text:
\section{Introduction}

A large fraction of galaxies show evidence of supermassive black holes (henceforth SMBH) residing in their center.
They are typically embedded in nuclear star clusters (NSC); if resolution allows to observe the NSCs,
they are among the densest clusters known.
Their size is similar to galactic globular clusters, but they are much heavier and brighter
\citep{BLV2002,BSM2004}. In massive galaxies NSCs may not be significant or even do not exist, however,
the SMBHs are still surrounded by enormous number of stars. SMBH residing in these NSCs will tidally
disrupt stars that come close to its tidal radius and eventually accrete the gaseous debris, which can
light up the central SMBH for a period of time \citep{Rees1988,EK1989}. This kind of event is a useful
tool to examine the relativistic physics near SMBH since the disruption occurs at a place very close
to the BH's Schwarzschild radius. Also it can help us to investigate SMBH in non-active galactic
center. Although tidal disruption of stars has been proposed for almost half a century, only until
last decade do people realize the importance of such events, after the discovery of a dozens of tidal
disruption candidates \citep{Komossa2002,KM2008}. \citet{LLK2014} discovered a candidate of binary
SMBH system by analyzing the break in the light curve of TD event, demonstrate it as a promising tool
for searching hidden SMBH binaries in quiescent galactic center. In order to compute the tidal
disruption event rate, many theoretic works have been
done in the past few decades \citep{FR1976,LS1977,MT1999,WM2004}. The core of the story is loss cone
theory, which was first established in the case of spherical symmetric systems.

Stars with orbital pericenter smaller than the tidal radius $r_t$ are defined to be inside the loss cone,
with $r_t$ be expressed by

\begin{equation}
r_t = \alpha r_\star \frac{3}{5-n} \Bigl(\frac{M_{\rm bh}}{ m_\star} \Bigr)^{\frac{1}{3}}\ ,
\end{equation}

where $r_\star$, $m_\star$ are the radius and mass of a star, $n$ is its polytropic index
(assuming the stellar structure can be approximated by a polytropic sphere) and
$\alpha$ is a free parameter used by us for scaling.
Stars with angular momentum $J < J_{lc} \approx
\sqrt{2 G M_{\bullet} r_t}$ are inside the loss cone. Typically, loss cone
stars are consumed in dynamical time scales. If no new star is
supplied to loss cone, there will be no more tidal disruption
event. Based on the status of loss cone, it can be divided into two
regime, namely empty and full loss cone. Due to the short ``lifetime"
of the loss cone stars, loss cone will become empty quickly. Refilling
of loss cone happens in relaxation timescales and is often referred to as
diffusion process in angular momentum space. Thus in empty loss cone
regime it is the refilling rate which controls the disruption rate.
Note that throughout this paper, and like in most if not all of the cited
papers on tidal accretion of stars onto SMBH, we assume that a star is
disrupted completely at $r_t$ and all its mass, energy and angular momentum
absorbed momentarily by the SMBH. We know that this is not realistic, and more
detailed numerical models of the process of disruption, possible disk formation
and accretion show that only fractions of the material are absorbed into the
SMBH after a number of orbits \citep{GRR2013,HSL2013}. However, the assumption that the process is fast is reasonable compared to the orbital time scales of stars further out in the cluster.

In a previous paper (\citet{ZBS2014}, henceforth Paper I) we have
shown that the classical loss cone approximation, for a spherically symmetric
system in the diffusive empty loss cone regime,
can be well reproduced by large direct $N$-body models with tidal accretion of stars
onto SMBH. Now we are focusing on the generalization to axisymmetric galactic nuclei
and compare our new results in an otherwise very similar study to those of Paper I.

Tidal disruption of stars is one possible way of growth for SMBH, especially
in quiescent galactic nuclei. Since most models assumed spherical stellar
clusters, SMBH growth rates by tidal disruption are very low, limited by the
very long relaxation time to refill the loss cone, and the contribution of
the process to the overall growth of SMBH is considered as relatively insignificant.
However, the stellar distribution in real galactic
nuclei might not be spherically symmetric. Many galactic nuclei show evidence
of rotation in their centers, even very close to the SMBH \citep{MMH1995,NM1995,GHB1995}.

According to the current standard model of structure formation massive galaxies
have undergone quite significant mergers (in number and mass ratio). Numerical
models of the merging process of galaxies show that the merger remnant shows
rotation, axial symmetry or even triaxiality in the central regions \citep{KJM2011,PBB2011,GM2012,BEB2013}.

In the center of our own Milky Way the NSC can be observed in unparalleled
high resolution \citep{FNS2014,SFK2014}. It consists of
$1.4\times10^{7} M_{\odot}$ within its effective radius ($4.2$
pc); kinematic data indicate that it possesses bulk rotation
\citep{FNS2014}. The formation mechanism of NSCs is still under
debate. There are two scenarios, \textit{in situ}
formation \citep{Milosav2004} and a sinking scenario (globular cluster sink to the center
and merge) \citep{TOS1975,LTF2001}. NSCs in a sample of nearby
galaxies observed by \citet{SDH2006,SBB2008} show that these objects
are non-spherical and even contain multi-component (younger disk plus older spherical component),which favor the
\textit{in situ} scenario. However, \citet{ACM2012} have performed a
series of $N$-body simulations to study the formation of NSCs, which
support the sinking scenario. The model NSCs formed in their simulations
by merging between infalling globular clusters initially have mildly
triaxial shape. After the final infall, the shape of the NSC will
gradually become axisymmetric in following dynamical evolution.

Despite the debate between different formation scenarios, we think that
it is quite likely
that NSC are non-spherical. This provides a good motivation
to study the tidal disruption rate in axisymmetric (and triaxial) clusters. Some
works have already been done but the mission is not
over. \citet{FS2010} used 2D Fokker-Plank model \citep{ES1999,KEL2002}
to study rotating dense stellar clusters with BHs and cross checked
with $N$-body models \citep{FPB2012}. Both works find that BH embedded
in rotating model have higher tidal disruption rate (hereafter TDR) compare to spherical models. BH mass
at the end of simulation is roughly 20\% higher in rotating case. They
find an excess of accreted prograde rotating stars which are
originated mainly outside the influence radius $r_h$ and call for a
further investigation of the roles of stars with non-conserved $J_x,
J_y$ angular momentum. As shown by the works of \citet{MP2004}, in
non-spherical systems chaotic orbits (existing in regions outside
$r_h$) can keep the loss cone full for sufficient long time, thus
tidal disruption can contribute a lot of mass within Hubble time and
could play an important role in the BH growth across cosmic time.

On the other hand, the loss cone itself might be enlarged as pointed
out by \citet{MT1999}, due to the fact that angular momentum $\bf{J}$
is not conserved in axisymmetric potential. \citet{VM2013}
confirmed this picture in a detailed analysis of the loss cone problem
in axisymmetric galactic nuclei. They analyzed the depletion and refilling
of loss cone orbits and found that tidal disruption rates could be increased
by a moderate factor due to axisymmetry as compared to spherical symmetry.
In their work chaotic orbits with low angular momentum, which can reach
just outside the influence radius at apocenter, but also get close to
the central SMBH at pericenter, cause some difficulty in comparison with
Fokker-Planck models, as was already found by \citet{MVN1993} (Note
that the last author of this paper is the same person than the last author
of \citet{MVN1993}, there was a mistake in re-translating the name from
Russian language).

In this work we follow an experimental numerical approach to the problem,
following Paper I for the case of spherically symmetric systems. We treat
particle number and tidal radius as free parameters and analyze the tidal
accretion rate of the system as a function of the strength of deviation
from spherical symmetry. We
measure the shape of the loss cone in axisymmetric potential and
and characterize the characteristic orbits of stars in the loss cone.
We find
that it is indeed enlarged and can account for the higher
TDR as compared to spherically symmetric galactic nuclei.

This paper is organized as follows: we describe the model setup of the
simulation in Section 2 and present the result of TDR measurement in
Section 3. Section 4 is devoted to the measurement of loss cone shape
in axisymmetric potential and we demonstrate the enlargement of loss
cone. In Section 5, we present the result for the origin and orbital
classification of disrupted stars. In Section 6, we discuss the
potential application of our results.

\section{$N$-body model}

We adopt the standard $N$-body unit definitions from \citet{HM1986}, namely $G$ = $M$ = 1
and $E$ = $-1/4$, where $G$ is the gravitational constant, $M$ is the
total mass of the model cluster and $E$ is the total energy. In our
$N$-body models we assume that all the particles have the same mass,
so $m=1/N$, where $m$ is the particle mass and $N$ is the total particle number.
To preserve the scale invariance of our $N$-body simulations we fix the
initial black hole mass relative to the total mass of the star cluster
(0.01) and use the particle number and the tidal radius $r_t$ in $N$-body units
(which is a dimensionless number) as free parameters. We have shown
in Paper I that the method of scaling to realistic parameters for $N$ and $r_t$
can be used to obtain astrophysically meaningful results from the collection of
our models. In order to support our scaling procedure we even do not change
the tidal radius during the simulations -
since the BH mass changes within one order of magnitude only
during the simulation, relative changes in tidal radius are small
(notice that $r_{t}\propto(M_{\bullet})^{1/3}$).

The initial distribution of particles follows a generalized King model with rotation.
The distribution function is \citep{ES1999,EGF2007}

\begin{equation}\label{Eq_King}
    f(E,J_z) = C\cdot[\rm exp(-\frac{E}{\sigma_{K}^2}) - 1]\cdot\rm exp(-\frac{\Omega_0 J_z}{\sigma_{K}^2}) ,
\end{equation}

where $\sigma_{K}$ is the King velocity dispersion and $\Omega_0$ is a
characteristic angular velocity. Since we are considering an isolated
system, the $\Phi_t$ is set to 0. This rotating King model has two
dimensionless parameters: $W_0$ and $\omega_0$. The King parameter
$W_0 = -\Phi_0/\sigma_{K}^2$, where $\Phi_0$ is the central potential,
controls the degree of central concentration. And the rotation
parameter $\omega_0 = \sqrt{9/(4 \pi G \rho_0)}\cdot\Omega_0$, where
$\rho_0$ is the central density, controls the degree of rotation.
$\omega_0 = 0$ will reduce the model to a usual non-rotating
spherically symmetric King model.

We limit our current study to only one concentration parameter
$W_0 = 6$ and two rotation parameters $\omega_0=0.3, 0.6$; the
density profile of King model with this concentration is similar to that
of the Plummer model used in Paper I, so it is possible to compare
with the previous results and focus on the effects of rotation and
axial symmetry only. The rotation is moderate (cf. e.g. \citet{ES1999})
and resembles that of Milky Way globular clusters.

For completeness we also employ non-rotating King model with $W_0 = 6$ and
$\omega_0 = 0.0$, which is used as a fiducial model and also a bridge to the results of Paper I,
confirming our claim that it indeed closely resembles the results for the Plummer model
used in Paper I (e.g. in the evolution of the TDR). In another test run we used a larger rotation with
$\omega_0 = 0.9$ - it experienced an unstable stage during which a bar formed but quickly
disappeared. This bar formation could probably be identified with the
radial orbit instability of \citet{AM1990}. We note that our standard models
with $\omega_0=0.3, 0.6$ remain fully axisymmetric during the entire simulation;
to study tidal disruption in triaxial systems with bars is beyond the scope of our current paper.

