrencelot has been nominated as Chancellor.
Would anyone object to changing the vote to a public vote in thread? There's been a couple of complaints about the lack of discussion in thread, and having a public vote may help remedy that.
Since votes are revealed anyway, I have no objections to public voting.
Does this mean votes can be changed before deadline?
Since we're all in agreement, I'll put this down.
Lawrencelot is hereby elected Chancellor.
It is now effectively night. No posting until moody7277 and Lawrencelot have enacted a policy.
I got a liberal and fascist policy and chose the liberal one.
Gopher of Pern or mpolo as Chancellor? Well, Gopher chose a liberal policy when he had to choose between liberal and fascist, as confirmed by Carlington.
Mpolo hasn't done anything that points to either way.
I was dealt two liberal and one fascist policies.
I'm happy enough on the face of things to nominate Gopher, but I do want to get home and update the tallies I'm keeping before I commit.
As far as I can see, we can just continue like this until a fascist policy gets up, that's when we're going to have to hesitate and ask questions about why it did.
At the end of each hand, do you just put all cards back into the deck and shuffle it, so the chances of drawing any given combo of cards are the same every time? If not, what's the process, do we play until the deck is empty and then shuffle it and start again?
IF everyone is telling the truth, there have been 6 policies of each type dealt. Which means there are 5 cards left in the deck, all of which are fascist. By my reading of the rules, the discards will be shuffled in after this turn, as there will not be 3 cards to draw, so they are all shuffled in before any are drawn.
Frankly, I would prefer mpolo to be nominated, as there is very little chance (no chance if everyone is truthful) of there being a single liberal policy.
Yes that seems correct. Alright, I agree with mpolo as chancellor then.