Fig.~\ref{fig_AxisRatio} shows the axial ratio ($c/a$) of the model clusters
as a function of radius up to $r = 2.0$ (within which most of stars are located).
We estimate the axial ratio for both rotating models, using the moment of inertia tensor
measured in concentric shells. One can see $c/a$ is close to 1 at the
innermost part and decreases outward: $\omega_0=0.3$ model decreases slowly
to its minimum value 0.9; $\omega_0=0.6$ model decreases faster and has a minimum value 0.71.
If we measure the $c/a$ for the whole cluster, the results for the two models
are 0.9 ($\omega_0=0.3$) and 0.75 ($\omega_0=0.6$). Fig.~\ref{fig_AxisRatio}
also shows that $c/a$ is almost unchanged during long time evolution, except
for the inner part of $\omega_0=0.6$ model, which exhibits slight decrease.

\begin{figure}[htbp] \begin{center}
  \includegraphics[width=\columnwidth]{AxisRatio-MOI.eps}
  \end{center}
  \caption{Axial ratio for rotating models as a function of radius. For each model we show the axial ratio measured
  at different evolution stage: T=0 (red); T=500 (green); T=1000 (blue). Lines with symbols are results for $\omega_0 = 0.3$ model, lines without symbols are for $\omega_0 = 0.6$ models.}
  \label{fig_AxisRatio}
\end{figure}

In rotating systems, there is a phenomenon called
gravo-gyro instability, which is caused by the negative specific
moment of inertia \citep{IH1978,Hachisu1979,Hachisu1982}. This kind of
instability happens in long term evolution of rotating cluster which
is much longer than our integration time \citep{EGF2007}.

The model set is summarized in Table~\ref{table_model}.

\begin{table}[htbp]
\begin{center}
\caption{Full set of our model runs.\label{table_model}}
\begin{tabular}{c|cccc}
  \tableline
  Model &   N/K    & $\omega_0$ &  $r_{t}$     &   T      \\
  \hline
  R20w00    &   64    & 0.0  &  $10^{-3}$     &  1500    \\
  R30w00    &  128    & 0.0  &  $10^{-3}$     &  1600    \\
  R21w00    &   64    & 0.0  &  $10^{-4}$     &  1500    \\
  R31w00    &  128    & 0.0  &  $10^{-4}$     &  1300    \\
  \hline
  R20w03    &   64    & 0.3  &  $10^{-3}$     &  1500    \\
  R30w03    &  128    & 0.3  &  $10^{-3}$     &  1500    \\
  R21w03    &   64    & 0.3  &  $10^{-4}$     &  2600    \\
  R31w03    &  128    & 0.3  &  $10^{-4}$     &  2000    \\
  \hline
  R20w06    &   64    & 0.6  &  $10^{-3}$     &  1500    \\
  R30w06    &  128    & 0.6  &  $10^{-3}$     &  1500    \\
  R21w06    &   64    & 0.6  &  $10^{-4}$     &  1600    \\
  R31w06    &  128    & 0.6  &  $10^{-4}$     &  2000    \\
  \tableline
\end{tabular}
\tablecomments{Column 1 : Model codename. Column 2 : Particle number in
the unit of K(=1024). Column 3 : dimensionless rotation parameter.
Column 4 : black hole's tidal radius. Column 5 : total integration time.
$r_{t}$ and $T$ are in model unit.}
\end{center}
\end{table}

We run the simulation for more than one initial half-mass relaxation
time ($t_{rh}$), which is estimated using the same formula in Paper I
and the values can be found there as well (Table 2).

All simulations are running with the \PGRAPE code \citep{BNZ2011},
which runs with high performance (up to 350 Gflop/s per GPU) on our
GPU clusters in Beijing (NAOC/CAS). This code is a direct $N$-body
simulation package, with a high order Hermite integration scheme and
individual block time steps. A direct $N$-body code evaluates in
principle all pairwise forces between the gravitating particles, and
its computational complexity per crossing time scales asymptotically with $N^2$;
however, it is {\em not} to be confused with a simple brute force
shared time step code, due to the block time steps. We refer more
interested readers to a general discussion about $N$-body codes and
their implementation in \cite{spurzem2011a,spurzem2011b}. The present
code is well tested and already used to obtain important results in
our earlier large scale few million body simulation ~\citep{KBB2012}.

\section{Tidal Disruption Rate (TDR)}
\subsection{Results of our work}

In this section, we present the TDR measured in simulations with our
rotating King models and compare it with the TDR of the non-rotating model of Paper I. In
Fig. \ref{fig_Mdot_comp-multi}, we show the TDR (both in terms of
mass and particle number) as it evolves with time for two different tidal radii; in each
panel two different rotation parameters are plotted together with the
data of the non-rotating system. The time is given in units of
initial half mass relaxation time $t_{rh}$, which is convenient for
comparison of simulations with different particle numbers.
To smooth out fluctuations due to particle noise we have plotted in the
figure the TDR averaged over a time interval
(here $1/4 t_{rh}$).

\begin{figure}[htbp] \begin{center}
  \includegraphics[width=\columnwidth]{Mdot_comp-multi.eps}
  \end{center}
  \caption{TDR as a function of time in units of initial half mass relaxation time; averaged over intervals of $1/4 t_{rh}$. Top panels: mass accretion rate; bottom panels: particle accretion rate; left and right panels for two different tidal radii as indicated. Curves with symbols are stand for 128K models, those without symbols are stand for 64K models. Line thickness indicate different rotating parameters.}
  \label{fig_Mdot_comp-multi}
\end{figure}

The TDR with a large tidal radius (i.e. $r_t = 10^{-3}$)
initially quickly rises in the $N = 64 K$ model to its peak value,
and then decreases; for the $N = 128 K$ model the TDR
almost decreases from the beginning. The initial phase is
connected with the formation of a central density cusp in the
surrounding stellar system and with the process of transition
from initially full to empty loss cone. The BH gains mass from the accreted
stars, thus the mass ratio between stars and the BH ($\gamma := m/M_{\bullet}$)
decreases with time, and as a result the BH's random motion damps.
We have discussed in Paper I that the status of the loss-cone is
connected with the BH's Brownian motion in the sense that once the
amplitude of Brownian motion is smaller than $~10 r_t$ the system
enters the empty loss-cone regime, during
which the cusp and central density are still growing but TDR begins to
fall. In the $N = 128 K$ model, the mass ratio $\gamma$ is smaller,
so the initial loss cone depletion is very short, practically invisible
in the plots, and the subsequent evolution is determined by cusp formation and
damping of BH motion.

In the models with small tidal radius ($r_t = 10^{-4}$), there
is always an initial growth phase of TDR, followed by the
convergent approach to a stationary state.
Due to the small $r_t$ their BH growth is slow, thus
they need more time to achieve the mass required to limit their
Brownian motion.

Fig. \ref{fig_Mdot_comp-multi} also shows the TDR dependence on
rotation parameter $\omega_0$ as a new result compared to Paper I.
For large tidal radius ($r_t=10^{-3}$),
faster rotation will result in a higher TDR, note that these models
are in empty loss-cone regime.
Table \ref{table_TDR} list out the numbers
for TDR measurement. One can see $\omega_0=0.3$ model has a TDR on average
13 percent higher than $\omega_0=0.0$ model. And TDR in $\omega_0=0.6$
model is on average 35 percent higher than that in $\omega_0=0.0$ model.
BH mass of these 3 models measured at $T=1500$ are 0.131, 0.143 and 0.167. The
fractional increase of final BH mass with increasing degree of rotation is
consistent with the result of \citet{FPB2012}.
The reason for this dependence of $\omega_0$ is that in these systems
the effective loss-cone is larger than classic one in spherical system.
We will investigate such an enlarged loss-cone in more detail in the next
section. For small tidal radius ($r_t = 10^{-4}$), however,
we observe a different behavior of TDR. From beginning to about
$\sim1.5 t_{rh}$, faster rotation result in a smaller TDR!
The argument presented by \citet{MT1999} may provide some hints: if BH's
wandering time-scale is shorter than dynamical time-scale, a decrease
in TDR will happen. We note in the simulation at this early stage the BH
is quickly wandering due to its small mass and slow growth.
Furthermore, in axisymmetric systems a star's
pericenter distance changes with time (even ignoring irregular
perturbations from other stars). So when the BH comes back to the place
where it was, it may still miss the star which is supposed to be
disrupted shortly before.

\begin{table}[htbp]
\begin{center}
\caption{TDR results for $r_t = 10^{-3}$ models.\label{table_TDR}}
\begin{tabular}{c|c|cc|cc}
  \tableline
  $t/t_{rh}$ &  $\dot{N}_0$ & $\dot{N}_3$ & $\dot{N}_3/\dot{N}_0$ & $\dot{N}_6$ & $\dot{N}_6/\dot{N}_0$ \\
  \hline
  0.25   &  14.96    & 15.41  &  1.03   &  16.30  &  1.09  \\
  0.50   &  12.89    & 13.67  &  1.06   &  17.30  &  1.34  \\
  0.75   &  10.44    & 12.07  &  1.16   &  14.52  &  1.39  \\
  1.00   &   8.73    & 10.32  &  1.18   &  12.65  &  1.45  \\
  1.25   &   7.97    &  9.73  &  1.22   &  11.09  &  1.39  \\
  1.50   &   6.99    &  7.93  &  1.13   &  10.04  &  1.44  \\
  \tableline
\end{tabular}
\tablecomments{Measured TDR for models with same N (128K) and $r_t$ ($10^{-3}$) but
 different rotating parameters, at different evolution time. $\dot{N}_0$ is TDR in classic King
 model ($\omega_0=0$); $\dot{N}_3$ and $\dot{N}_6$ are results for $\omega_0=0.3$ and $\omega_0=0.6$ models.
 We also give the boost factor $\dot{N}_3/\dot{N}_0$ and $\dot{N}_6/\dot{N}_0$.}
\end{center}
\end{table}

Afterwards the system begins to enter the empty loss cone regime, and all
TDR curves converge to each other; for small tidal radius more
tidally disrupted stars originate from inside the BH influence radius,
where the system is approximately spherically symmetric. Any deviation
from spherical symmetry in our rotating models prevails near and outside
the influence radius. Convergence of TDR reflects the original results
obtained in Paper I for spherical systems.

\begin{figure}[htbp] \begin{center}
  \includegraphics[width=\columnwidth]{Mdot_comp_Plum_w000.multi.eps}
  \end{center} \caption{$x$ axis is time in unit of initial half-mass
  relaxation time. $y$ axis for panel a) and b) is the averaged mass
  accretion rate in given time range (i.e. 1/4 $t_{rh}$); $y$ axis for
  panel c) and d) is the number accretion rate. Panel a) and c) show
  the result for $r_t = 10^{-3}$. Panel b) and d) show the result for
  $r_t = 10^{-4}$.}  \label{fig_Mdot_comp-Plum_w000} \end{figure}

Fig. \ref{fig_Mdot_comp-Plum_w000} compares the TDR of classic King
model ($W = 6, \omega_0 = 0.0$) with that in Plummer model. In $r_t =
10^{-3}$ models, except the initial higher accretion rate in King
model, the two models have similar TDR in following evolution. While
in the case of $r_t = 10^{-4}$, King model have a higher accretion
rate during most of the time, but later on they gradually come to the same
level as the Plummer model. The higher rate in King model could be
explained by the slightly higher density in the core region at
beginning. In the following evolution of $r_t = 10^{-3}$ models, the
two models form cusp similar to each other so they have roughly same
accretion rate. In the case of $r_t = 10^{-4}$, the initial accretion
rate ratio $\dot{N}_{King}/\dot{N}_{Plum}$ is higher than those in
$r_t = 10^{-3}$. BH inside King cluster growing faster and also the
growth of cusp, in the following evolution King model always have a
higher density in the cusp which in return gives a higher accretion
rate. Only after the BH gain enough mass and become a ``static"
object, the accretion rate slowly reaches a maximum and begins to drop
afterward.

Up to this point, all results were presented in model units ($N$-body units).
As in Paper I (see Sect. 5 and Appendix therein) we will discuss now any conclusions which can be made for the
case of real galactic nuclei and environments from our results. This will be
useful for observational programmes on TDR.
To predict the TDR in real galactic nuclei, we use the method of scaling. The TDR
obtained in our simulations has to be scaled up in two ways: first from relatively low ($N\sim 10^{5}$)
to more realistic high particle numbers ($N \sim 10^{8}$). Second,
our accretion radius $r_t$ has been chosen very large compared to any realistic tidal radius
(for smaller $N$ simulations it has to be done in order to get any meaningful results on TDR).
So, we also have to discuss how to scale down the TDR from our simulated values of $r_t$
($10^{-3}, 10^{-4}$) to the small more realistic regime of $r_t$ ($10^{-7}$).
This can be done by applying scaling relations from known scaling laws (obtained e.g. from
Paper I and other literature) for $N$, and an empirically determined one for $r_t$. We have
shown above that the TDR in King ($W_0=6$) and Plummer models
is very similar, so we expect the scaling formula (A10) derived in Paper I for a Plummer model
to be also valid for our King model used here.
So, we apply the same boost factor of TDR with respect to the axisymmetry of a galactic nucleus
for the real galactic nucleus as we find here in this paper for our simulated systems.
For example, in Paper I we estimated the TDR
of the Milky Way SMBH to be $1.09\times10^{-5} \rm yr^{-1}$ after a scaling procedure with respect
to $N$ and $r_t$. By fitting surface brightness
profile to mid-infrared images of the nuclear cluster in our Milky Way, \citet{SFK2014}
reported the mean ratio between minor and major axes is 0.71, which is close to
our rotating $\omega_0=0.6$ model. For this model we find a boost of TDR by 35\% in our simulations,
and we apply the same factor here for the case of axisymmetry, to get a higher TDR of
$1.47\times10^{-5} \rm yr^{-1}$.

\subsection{Relation to other current papers in the field}

With regard to the enhancement of TDR in axisymmetric systems we have shown that our
results are in agreement with \citet{FPB2012}; but recently numerical simulations
published by \citet{VM2013} and \citet{Vasiliev2014} seem to contradict our findings.
They claimed that the TDR in axisymmeric nuclei can be a few times larger than in the spherical case.
Also \citet{LHBK2014} analyzed the distribution of stellar orbits in an axisymmetric galaxy and
found that total number of stars that can interact with the central SMBH binary is
six times larger than in the spherical system. In this subsection we will discuss why
there is such a discrepancy to our results - we find a much smaller enhancement of
TDR in axisymmetric systems.

The main difference between the cited papers and our work is the initial model. In all of the
above mentioned papers, a flattened Dehnen model is used (their density profile,
given the parameters they chose, is identical also to the Hernquist model).
Their models possess a fixed axial ratio ($c/a = 0.75$) throughout
the entire cluster and an initial central cusp, while our rotating initial model has initially a core
density distribution in the center, and we have a
radial variation of $c/a$ from nearly spherical ($c/a\approx 1$) to about $c/a \approx 0.7$ in
the outskirts (see Fig.~\ref{fig_AxisRatio}).
However, in the radius range where most of the disrupted stars originate from
(c.f. Fig.~\ref{fig_Rmax2D_R}), the system deviates significantly from spherical symmetry, thus
we can confirm that the enhancement of TDR is connected with the non-spherical geometry.
But in the relevant region of our $\omega_0=0.6$ deviation from spherical symmetry is
less than in the other cited papers, which may be an explanation for the weaker effect in
our case.

We also notice that even within the cited other papers there are some discrepancies in the results
even for models with the same initial density profile.
For example, the enhancement of the number of accreted stars in \citet{VM2013} was
smaller than 100\% (see Table 2 in their paper), while \citet{LHBK2014} found a factor of six.
On the other hand some of the models in \citet{VM2013} only show mild
enhancement which is in the same level as ours. Another example comes from the debate about the
``final parsec problem'' in SMBH binary evolution. Based on their simulation results, \citet{KHB2013}
claimed that the ``final parsec problem" is not a problem in axisymmetric host galaxies,
while \citet{VAM2014} reached an opposite conclusion according to their simulation. We
notice that both of these work employs similar flattened galaxies model, however, they
used a different method to generate the initial model.

\citet{VM2013}, \citet{Vasiliev2014} and \citet{VAM2014} utilized the orbital superposition
method of \citep{Schwarzschild1979} to construct their model. On the other hand, \citet{KHB2013} and \citet{LHBK2014}
used another method called ``adiabatic squeeze technique" developed by \citet{HBMS2001}.
We notice that in the process of adiabatic squeeze, which contains a step which applies a slow and smooth velocity
change on the stars in the $z$ direction. This step may artificially reduce the energy and angular
momentum of the stars in the model cluster. Although the radius and velocity vectors of the stars
are rescaled after the squeeze, it is not clear how the rescaling affects the phase space distribution.
Thus it might be possible that the process produces more stars of low energy and low angular
momentum. Another evidence of a similar effect can be derived from \citet{Vasiliev2014}; while they
still use the orbital superposition method they changed the generation of their initial model so
that it creates more low energy and low angular momentum stars. In their test run (Fig. 2 in their paper)
we see a much larger enhancement of the number of accreted stars compared to \citet{VM2013}.
So to add more low energy and angular momentum stars seems to be promising in abridging the different
enhancement factors between \citet{VM2013} and \citet{LHBK2014}. We suggest that a detailed
comparison between models constructed with these two methods (and their phase space distribution) should
be performed in order to explain the discrepancy.

According to \citet{LHBK2014} the central two parsecs of their model galaxy exhibit a slight triaxiality, which
could also introduce some additional centrophilic orbits, thus increase the number of stars that can interact with
the central SMBH binary.

Before finishing this section, we want to make a final remark on the result of \citet{LHBK2014}. Their model
integrates individual orbits in a fixed model potential with one SMBH
in the center, in a static way. So the number of stars that can interact with the central SMBH binary according
to their results should be
considered as an upper limit. Once two-body relaxation is turned on, some of the stars that are
supposed to be inside the loss cone might be scattered out. And the presence of a SMBH binary in an evolving
system may also affect the result of how many stars can interact with them.

\section{Loss cone in axisymmetric potential}

First, we summarize the loss cone theory for stellar orbits in a spherically symmetric gravitational
potential, in order to discuss different behavior in an axisymmetric potential later.
If a stellar orbit has a pericenter distance less than the tidal radius it is considered to be in the loss cone.
In  spherical symmetry the boundary of the loss cone can be expressed in terms of a critical loss
cone angular momentum
$J_{lc} \approx \sqrt{2 G M_{\bullet} r_t}$ (if $r \gg r_t$; cf. e.g. \citet{AFS2004}).
The loss cone is then defined as the region in phase space where the angular momentum $J$ of a star
fulfils $J < J_{lc}$. All stars inside the loss cone will reach the tidal radius within
a dynamical (orbit) time scale. As a consequence the loss cone would become empty in that
relatively short time. Once a star is inside the loss cone and reaches the tidal radius,
we assume that it will be destroyed by the BH's tidal force instantaneously and add its total mass
to the black hole at the same moment. Most authors studying stellar dynamics and TDR of star clusters around a BH
used similar approximations. Rees (1988) already argued that the stellar debris after
tidal disruption will make several orbits until it is finally accreted by the BH; nevertheless
the orbital time near the BH is very short compared to the original orbital time of the star before
its disruption.
Recent detailed simulations on tidal disruptions \citep{GRR2013,HSL2013,HSL2015}
show that in some case not all material of the star may be accreted and that
general assumptions about the tidal fallback rate are not correct; for example
in a longer lived accretion disk may form, which would delay the black hole growth.
In a spherical system, without interactions between the stars, angular momentum $\bf{J}$ would
be strictly conserved. So,
without any repopulation of the loss cone, the accretion process would stop after a few dynamical
times. But stars do interact with each other while moving inside the star cluster by two body relaxation
through mutual encounters; in this process they can exchange angular momentum and energy and
so the loss cone will be repopulated in the two body relaxation time scale, which is generally
long compared to the dynamical time \citep{CK1978,AFS2004}. The repopulation of the loss cone is modelled
in these papers as a diffusive process using the Fokker-Planck approximation.

In an axisymmetric potential, the situation is more complex since $\bf{J}$ is not a conserved quantity. It changes
continuously due to the non-central force resulting from the geometry of the potential. In this case, stars
with $J > J_{lc}$ may have a chance to drift into the loss-cone and get disrupted. In other words, the loss cone
is enlarged in the $J$ dimension in axisymmetric potential. However, the $z$ component of angular momentum $J_z$
is still conserved, so a solid boundary of the loss-cone is $J_z \leq J_{lc}$. \citet{MT1999} investigated
this topic using a symplectic map introduced by \citet{TT1997}. In this work, we analyze the enlarged
loss cone in phase space in terms of energy $E$, modulus of angular momentum $J$ and the $z$ component of
angular momentum $J_z$ for stellar orbits near the BH. We use a different approach as \citet{MT1999}
here, which is based on a numerical particle scattering experiment.
In what follows, we first describe the method we used in this experiment, then present our results.

First step, we need to know the smooth gravitational potential as a function of position without
the fluctuations due to the discrete particle structure. We use a so-called self-consistent
field code (SCF, \citet{OH1992}) to generate the analytical function for the gravitational potential.
The expansion coefficients
$C_{lm}, D_{lm}, E_{lm}, F_{lm}$ used in computing forces (Eq.(3.21)-(3.23) in \citet{OH1992})
are computed based on snapshot data generated during the direct $N$-body simulation. By default, the code
uses radial basis functions labeled from $n=0$ to $n_{max}=14$, and spherical harmonic function truncated at $l_{max}=10$.

Our particle distribution is self consistently achieved as a consequence of the
co-evolution of stars and BH. Using the SCF code means that all two-body interactions are smoothed out in the
experiment. Because we assume that most of the two-body interactions happens during the apocenter passage,
which is also used in \citet{TT1997}. After getting the coefficients, we can calculate the acceleration,
jerk and do orbit integration using a Hermite $4^{th}$ integrator with variable time steps, developed by
ourselves. This code works very well and the energy and angular momentum errors of the test particle stays
in the level of $10^{-9}$ over long time integration. In an axisymmetric system all coefficient with $m\neq 0$
should be 0. But in practice one will get some small numbers very close to 0 due to particle noise. We just
ignore these terms, otherwise $J_z$ would no longer be conserved. We also ignore coefficients with
odd $l$, because the rotating system should be symmetric about the equatorial plane and do not have
pear-like shape.

Next step is to generate initial positions and velocities for test particles. The basic idea of this experiment
is to do parameter space scanning. We uniformly sample $E, J$ and $J_z$, all test particles are initially put
at their apocenter. Firstly, we choose a particular energy and calculate $J_{lc}$ through equation
$J_{lc} = r_{t}\sqrt{2(\Phi(r_t)-E)}$. Then we choose a pair of $(J,J_z)$, $J$ can be a few times larger than
$J_{lc}$ but $J_z$ keeps smaller than $J_{lc}$. Given the combination of $(E,J,J_z)$ and the potential
distribution we can find the apocenter position given by $(r,\theta)$. Here $r$ is distance to center
and $\theta$ is the angle between position vector and $z$-axis. We note that there
are actually four parameters $(E,J,J_z,\theta)$ to define the initial conditions for a particular orbit.
So we further sampled 100 data points in $\theta$ dimension. In order to plot the result in a
2D plane, we introduce a filling factor $P$ for every $(E,J,J_z)$ combination to describe this $\theta$
dependence, which is the fraction of stars in the loss cone for a given combination of
$(E,J,J_z)$ (number of data points in loss cone divided by total sample size, e.g. 100), meaning that among
all stars with same $(E,J,J_z)$ only a fraction of $P$ are inside the loss cone.

By our definition a star in the loss cone will be disrupted by the BH within one dynamical time,
so for every test particle
we only integrate their orbits for one orbital cycle. If a particle comes back to its apocenter,
we consider it as out of the loss cone and move to the next integration with new initial orbital data.

\begin{figure}[htbp]
  \begin{center}
  \includegraphics[width=\columnwidth]{EJJz-multi.eps}
  \end{center}
  \caption{Filling factor $P$ of the loss coneas a function of $J$ and $J_z$ for different energies;
the $x$ axis is the modulus of the total angular momentum $J$, while the $y$ axis is its $z$ component $J_z$.
Panel a) correspond to $E=-1.3$, b) $E=-1.5$, c) $E=-1.7$, d) $E=-1.9$. Colors represent the
filling factor $P$ in percentage. All data are given in standard $N$-body units.}
  \label{fig_EJJz-multi}
\end{figure}

Fig. \ref{fig_EJJz-multi} shows results from the experiment in a slowly rotating model ($\omega_0 = 0.3$),
it represents the loss cone shape in phase space. Since $J$ is not conserved we use its
initial value at apocenter for the figure;
at the time of disruption $J$ must be less than $J_{lc}$. From panel a) to d), the energy of the test
particles are in descending sequence, so their position of apocenters are getting closer and closer to
central BH. One can see that the whole plane comprises 3 regions: 1) inner region where $P$ equals 1,
meaning particles with these $(E,J,J_z)$ can hit the BH within one dynamical time scale; 2) transition
region where $P$ is non-zero but less than 1, particles with these $(E,J,J_z)$ have a chance to hit the BH
depending on their apocenter position ($\theta$ value); 3) outer region where $P=0$, none of particle in
this region can hit the BH. In panel a) one can see only a few points are red and a lot of points are
located in transition region. From a) to d), the fraction of $P=1$ points in the $(J,J_z)$-plane
increases and the transition region is compressed
by the inner and outer region in horizontal direction ($J$ dimension). This is because test particles with
high energy (loosely bound or unbound with respect to the BH) can go beyond the BH's influence radius
to the intermediate and outer regions of the cluster, where the axisymmetric
stellar potential dominates. The angular momentum of these test particles will have large variations.
So a wide transition region exists in high energy cases. But in the low energy case (stars
strongly bound to the BH), e.g. panel d),
test particles are moving inside the BH's influence sphere where the potential is dominated by the
BH and thus approaches spherical symmetry. All loss cone stars following the classical loss cone
approximation, should have both $J$ and $J_z$ to be smaller than $J_{lc}$. In all panels of Fig. \ref{fig_EJJz-multi},
on the contrary, we see how stars with $J > J_{lc}$ could be still in the new, extended loss cone of an
axisymmetric system with a certain non-zero probability.

\begin{figure}[htbp]
  \begin{center}
  \includegraphics[width=0.47\columnwidth]{J-Jz_Prob-w3.eps}
  \includegraphics[width=0.47\columnwidth]{J-Jz_Prob-w6.eps}
  \end{center}
  \caption{Comparison between 2 models with same test particle energy $-1.5$. $x$ axis is module of
angular momentum in $N$-body unit. $y$ axis is $z$ component of angular momentum. Left panel correspond
to $\omega = 0.3$; right panel $\omega = 0.6$. Colors indicate the filling factor $P$ in percentage. }
  \label{fig_EJJz-compare}
\end{figure}

For faster rotating models ($\omega_0 = 0.6$) the results are similar. Three regions are presented on
the $(J, J_z)$ plane, however, the extent of each region is different from the counterpart of same energy
in slow rotating model. Fig. \ref{fig_EJJz-compare} gives an example, in both left ($\omega_0 = 0.3$) and
right ($\omega_0 = 0.6$) panel the test particle have same energy, however, the resulting appearances are
quite different. In the left panel we see the the outer border extended to $J = 0.024$, while in the right one the
outer border goes to $J = 0.04$ and is not as clear as that in the left panel. Also in the right panel the
red region is almost disappeared. These results show how rotation modifies the loss cone shape
in phase space. In both of these plots, the maximum radius stars can achieve are roughly the same.
However, faster rotation means we have a more flattened cluster shape, which enhances the torque acting on stars,
thus the variation in $J$ becomes larger. So, the higher the degree of rotation in the stellar system,
the larger is the extension of the loss cone in $J$ direction.

On first glance at Fig.~\ref{fig_EJJz-multi} (also Fig.~\ref{fig_EJJz-compare}) one might think that
the loss cone is generally enlarged by a significant factor.
However, as we pointed out above, there is a filling factor $P$ for every point
on the $(J,J_z)$ plane. To find the net enlargement of the loss cone in axisymmetric potentials
we introduce an effective area $S$ of the loss cone in these plots
by integrating the filling factor $P$ over the $(J,J_z)$ plane.
For example, the effective area of the classical loss cone is just given by the size of the triangle $J,J_z < J_{lc}$
in our plots, since in the classical case $P$ is unity everywhere in this triangle region.

Now we compare the loss-cone size comparing the integrals $S$ with each other. We define the quotient
$\alpha_{lc} = S_{eff}/S_{lc}$, where $S_{lc} = J_{lc}^2/2$ is the classical loss cone integral.
$\alpha_{lc}$ is plotted in Fig.~\ref{fig_EffArea} as a function of binding energy $|E|$.
In the plot we show both slow and fast rotating models at two different evolution times. For the slow rotating model
the ratio $\alpha_{lc}$ is even smaller than unity for binding energies larger than 1.4 - 1.5, meaning that
at large $|E|$ the loss cone is smaller compared to the classical one. This is caused by the reduction
of the probability $P$ at the boundary and inside the classical loss cone region $J \le J_{lc}$.
$P$ is decreasing from inside toward outside. While for intermediate $|E|$ case,
although $P$ is still decreasing function of $J$, the large number of valid points overwhelms, so the net
effect is increasing the effective area. However, if one goes further toward small $|E|$ the ratio will
drop again, like the case of fast rotating model. This is just because $P$ is sufficiently small in this
case and win the game. For fast rotating model, another interesting feature is the ratio drops below 1 at
$|E| = 1.8$.
From this figure we see that the enlargement of loss cone, quantified by the ratio
$\alpha_{lc}$ as a function of binding energy.
Interestingly, the change of the effective loss cone size in every energy slice is less than 5-10\%.
These mild changes seem unable to raise TDR with the amount observed in the simulation, to address this it will
be useful if we can estimate the TDR based on the effective loss cone measurement and compare with simulation.
However, the knowledge of how stars are distributed in energy and angular momentum is required. With the limited
particle numbers of the model cluster, it is difficult to get an accurate and reliable distribution function. Also in
current work, we sample the energy space with large intervals ($\Delta E = 0.1$), which may cause large errors in the
estimated TDR. So we did not make the estimation. There are still plenty of works could be done with this topic.

\begin{figure}[htbp]
  \begin{center}
  \includegraphics[width=\columnwidth]{EffArea-compare.eps}
  \end{center}
  \caption{Ratio between effective area $S_{eff}$ of loss-cone in axisymmetric system and $S_{lc}$ in
spherical system.}
  \label{fig_EffArea}
\end{figure}

\section{Orbital properties of disrupted stars}

In this section, we investigate the origin of disrupted stars. Under the assumption that stars in
loss cone can survive for only one orbital period, the origin of these stars can be
examined by looking at their energy and angular momentum, as well as their origin (apocenter)
in spatial coordinates (radius and angle $\theta$).
In spherical systems one can use effective potential to compute the apocenter of orbit, but
in the axisymmetric case we do not have such convenient solutions except to run the simulation twice.
In the first run we find out the ID for those stars that will be disrupted by BH. Then, in the second run
we make records for these stars more frequently than other stars, in order to catch their last apocenter position.

\begin{figure}[htbp]
  \begin{center}
  \includegraphics[width=\columnwidth]{E_stat.multi.eps}
  \end{center}
  \caption{Panel a) and b) show normalized distribution of binding energy $|E|$ of tidally disrupted stars, for different rotating models and for three different time intervals (indicated by color) in the full $N$-body simulation with $r_t = 10^{-3}$. The distribution is normalized to the total number of disrupted stars in each time interval. Panel c) and d) show cumulative fraction profile corresponding to a) and b), respectively.}
  \label{fig_E_stat}
\end{figure}

\begin{figure}[htbp]
  \begin{center}
  \includegraphics[width=\columnwidth]{J_stat.multi.eps}
  \end{center}
  \caption{Same as Fig.~\ref{fig_E_stat}, but here for the distribution of total angular momentum of the disrupted stars.}
  \label{fig_J_stat}
\end{figure}

We found in the beginning that the total TDR, especially for small $r_t$ does only marginally
depend on the rotation of the system; consistent with this we found in the previous chapter
that the loss cone structure does change significantly, but the total integral over the loss
cone space for axisymmetric systems yields only relatively small changes.
Still it is interesting to study how the orbital properties of stars, which are tidally disrupted,
change with the rotation of the system.
In order to address this, we now turn back to our full $N$ body simulations and study
the distribution of $|E|$ (Fig. \ref{fig_E_stat}) and $J$ (Fig. \ref{fig_J_stat}) of the disrupted stars at their apocenter passage in three time intervals. From Fig. \ref{fig_E_stat} one can see that most of the tidally disrupted stars have a binding energy between 1 and 2, coincident with the small bumps in Fig.~\ref{fig_EffArea} where $\alpha_{lc} > 1$. Another
evidence comes from the distribution of $J$ as shown in Fig.~\ref{fig_J_stat}, where one can see the peaks
are lying outside of the $J_{lc}$ which is roughly 0.015. The peaks are moving toward larger $J$, which is
caused by the increase of BH mass (recall the expression for $J_{lc}$). A significant fraction of stars
comes from places outside of the classical loss cone in $(J,J_z)$ plane.

\begin{figure}[htbp]
  \begin{center}
  \includegraphics[width=0.9\columnwidth]{Rmax2D_stat_6.3-R.eps}
  \end{center}
  \caption{Distribution of last apocenter distance of disrupted stars in 3 different time interval. Each curve are normalized to the total number of disrupted stars in given time interval.}
  \label{fig_Rmax2D_R}
\end{figure}

\begin{figure}[htbp]
  \begin{center}
  \includegraphics[width=0.47\columnwidth]{Rmax2D_stat_6.3-T.eps}
  \includegraphics[width=0.47\columnwidth]{Rmax2D_stat_n30-T.eps}
  \end{center}
  \caption{Normalized distribution of zenith angle $\theta$ of last apocenter of disrupted stars. Left panel is axisymmetric model, right panel is spherical model.}
  \label{fig_Rmax2D_T}
\end{figure}

In spherical systems it is usually sufficient to describe the apocenter of an orbit by its radial
distance from the center (the BH); the orientation of the orbit does not play any role for the orbital
time and the nature of the encounter with the central BH. However, in axisymmetric systems, orbits with
different angle $\theta$ (the angle between position vector of the star at apocenter and the $z$-axis)
will differ from each other significantly. Therefore we have to describe the distribution of apocenters
of tidally disrupted stars in terms of both the
$r$ (Fig.~\ref{fig_Rmax2D_R}) and $\theta$ (Fig.~\ref{fig_Rmax2D_T}) dimension. From
Fig.~\ref{fig_Rmax2D_R} one can see the peaks are quite far from the BH, in a region
comparable to the BH influence radius, which is similar to the apocenter
distribution in spherical systems (Paper I). The difference turns out to be in the $\theta$ dimension,
as shown in Fig.~\ref{fig_Rmax2D_T}. We compare the $\theta$ distribution between spherical and
axisymmetric systems. Imagine we project all the apocenter points onto a sphere with radii equals 1.
The measured number counts in each $\theta$ bin $\Delta N(\theta)$ are computed by
$2\pi\cdot\Sigma(\theta)\cdot\sin(\theta)\Delta\theta$, where $\Sigma(\theta)$ is the surface density
of projected points on the unit sphere. If apocenters are uniformly distributed with $\theta$,
$\Sigma(\theta)$ is constant, then $\Delta N(\theta) \propto \sin(\theta) \Delta\theta$. Here we choose
an equal bin size, so the measured number count should follow a $\sin(\theta)$ curve. The right panel of
Fig.~\ref{fig_Rmax2D_T} plots $\theta$ distribution for spherical model, which is taken from our last
work (Paper I). In left panel we see the last apocenter distribution have deficit at polar region comparing
to $\sin(\theta)$ curve, and excess at places beyond and below the equatorial plane, showing a double peak
feature. The deficit at the polar region may have something to do with the flattening of the cluster, however, this
is not the only reason. The double peak feature around the equatorial plane obviously does not relate to a
geometrical origin, otherwise the peak should be placed at the equatorial plane. In Fig.~\ref{fig_Rmax2D_T_comp}
we compare the $\theta$ distribution between slow and fast rotating models. One can see that in fast
rotating model, the double peaks are more significant, accompanied by a further deficit in the angle range
$0.2 - 0.4 \pi$ and $0.6 - 0.8 \pi$.

\begin{figure}[htbp]
  \begin{center}
  \includegraphics[width=0.9\columnwidth]{Rmax2D_Theta_comp.eps}
  \end{center}
  \caption{Normalized distribution of zenith angle $\theta$ of last apocenter of disrupted stars.
  Compare between slow (w030) and fast (w060) rotating models.}
  \label{fig_Rmax2D_T_comp}
\end{figure}

In order to understand the double peak feature, we turn to the orbit structure of these disrupted stars.
In non-spherical symmetric stellar system with a SMBH in its center, the space populated by stars can be
divided into three parts depending on the distance to the BH, namely the regular, chaotic and mixing region
\citep{PM2001}. Inside the BH's influence radius $r_h$, the potential felt by the star is dominated by the BH plus
a small perturbation from the non-spherical stellar potential. In this region, the motion of stars is
essentially regular, as in a spherical potential. Outside of $r_h$, stars passing the center
will suffer a large angle deflection by the BH, which in conjunction with the non-spherical potential
near and outside $r_h$, could make their orbits stochastic.

We are interested in stellar orbits in an axisymmetric stellar potential, which can get close to the central BH. These are typically two classes of orbits, short-axis tube (SAT) and saucer (see \citet{Vasiliev2014} for example); they can be distinguished by their third integral of motion $I_{3}$. Although $I_{3}$ may help us quickly distinguish orbit families, finding the functional form of $I_{3}$ is difficult (see \citet{LG1987} and discussion in \citet{ST1999}) and is beyond the scope of this paper. We choose alternative ways to do orbit classification, such as Surface of Section (SoS) plot and Fourier analysis of $J_x$ (see Appendix).

\begin{figure}[htbp]
  \begin{center}
  \includegraphics[width=0.47\columnwidth]{Orbit-SAT.eps}
  \includegraphics[width=0.47\columnwidth]{Orbit-saucer.eps}
  \end{center}
  \caption{Examples of orbital structure for SAT (left) and saucer (right) orbit. Stars achieve maximum
  $J$ when their instant orbital plane coincide with \textbf{B} plane, while minimum when coincide with
  \textbf{A} plane.}
  \label{fig_Orbit_R-z}
\end{figure}

Fig.~\ref{fig_Orbit_R-z} gives examples of SAT and saucer orbits in configuration space. The plot is made
in cylindrical coordinates so that one can catch the main point easily. For SAT orbit, one can see its
apocenter can go both above and below the equatorial plane. While apocenter of saucer orbit can only exist
on one side of mid-plane, due to restrictions by the 3rd integral.
We also check the value of $J$ at each apocenter passage. We find that SAT orbit
achieve its minimum $J$ at the equatorial plane; a saucer orbit cannot reach the
equatorial plane, but its minimum $J$ is achieved at the place which is next to the equatorial plane as marked
in the plot by \textbf{A} plane. Recall in the last section we said no matter what $J$ one star has at the
apocenter, at the time of disruption it must be smaller than $J_{lc}$. So the last apocenter place should
be around the \textbf{A} plane. This seems to be promising to explain the double peak in $\theta$ distribution,
however, need to be confirmed. In order to see this we try to do orbit classification for the disrupted
stars, which is computationally expensive. So we just randomly select a sub-sample of disrupted stars
and divide them into 3 orbit families: SAT, saucer and others (here ``others" means they do not belong to the
former two families, and may be chaotic orbits). Among the 2943 sample stars, 1719 are classified as
``others'', 757 as saucer and 467 as SAT. Then we re-plot the $r$ and $\theta$ distribution for different
orbit families in Fig.~\ref{fig_Rmax2D_Class}.

\begin{figure}[htbp]
  \begin{center}
  \includegraphics[width=0.9\columnwidth]{Rmax2D_stat_Class_R.eps}
  \includegraphics[width=0.9\columnwidth]{Rmax2D_stat_Class_T.eps}
  \end{center}
  \caption{Normalized distribution of apocenter distance $r$ and zenith angle $\theta$ of last apocenter of disrupted stars for different orbit families. The distribution is normalized to the number of stars in each orbit family.}
  \label{fig_Rmax2D_Class}
\end{figure}

The results show that the apocenter distribution of different orbit families not only differs in $\theta$ but
also in $r$. One can see the innermost region is dominated by SAT orbits, and concentrated to the equatorial
plane. Intermediate radius is mostly occupied by saucer orbits, and the distribution in $\theta$ shows
double peaks as expected. Further out is the region dominated by orbits marked as others. These orbits
can go outside of the influence radius and are basically chaotic orbits. From Fig.~\ref{fig_Rmax2D_Class}
one can also find out the fractions of each orbit family contributing to the budget of disrupted stars:
the largest fraction comes from chaotic orbits; SAT orbits contribute least to the budget because they are
deeply buried in the cluster center where the total star number is small; the intermediate contribution is from
saucer orbits which create the two peaks in the $\theta$ distribution.

\section{Conclusions and Discussions}

Tidal Disruption (TD) of stars by supermassive central black holes (SMBH) from dense rotating star
clusters is modelled
by high-accuracy direct $N$-body simulation. As in a previous paper on spherical star clusters we study the
time evolution of the stellar tidal disruption rate and the origin of tidally disrupted stars, now according to
several classes of orbits which only occur in rotating axisymmetric systems (short axis tube and saucer).
In empty loss cone regime, comparing spherically symmetric and axisymmetric systems we find a higher TD rate in large $r_t$ models in axisymmetric case, but for small $r_t$ case - somewhat surprisingly - there is virtually no difference in the TD rate, maybe a small increase due to axisymmetry.

We define an extended loss cone by the condition that stars in the axisymmetric potential reach the BH
within one orbit. A detailed analysis shows that the structure of the loss cone significantly differs
from the spherical case; if $J_{lc}$ is the critical angular momentum to be in the loss cone in a
spherical system, and $J,J_z$ are the total and $z$-component of the angular momentum of a stellar
orbit, there are many stars with $J > J_{lc}$ in the loss cone; since, however, there are also
some stars with $J > J_{lc}$, which are now {\bf not} in the loss cone. In the total balance the
number of loss cone stars is only very moderately increased.

In the experiment of measuring the shape of loss cone, we assume the test star can survive only one dynamical time in collisional system, after one orbit it will be ``kicked" to another place in phase space due to interactions with other stars. However, in collisionless limit, if we allow the test star to survive more orbit cycles, test star with much higher $J$ will also have chance to get rid of its angular momentum and be disrupted by BH. Then it is possible that an even larger loss cone region in phase space than what we presented here may exist, and result in a higher TDR. In order to check this, simulations with much more particles are needed and we would like to leave this task for future work.

The orbit type of disrupted stars strongly depends on energy
as we discuss in detail in the previous sections. TD of stars most strongly bound to the BH are
dominated by short-axis tube (SAT) orbits. In intermediate regions saucer orbits dominate, which create a characteristic double peak structure in the last apocenter position of their orbit relative to the equatorial plane. And further out chaotic orbits.

It is known for almost half a century that tidal disruption of stars should occur near SMBH, but only
much more recently the X-ray emission of tidal disruption events has been detected \citep{Komossa2002,KM2008}.
A simple argument on the fallback time for tidal debris by \citet{Rees1988} has led to the prediction of
a characteristic power law of the light curve with time, which can be used to distinguish TD events from
other transients. It is interesting that a SMBH binary can cause characteristic disruptions in such an
otherwise standard TD light curve \citep{LLK2014}. Hayasaki and collaborators claim that
eccentric TD events lead to somewhat longer lived central accretion disks \citep{HSL2013,HSL2015}. It will be very interesting to see whether and how the evolution of tidal debris and the
fallback rate are affected by different orbits of the disrupted stars as discussed here.

It has been claimed that rotation may help to quickly refill loss cones around binary supermassive black holes,
which helps significantly to accelerate shrinking and final coalescence of SMBH binaries in cosmologically
short time scales
\citep{Berczik2006,PBB2011,KHB2013,Khan2014}. In our paper we study by direct $N$-body
simulation the tidal accretion of stars and their orbital parameters in rotating axisymmetric systems.
We confirm the result of \citet{VM2013} that there is an increase in the rate of refilling
of the loss cone, but it is moderate. However, the situation deserves more detailed study, because
a SMBH binary creates a much stronger deviation from spherical symmetry than the one used in our
models with single SMBH. And second the detailed structure of the rotation in a central nuclear
star cluster could affect the enhancement of the loss cone.

\section*{Acknowledgements}

We acknowledge support by Chinese Academy of Sciences through the Silk Road
Project at NAOC, through the Chinese Academy of Sciences Visiting Professorship
for Senior International Scientists, Grant Number 2009S1-5 (RS), and through the
``Qianren" special foreign experts program of China.

The special GPU accelerated supercomputer laohu at the Center of Information and
Computing at National Astronomical Observatories, Chinese Academy of Sciences, funded
by Ministry of Finance of People's Republic of China under the grant ZDY Z2008-2,
has been used for the simulations.

PB acknowledge the special support by the NAS Ukraine under the Main Astronomical
Observatory GPU/GRID computing cluster project.

SZ thank Yohai Meiron for providing the SCF source code which is used in this work.

\newpage

redpajama_set_name: RedPajamaArXiv


text:
Take Action: Ask your councilmembers to support taxing and regulating marijuana
Medical cannabis program allows home delivery during COVID-19 crisis
On April 14, Mayor Bowser and the Department of Health announced emergency rulemaking to permit D.C.'s seven licensed dispensaries to provide medical cannabis delivery and curbside pickup to registered D.C. patients and caregivers.
The measures — which include regulations governing delivery and curbside pickup — went into effect immediately and will expire either August 12 or 45 days after D.C.'s public health emergency order is lifted, whichever is later.
These actions are critically important to ensure patients can access their medicine while promoting social distancing. You can find a list of licensed dispensaries in D.C. here.
Congress continues to block D.C from taxing and regulating marijuana sales
In November 2014, D.C. voters overwhelmingly approved Initiative 71, which legalized the possession and cultivation of limited amounts of marijuana by adults 21 and older. However, due to the fact that D.C. cannot control its own budget, Congress has been able to block the District from taxing and regulating marijuana sales via the "Harris rider."
In 2019, the House of Representatives removed the "Harris rider" from its annual spending legislation, but the rider was unfortunately included in the Senate version and remained there after both chambers hashed out a compromise bill. The congressional block will continue through at least September 2020.
The lack of any lawful place to purchase non-medical cannabis has led to a proliferation of "grey market" operators and a significant increase in arrests for the distribution of marijuana, which have returned to pre-legalization levels. It also means D.C. is losing out on millions of dollars in tax revenue and hundreds of good jobs. If you live in D.C., urge your councilmembers to support taxing and regulating marijuana sales for adults 21 and older.
Council committee holds hearing on employment protection bills
On September 25, 2019, the D.C. Council Committee on Workforce and Development held a hearing on two bills that would protect D.C. residents and medical cannabis patients from employment discrimination. The "Prohibition of Marijuana Testing Act of 2019" seeks to prohibit marijuana testing as a condition of employment with some exceptions — for both adult-use consumers and medical patients. The Medical Marijuana Program Patient Employment Protection Act of 2019 seeks to prohibit the D.C. government from discriminating against patients participating in the medical cannabis program. The bills — which MPP's Olivia Naugle testified in favor of — are awaiting further action in committee.
MPP Legislative Analyst Olivia Naugle testifying at the D.C. Committee
on Labor & Workforce Development public hearing in September 2019.
D.C. now accepts medical cannabis cards from any state
In August 2019, Mayor Muriel Bowser announced that non-District residents with a medical marijuana card from any state may obtain their medicine from a D.C. dispensary while they are visiting the District.
The Department of Health had already authorized certified patients from some states to access D.C's medical cannabis dispensaries with the approval of B21-0210 back in 2016. The mayor's new rulemaking expands the number of states whose medical cards the District recognizes from 19 to at least 27.
New states added by the action are Alaska, Arkansas, California, Nevada, New Mexico, New York, and Vermont. Louisiana, Minnesota, Oklahoma, and West Virginia are under review. Cards from Colorado, Connecticut, Delaware, Florida, Hawaii, Illinois, Maine, Maryland, Massachusetts, Michigan, Montana, New Hampshire, New Jersey, North Dakota, Ohio, Pennsylvania, Rhode Island, and Washington State were already recognized.
Thank you for supporting the Marijuana Policy Project. To stay updated on the status of marijuana policy reform in Washington, D.C., be sure to subscribe to MPP's email alerts, if you haven't done so already.
The Marijuana Legalization and Regulation Act of 2019 Summary
Summary of D.C. Mayor Muriel Bowser's Safe Cannabis Sales Act of 2019
Progress Report: D.C.'s Medical Marijuana Program
Talking Points on Ending D.C.'s Social Use Ban
D.C.: Urge your council members to oppose the social use ban!
Marijuana Possession Decriminalization Amendment Act of 2014
Summary of D.C.'s Initiative 71

redpajama_set_name: RedPajamaCommonCrawl


text:
The Hielanman's Umbrella () is a landmark in the centre of Glasgow, Scotland. It is the local Glaswegian nickname for the glass walled railway bridge which carries the platforms of Glasgow Central station across Argyle Street. It is built in Victorian style.

History
Due to the forced displacement of people during the second phase of the Highland Clearances in the 19th century, 30,000 highlanders who spoke Scottish Gaelic, but not English, came to Glasgow to find work. When arriving in the city they were housed in many different areas of Glasgow.

The highlanders predominantly found work within domestic service in areas like Park Circus or in one of the many industries, where they would work, for example, for the river ferries. Over many years highlanders continued to arrive and began to keep in touch by meeting under the bridge, mostly at weekends. With the city's inclement weather and the meeting of the highlanders it came to be known as the Hielanman's Umbrella. At the meetings they would share news and gossip from the homelands and of events in the city.

The Umbrella tradition reached its height in the '20s and '30s, however, due to the Second World War and the resulting blackout, the tradition of meeting under the bridge died.

The first long-distance television pictures transmitted in the UK were sent to Glasgow Central Station in 1927.

Recent Development
Glasgow Central Station and the Hielanman's Umbrella has been renovated several times.

In 1998, the bridge was substantially refurbished by Railtrack (which later became Network Rail in 2002) in line with the rest of the station - its distinctive Venetian style windows were reglazed, and the gold "Central Station" lettering was applied.  Efforts were also made to improve the environment underneath the bridge to encourage retailers back into the shop units - high powered lighting and extractor fans were installed.  The street level entrances to Central Station under the bridge were also upgraded.

In 2001, a new entrance to the burgeoning Arches nightclub and restaurant complex was added under the bridge which has led to the level of pedestrian footfall increasing markedly.

In 2015 The Hielanman's Umbrella, as part of the Glasgow Central Station, won the Scottish Design Award.

In November 2019 a ten-year-regeneration plan for the Glasgow city centre was announced, including a plan of turning the Hielanman's Umbrella into a light and attractive station lobby.

Appearances in Literature
The Hielanman's Umbrella is mentioned in Jackie Kay's novel Trumpet from 1998:

It also appears in Simon Jenkins' book Britain's 100 Best Railway Stations from 2017.

References

External links

Highland Clearances
Buildings and structures in Glasgow
Bridges in Glasgow
1879 establishments in Scotland
Bridges completed in 1879

redpajama_set_name: RedPajamaWikipedia


Christmas is just around the corner. Here at the Nook our local artists and craftspeople have been producing unique, handmade gifts for someone you love. We have a wide selection of gifts catering to all tastes, within a reasonable budget. Pop in and find out why our gifts are not available elsewhere.
MERRY CHRISTMAS and HAPPY HOLIDAYS from The NOOK!
This entry was posted in News and tagged Art, bags, Blue Mountains, bluemtnsmakers, candles, cards, ceramics, clothing, costumes, Craft, giftideas, gifts, handmade, jams, jewelery, knitting, Leura, leurachristmas, leuravillageau, mtnsmade, painting, shoplocal, supportlocalbusiness, thenookleura, toys, wearable art. Bookmark the permalink. Both comments and trackbacks are currently closed.


At One Love Beach we try to source products that are made ethically, are sustainably produced, benefit the planet, support a local artist, promote positivity and encourage an active lifestyle. Below are just a few of the many products available at One Love Beach. Stop in the store to see everything we offer!


September 11: In memory of Joe Angelini, Jr.
This post honors three heroes of September 11, 2001: a father and two sons. Two died, one survived.
Joseph Angelini Jr. may have lived for the New York City Fire Department, but he didn't hang around when his tour ended.
"Gotta get home to the kids," he'd tell the guys in Manhattan's Ladder Co. 4 before heading to the 6:33 p.m. train to Lindenhurst.
Angelini's wife, Donna, has scheduled a memorial service for today to help 7-year-old Jennifer, 5-year-old Jacqueline and 3-year-old Joseph Angelini III to finally understand that he won't be coming home anymore.
"My son asks everyone he sees in uniform, 'Did you find my daddy, did you find my daddy?'" Donna Angelini said Friday.
The seven-year department veteran followed in the footsteps of his father, Joseph Angelini Sr., 63, who was the senior member of Brooklyn's Rescue Co. 1 and also perished in the World Trade Center attacks.
But at home, he was a cook, craftsman and avid gardener who grew pumpkins, zucchini, eggplants and hot peppers and filled the house with the smells of pizza and focaccia.
Angelini also is survived by his mother, Anne, a grandmother, Mary, sister Annmarie Bianco and brother, Michael, all of Lindenhurst; sister Mary Angelini of Washington D.C.; and by seven nieces and nephews.
A memorial service will be held today at 11 a.m. at Our Lady of Perpetual Help Roman Catholic Church in Lindenhurst.
CNN.com profile of Joe Jr.
Living Tribute to Joseph Angelini, Jr.
Joseph J. Angelini Sr. and his son, Joseph Jr., were firefighters, and neither survived the twin towers' collapse. "If he had lived and his son had died, I don't think he would have survived," said Alfred Benjamin, a firefighter at Rescue Company 1 in Manhattan who was partnered with Mr. Angelini for the last six months.
The elder Mr. Angelini, 63, was the most veteran firefighter in the city, with 40 years on the job. He was tough and "rode the back step" like everyone else. His 38-year-old son, who worked on Ladder Company 4 on 48th Street, was on the job for seven years.
"If you mentioned retirement to Joey, it was like punching him," Mr. Benjamin said. Joseph Jr. was proud of his father's reputation and tried to copy him any way he could, said Joseph Jr.'s wife, Donna.
A brother, Firefighter Michael Angelini, was there as well, but, in a move that probably saved his life, left when asked to help carry out the body of the Rev. Mychal Judge, the fire department's chaplain.
Michael's choice: remain with his mother, Anne, in Lindenhurst and support his family during the wake, today, and the funeral, tomorrow, for his father, New York firefighter Joey Angelini, 63; or, return to The Pile to continue searching for his missing brother, New York firefighter Joey Angelini Jr., 38.
Michael works for the Fire Patrol of New York, which operates under the New York Board of Underwriters, protecting the interests of insurers during and in the aftermath of commercial property fires. Wearing the same firefighting gear, except for the distinctive red helmet that denotes Fire Patrol, he responded to the World Trade Center disaster last Tuesday morning, as did his father, a 40-year FDNY veteran assigned to Rescue 1, and his brother, of Ladder Co. 4 in the Theater District. "We were all in the same area, and none of us knew it," he said.
Michael entertained a slender hope that his brother might have finished his tour early and gone home. He suspected otherwise, and he learned later that afternoon that Joey had done what his father would have done and what so many other firefighters did who were supposed to be ending their tours at 9 a.m. They went to work.
"Since then," Michael said, "I saw him taking on more and more of my father's traits. Before, we used to go out a lot, he and I. He was silly, funny. Now, getting him to go out was like pulling teeth. I tell old stories to guys he worked with, and they'll look at me like I'm talking about somebody they don't know. He had become so, like, straight. He just wanted to be with his family. He was showing more and more of that integrity, that seriousness, like my father.
The elder Angelini was in special operations that morning, and Michael hoped he too might have been sent elsewhere, but he really knew better. His father was legendary in the department for loving the work, for loving "to get dirty," for loving "making a grab [rescuing somebody]," for routinely walking out of a mostly extinguished inferno and lighting a cigarette while younger firefighters lay sprawled around him, exhausted.
Rescue workers found the body of Joey Angelini on Monday. He had been listed as missing since the day after the attack. Joey Jr. still is missing. After tomorrow's funeral Mass at Our Lady of Perpetual Help in Lindenhurst, Michael probably will return to the site.


How were the reservations formed and who lives there?
How did the Michif language develop?
What causes individuals to not want to leave the reservations?
How do I feel about being near to my family?
What decisions do I make in my life based on my family?
Have I ever turned down an opportunity because it would have caused me to be away from my family? How did that feel?
How might remembering that "You're no better…but you're no worse" help as I move through life? Is there a time that this belief has helped me?


text:
Q: Disqus: change captions after success with jQuery Disqus automatically places defined captions upon request. For example: Add new Comment
I've tried to change its value with jquery on ready():
$('#dsq-new-post h3').text('Paticipa con tu cuenta favorita');

No success :( ... how can i know when disqus script is finished parsing the data so i can change the caption value of h3?
BTW, this is Disqus' call:
(function(){
var dsq = document.createElement('script');
dsq.type = 'text/javascript'; dsq.async = true;
dsq.src = 'http://xxxxxxxx.disqus.com/embed.js';
(document.getElementsByTagName('head')[0] || document.getElementsByTagName('body')[0]).appendChild(dsq);
})();

A: Here is the answer andufo. It works:
$(document).ready(function() {
  window.disqus_no_style = true;

  $.getScript('http://sitename.disqus.com/embed.js', function() {
    var loader = setInterval(function() {
      if($('#disqus_thread').html().length) {
        clearInterval(loader);
        disqusReady();
      }
    }, 1000);
  });

  function disqusReady() {
    //whatever you can imagine
  }
});

You can comment out the $.getscript line and ending }); as well as the window.disqus_no_style = true; line.
I had a similar problem and posted this question. Mohamed attempted to answer me and his answer did not work but he'd posted a link to his code at github and I found the right answer there.
Chrome Extension iframe dom reference disqus
https://gist.github.com/471999

A: This simple solution also works, although the original text appears first, then is replaced with the new text, which is less then ideal.
function disqus_callback() {
  $('#dsq-reply h3').text('Add Your Answer');
}

redpajama_set_name: RedPajamaStackExchange


text:
Q: R Function that parse text file and extract a specific value I have two files: csv file & text file. in the csv file, i have commmit ID only, whereas in the text file, i have commit log which include commit ID and its related information.
I need to write a function in R that do the following:

*

*Read the two files.

*For each commit ID in csv, find that ID in
the text file, parse the text after the ID, and get the number after
"'" and before the space " "  (which is 4 in the example above).

*Save the extracted number in a new column in csv file.

Code
birt =read.csv("C:/path/Obirt.csv", header =T)
cvs = data.frame(CID = C(birt$commitID)
txt = readLines("C:/path/summary.txt")
tail(unlist(strsplit(txt,"'")), 2)
tmp = data.frame(t(sapply(txt, function(x) c(unlist(strsplit(unlist(strsplit(x, "'"))[2], ';')), tail(unlist(strsplit(unlist(strsplit(x, "'"))[3], '  ')), 2)), USE.NAMES = F)))
colnames(tmp) = c('CID', 'COMMIT_NAME', 'COMMIT_TIME', 'COMMIT_SUB', 'NUM1', 'NUM2')
newcsv = merge(cvs, tmp, by='CID')
write.csv(newcsv, 'C:/Users/abdul/desktop/umbc/birt/newcsv.csv', row.names = F)

However, it is unable to merge the data.
The text file format is 'commit ID; commiter name; commit time; description' whereas some records include additional info 'commit ID; commiter name; commit time; description' num num  patch file (like commit ID ba37902179 below).
Example:
'99e88cb4c9;Yulin Wang;Mon Sep 11 08:43:32 2017 -0700;Merge pull request #418 from ZwoCa/master'
'9be3838165;Sebastian;Mon Sep 11 15:06:07 2017 +0200;Merge pull request #1 from ZwoCa/ZwoCa-patch-1'
'ba37902179;Sebastian;Mon Sep 11 15:00:33 2017 +0200;Fixed inverted assertion'
1   1   data/org.eclipse.birt.data/src/org/eclipse/birt/data/engine/executor/transform/SimpleResultSet.java'f6d86d5f95;Gary Xue;Mon Aug 28 20:51:37 2017 -0400;Merge pull request #417 from Bharadwaj14/master'
'95acb82708;Gary Xue;Mon Aug 28 20:50:29 2017 -0400;Merge pull request #416 from rrimmana/master'
'3ff8e99b70;Bharadwaj Tirunagaru;Mon Aug 28 15:18:13 2017 +0530;removing 3289.patch'
0   102 3289.patch'1dbc5116ae;rrimmana;Mon Aug 28 15:06:13 2017 +0530;A report that based on Mongo ODA driver with Kerberos authentication turned off where connection to Mongo DB, using ODA driver is throwing NPE. Its a backward compatibility bug.'
2   5 data/org.eclipse.birt.data.oda.mongodb/src/org/eclipse/birt/data/oda/mongodb/impl/MongoDBDriver.java'
based on the example, i think the solution would be something like
tmp = data.frame(t(sapply(txt, function(x)unlist(strsplit(unlist(strsplit(x, "'"))[2], ';')))))
   if (//there is Not"''" at the end of a tail//) // i am not sure how to make
                                                       such condition
   Then tmp = c(tail(unlist(strsplit(unlist(strsplit(x, "'"))[3], '  ')), 2),
                USE.NAMES = F)

A: This code will parse the data that you provided and merge the elements with a matching commit ID in a separate data frame and then write the new data frame out as a CSV. The two commented lines are what you would use for your actual data. It is highly dependent on the format being the way you specified in your question so if there are any deviations in the log files it will not parse the lines correctly. Also the column name CID will need to be changed to match whatever it really is in your CSV file.
csv = data.frame(CID = c('A1234', 'B1234', 'C1234'))
#csv = read.csv('csvfile.csv')
txt = c("'A1234;commmiter name;commmit time;commmit subject' 4 1","'B1234;commmiter name;commmit time;commmit subject' 5 1","'C1234;commmiter name;commmit time;commmit subject' 6 1")
#txt = readLines('textfile.txt')
tail(unlist(strsplit(txt, "'")), 2)
tmp = data.frame(t(sapply(txt, function(x) c(unlist(strsplit(unlist(strsplit(x, "'"))[2], ';')), tail(unlist(strsplit(unlist(strsplit(x, "'"))[3], ' ')), 2)), USE.NAMES = F)))
colnames(tmp) = c('CID', 'COMMIT_NAME', 'COMMIT_TIME', 'COMMIT_SUB', 'NUM1', 'NUM2')

newcsv = merge(csv, tmp, by='CID')
write.csv(newcsv, 'newcsv.csv', row.names = F)

A: By observing the format in the text file, i think the unlist(strsplit) function should be something like
tmp = data.frame(t(sapply(txt, function(x)unlist(strsplit(unlist(strsplit(x, "'"))[2], ';')))))
   if (//there is Not"''" at the end of a record//) // i am not sure how to make
                                                       such condition
   Then tmp = c(tail(unlist(strsplit(unlist(strsplit(x, "'"))[3], '  ')), 2),
                USE.NAMES = F)

because not all tail has the two numbers after. but i am not sure how to formulate the IF condition above.


Film starring Jason Clarke as Ted Kennedy is a low-key, generally absorbing, if somewhat lackluster, procedural.
It was six years since the assassination of John F. Kennedy and a year since Bobby was gunned down. But the Kennedy machine churned on. Jack Kennedy's ambition to reach the moon was being realized by Neil Armstrong. Edward M. ("Teddy") Kennedy, already seven years a senator, having filled his brother's Massachusetts seat, was Joseph Kennedy's only living son left and a likely future president.
Those aspirations effectively crashed when 37-year-old Teddy drove an Oldsmobile off a narrow bridge on a remote beach road on Chappaquiddick Island, off Martha's Vineyard, late at night on July 18. With him was 28-year-old Mary Jo Kopechne, a former campaign worker for Bobby (played by Kate Mara in the film), who died underwater. Kennedy escaped from the car, submerged in eight feet of water. Whatever his efforts were to free Kopechne, they were futile. It took him 10 hours to report the incident to the police. Kennedy attributed the delay to a concussion and exhaustion.
Chappaquiddick has long loomed in the political imagination as a kind of definitive-yet-murky scandal. Curran's film is principally an effort to visualize and understand that evening. It's a low-key, generally absorbing, if somewhat lackluster, procedural that ominously reflects on the darker shadows that loom behind even the brightest shining political hopes.
Kennedy, of course, went on to serve four more decades in the Senate. So what's the legacy of Chappaquiddick? How are Kennedy's accomplishments to be reconciled with that night? Those aren't questions much pursued in the largely self-contained "Chappaquiddick." Curranis content to let the record speak for itself and perhaps suggest: Some politicians get away with more than they ought to.


My husband and I were extremely happy with the dedication Jessica put into the planning of our wedding. Jessica's knowledge made us feel very at ease and stress-free throughout the wedding planning process. She had great time management and prompt communication with us and our many vendors. On the day of our wedding, everything ran right on time and without a hitch because of her organizational skills. We were very thankful and could not have asked for a better wedding coordinator.


Surya Cosmopolitan Rug Home Interior | Parrisislandosc surya cosmopolitan rug. surya cosmopolitan area rug cos 9209. surya cosmopolitan area rug.
Endearing Surya Cosmopolitan Rug At COS 9265 Navy Beige Grey Area. Amazing Surya Cosmopolitan Rug Of COS 9262. Attractive Surya Cosmopolitan Rug In Navy Dark Blue Light Gray Khaki. Lovely Surya Cosmopolitan Rug On Cos 9278 Area 141361. Remarkable Surya Cosmopolitan Rug Of Example Image No 5 Wanderpolo Decors Up. The Best Of Surya Cosmopolitan Rug Area Gray Products. Enthralling Surya Cosmopolitan Rug Of COS 9175 Blue Area Kaoud Rugs. Inspiring Surya Cosmopolitan Rug On COS 9263. Terrific Surya Cosmopolitan Rug In Rugs At Studio. Captivating Surya Cosmopolitan Rug On Sand Teal Walmart Com. Eye Catching Surya Cosmopolitan Rug In COS9200 Yellow Area Free Shipping. Magnificent Surya Cosmopolitan Rug At COS 9280 Blue Area RugSale Com. Unique Surya Cosmopolitan Rug In COS 9278 Area Incredible Rugs And Decor. Picturesque Surya Cosmopolitan Rug In COS 9217 Closeout Area. Sophisticated Surya Cosmopolitan Rug In COS 9169 Area SURYA At Homelement Com.


text:
All Games > Action Games Games > Tom Clancy's Ghost Recon® Desert Siege™
Tom Clancy's Ghost Recon® Desert Siege™
East Africa, 2009. A 60-year conflict boils over as Ethiopia invades its smaller neighbor Eritrea, threatening the world's most vital shipping lanes in the Red Sea. An elite team of U.S. Army Green Berets, known as the Ghosts, moves in to safeguard the seas and free Eritrea.
Action	Shooter	First-Person	FPS	Tactical	Strategy
English	 ✔
Title: Tom Clancy's Ghost Recon® Desert Siege™
Developer: Red Storm Entertainment
Notice: Requires the Steam version of Tom Clancy's Ghost Recon.
Buy Tom Clancy's Ghost Recon™: Desert Siege™
WEEK LONG DEAL! Offer ends January 25
East Africa, 2009. A 60-year conflict boils over as Ethiopia invades its smaller neighbor Eritrea, threatening the world's most vital shipping lanes in the Red Sea. An elite team of U.S. Army Green Berets, known as the Ghosts, moves in to safeguard the seas and free Eritrea. As the war rages on, the Ghosts are drawn from Eritrea's shores to the heart of Ethiopia in their deadliest battles yet.
New multiplayer modes - Team-based Siege and Domination modes allow teams to attack or defend territory.
Both new modes are fully compatible with your original Ghost Recon game - play for hours on the original maps.
8 new single-player missions.
4 new dedicated multiplayer spaces.
9 new multiplayer weapons, including the Bizon submachine gun, the M98 sniper rifle, and the fearsome M-60 machine gun.
Supported OS: Microsoft Windows® 2000/XP
Processor: Pentium® II 450 MHz, AMD K6 III 500, or equivalent
System Memory: 128 MB of RAM or above
Video Card: 16 MB DirectX® 8.0-compliant 3D card; Voodoo™ cards not supported
Sound Card: DirectX 8.0-compliant sound card
DirectX Version: DirectX® version 8.0 or higher
Hard Disk: 2 GB available hard disk space
Multiplay: Properly configured TCP/IP connection at 56 Kbps or faster
Note: For an up-to-date list of supported chipsets, video cards, and operating systems, please visit the FAQ for this game at: http://support.ubi.com.
© 2002 Red Storm Entertainment, Inc. Red Storm and Red Storm Entertainment are trademarks of Red Storm Entertainment, Inc. Red Storm Entertainment, Inc. is a Ubisoft Entertainment company. Desert Siege is a trademark of Ubisoft Entertainment, Inc. All Rights Reserved. Tom Clancy's Ghost Recon is a trademark of Rubicon, Inc. under license to Ubisoft Entertainment.


text:
require 'ansible/ruby/modules/base'

module Ansible
  module Ruby
    module Modules
      # Manage an AWS Network Elastic Load Balancer. See U(https://aws.amazon.com/blogs/aws/new-network-load-balancer-effortless-scaling-to-millions-of-requests-per-second/) for details.
      class Elb_network_lb < Base
        # @return [Symbol, nil] Indicates whether cross-zone load balancing is enabled.
        attribute :cross_zone_load_balancing
        validates :cross_zone_load_balancing, type: Symbol

        # @return [Symbol, nil] Indicates whether deletion protection for the ELB is enabled.
        attribute :deletion_protection
        validates :deletion_protection, type: Symbol

        # @return [Array<Hash>, Hash, nil] A list of dicts containing listeners to attach to the ELB. See examples for detail of the dict required. Note that listener keys are CamelCased.
        attribute :listeners
        validates :listeners, type: TypeGeneric.new(Hash)

        # @return [String] The name of the load balancer. This name must be unique within your AWS account, can have a maximum of 32 characters, must contain only alphanumeric characters or hyphens, and must not begin or end with a hyphen.
        attribute :name
        validates :name, presence: true, type: String

        # @return [Boolean, nil] If yes, existing listeners will be purged from the ELB to match exactly what is defined by I(listeners) parameter. If the I(listeners) parameter is not set then listeners will not be modified
        attribute :purge_listeners
        validates :purge_listeners, expression_inclusion: {:in=>[true, false], :message=>"%{value} needs to be true, false"}, allow_nil: true

        # @return [Boolean, nil] If yes, existing tags will be purged from the resource to match exactly what is defined by I(tags) parameter. If the I(tags) parameter is not set then tags will not be modified.
        attribute :purge_tags
        validates :purge_tags, expression_inclusion: {:in=>[true, false], :message=>"%{value} needs to be true, false"}, allow_nil: true

        # @return [Array<Hash>, Hash, nil] A list of dicts containing the IDs of the subnets to attach to the load balancer. You can also specify the allocation ID of an Elastic IP to attach to the load balancer. You can specify one Elastic IP address per subnet. This parameter is mutually exclusive with I(subnets)
        attribute :subnet_mappings
        validates :subnet_mappings, type: TypeGeneric.new(Hash)

        # @return [Array<String>, String, nil] A list of the IDs of the subnets to attach to the load balancer. You can specify only one subnet per Availability Zone. You must specify subnets from at least two Availability Zones. Required if state=present. This parameter is mutually exclusive with I(subnet_mappings)
        attribute :subnets
        validates :subnets, type: TypeGeneric.new(String)

        # @return [:"internet-facing", :internal, nil] Internet-facing or internal load balancer. An ELB scheme can not be modified after creation.
        attribute :scheme
        validates :scheme, expression_inclusion: {:in=>[:"internet-facing", :internal], :message=>"%{value} needs to be :\"internet-facing\", :internal"}, allow_nil: true

        # @return [:present, :absent] Create or destroy the load balancer.
        attribute :state
        validates :state, presence: true, expression_inclusion: {:in=>[:present, :absent], :message=>"%{value} needs to be :present, :absent"}

        # @return [Object, nil] A dictionary of one or more tags to assign to the load balancer.
        attribute :tags

        # @return [Symbol, nil] Whether or not to wait for the network load balancer to reach the desired state.
        attribute :wait
        validates :wait, type: Symbol

        # @return [Object, nil] The duration in seconds to wait, used in conjunction with I(wait).
        attribute :wait_timeout
      end
    end
  end
end

redpajama_set_name: RedPajamaGithub


Garg, Anjali & Gulaty, Sachin, 2004. "Regulation in India: Assessing Impact in the Power and Water Sectors," Centre on Regulation and Competition (CRC) Working papers 30684, University of Manchester, Institute for Development Policy and Management (IDPM).
All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:ags:idpmcr:30684. See general information about how to correct material in RePEc.


text:
Q: Removing zombie locks in Subversion I'm trying to find a way to remove zombie locks using the Subversion command line tools.  The eventual goal is to do this from a hook script, but I haven't been able to work out the command line to use when you only have a physical repository path.  (Using svnadmin rmlocks only seems to work for locks which exist in the HEAD revision.)
Ideally, I'd like to do this via the post-commit hook script using the command line tools. (I'm aware of the python script for this purpose, but we'd prefer not to install python on that server for this single use.)  We're a .NET shop, so creating a tool with the SharpSVN library is also a possibility, but the only unlock capability there appears to be in the SVNClient class.
So it's really two questions: Is there a way to do this with the command line tools?  If not, is there a way to do it from SharpSVN?  (Or perhaps another library?)
== Update Dec 3, 2012 ==
I've had to revisit this problem recently and discovered this question is still drawing traffic. The python script mentioned in the original question and Don's answer has since moved to: http://svn.apache.org/repos/asf/subversion/trunk/contrib/hook-scripts/remove-zombie-locks.py  (I assume that's what most folks are looking for.)
Ironically, even though the repository has moved to Linux, we're using the C solution.

A: There's a Python script (referenced here: http://subversion.tigris.org/ds/viewMessage.do?dsForumId=1065&dsMessageId=2369399).  I'd either use that, or translate it to .NET if you needed to.

A: It looks like the answer is "You can't get there from here."

*

*Svnadmin provides a command-line for removing locks with a repository path, but it doesn't seem to work with zombie locks.

*SharpSVN is primarily client-side; it does have a few methods for connecting with a repository path, but those (per the docs) are mostly for use in the library's unit tests.

So rewriting the python script in C using the Subversion API library.

A: If you know the repository path to the deleted file that is zombie-locked, it is so simple that I couldn't believe it at first:
svn unlock --force https://path/to/my/file

This works even though the deleted file does (by definition) not exist in the repository's head. No peg revision required nor allowed. The force option is only necessary if the lock is from another user.

A: Common problem with zombie lock is, svn prevent removal of a directory till lock is removed from all files and sub-folder under it. Suppose you want to remove a folder named codes from your svn repo "svn://192.168.0.1/trunk/codes".
You can use command line tool svn in following way to accomplish the folder removal.
svn rm -m "not required"  svn://192.168.0.1/trunk/codes
Now svn responds with error like svn: warning: W160040: No lock on path '/trunk/codes/abc.txt
You can then unlock this non-existent abc.txt via following command
svn unlock --force  svn://192.168.0.1/trunk/codes/abc.txt (see use of svn path instead of local path)
If no more locked non-exitent file present, next command to remove the folder ie.  svn rm -m "not required"  svn://192.168.0.1/trunk/codes is success.


"Growing up in Nebraska, I'd always planned on moving to New York to paint, but when I graduated college in 1966, a foolish and addled road trip sidetracked me to San Francisco, where I've now lived for half a century. These subjects that had been of longtime interest subjects had less to do with engineering than something deep inside: a probing for mystery, meaning, power, and identity. The works looked very different from the non-objective, painterly work I'd been doing in San Francisco; they included photo transfers and printouts from magazines of the time. (I had kept them all those years!) I spent one or two years working on them, both in Manhattan and later back in our home in San Francisco.
Ward Schumaker is an award winning designer and illustrator whose fine art work is regularly shown in New York, Los Angeles, San Francisco, and Shanghai. Schumaker's design and illustration work has been featured in The Washington Post, the San Francisco Chronicle, and The New York Times and for The Yolla Bolly Press, Hermès, Paris, and Deutsche Grammophon.


Pregame for meals with water. Drinking water throughout the day and during your meals promotes proper digestion so you don't get backed up and bloated. But some research suggests downing two glasses of water glasses before meals can make you feel fuller when you take that first forkful, leading you to eat less overall.
Don't make dinner your heaviest meal. Research suggests that people who eat their largest meals later in the day lose less weight than people who eat their heaviest meals early on, mostly because the body digests food differently at different times — and more slowly at night, according to Luciani.


After seeing some adorable girls, it's time for the boys. Patrick and Andrew were a lot of fun to photograph. This is the last post on the Easter Bunny Portraits themed series and I hope you enjoy it.
We are already working on our next themed series. Make sure you subscribe to our newsletter to find out first the details (or like our Facebook page).
This is another session from the Easter Bunny Portraits series. As you can see, studio portraits don't have to be boring. One comment I received: they look like they are from a story book. Enjoy!
Next week, we'll feature some boys too.
Last week we announced our first themed sessions for the year. Here are some images for your enjoyment from the Easter Bunny portrait sessions.
Easter bunny mini sessions – custom designed set and no waiting lines. There are still a few spots available (if you want first chance of reserving your spot, signup for our newsletter; it goes out before we make it available to the public).
Welcome back! This is the evening gown portion of Miss Philadelphia 2013. And, at the end, we'll reveal this year's new Miss Philadelphia.
First, let's start with another beautiful performance by Miss Philadelphia 2012, Lauren Bilski.
Let's enjoy one more time the beautiful contestants in their evening gowns ….
And, Miss Philadelphia 2013 is …..