'The Fork, the Witch, and the Worm' by Christopher Paolini.
It was a late-night tweet that sparked Christopher Paolini's newest collection of tales from Alagaësia - the fantasy world of dragon riders first introduced in his novel Eragon in 2001.
Almost a decade later a fan wanted to know a random fact about Murtagh, one of the players from the series. Paolini responded in his signature playful style: "At one point, Murtagh enchanted a fork to be as deadly as any sword. He called it Mr Stabby. Thorn was not amused." The idea remained, and The Fork, The Witch, and The Worm was born.
The book is a collection of three new stories, all set in the same world as The Inheritance Cycle. The first book of that series, Eragon, was self-published when he was just 16 and republished in 2003. The book became a publishing phenomenon and was followed by three more books in The Inheritance Cycle series and a movie adaptation starring John Malkovich.
Paolini may have grown up since then (he is now 35), but he has never really left Alagaësia. He counts this collection as book five set in the world of his Dragon Riders, and already has plans for another.
Times have changed, but Paolini's stories remain just as powerful, even to this new generation of digital-savvy readers. Paolini believes this is because his books draw on universal themes that continue to resonate.
"Transformation is a theme I return to again and again and adolescence is the great transformation we all go through. We all feel that powerlessness and fear of what's to come in adulthood. Fantasy can make those fears and feelings a physical reality. It externalises what is otherwise internal. And it's that challenge that resonates with readers."
The Fork, The Witch and The Worm is in some ways a tying up of loose ends, and a beginning of a new chapter. Beloved characters like dragon rider Eragon return, as well as a few new faces. Paolini's sister Angela also contributes writing for The Witch.
For Paolini, writing has always been a family affair. His parents helped him publish his first novel as a teenager and his sister is collaborator and soundboard for his ideas. But he has also experienced the isolation that many writers face.
That changed when he joined Twitter. "Social media has changed the way I interact with fans. It's fun. If you behave yourself online, people react positively. It's nice to know there is an audience and that people care about your work."
The author believes the rise of eBooks and social media has produced an influx of new readers, a trend he encourages by regularly releasing exclusive web content and deleted scenes, for which he receives encouragement in return. "It's motivating," he says.
We are giving away three copies of The Fork, the Witch and The Worm by Christopher Paolini. To enter, name the first book in The Inheritance Cycle series. E-mail your answer to lifestyle@sundaytimes.co.za with DRAGON as the subject. Remember to include your name and contact number. Only one entry per person. Competition closes on Friday April 19. Ts & Cs apply.


text:
\section{Introduction}
Ever since the dawn of modern core-collapse supernova (CCSN) theory,
the neutrino-heating mechanism \citep{colgate},
 in which a supernova shock is revived by neutrino energy deposition
to trigger explosions \citep{wils85,bethe85},
has been the leading candidate for the explosion  mechanism
  for more than four decades.
 However, the simplest, spherically-symmetric (1D) form of this
mechanism fails,  except for super-AGB stars
at the low-mass end \citep{bernhard12a}, to explode canonical massive stars
\citep{Rampp00,lieb01,thom03,Sumiyoshi05}.
 Pushed by accumulating supernova observations of the blast
morphology
 \citep[e.g.,][and references therein]{wang08,tanaka12},
a number of multi-dimensional (multi-D)
hydrodynamic simulations have been reported so far,
which gives us a confidence that hydrodynamic motions associated with convection
\citep[e.g.,][]{Herant92,Burrows95,Janka96,frye02,fryer04a}
and the Standing-Accretion-Shock-Instability
\citep[SASI, e.g., ][]{Blondin03,Scheck04,scheck06,Ohnishi06,ohnishi07,ott_multi,Murphy08,Foglizzo06,thierry07,endeve12,thierry12,iwakami1,iwakami2,rodrigo09_2,rodrigo09,rodrigo10,hanke,rodrigo13}
can help the onset of neutrino-driven explosions
\citep[see collective references in][]{thomas12,kotake12}.

In fact, neutrino-driven explosions have been obtained
in first-principle two-(2D) and three-(3D) dimensional simulations
in which spectral neutrino transport is solved by various
approximations \citep[e.g.,][]{kotake12b}.
The Garching group
\citep{Buras06a,Buras06b,Marek09, hanke13, bernhard11,bernhard12a,bernhard12b,bernhard13}
included one of the best available neutrino transfer approximations
by the ray-by-ray variable Eddington factor method.
The Oak Ridge group \citep{bruenn09,bruenn13}
included a ray-by-ray multi-group flux-limited diffusion transport
with the best available weak interactions.
The Nippon group\footnote{"Nippon" stands for Japan in Japanese, and from
 now on we like to call our team as so whose members come all around Japan.} \citep{Suwa10,Suwa11,suwa12,Takiwaki11,takiwaki13}
employed a ray-by-ray isotropic diffusion source approximation \citep{idsa}
with a reduced set of weak interactions\footnote{See \citet{sumiyoshi12} for collective references about detailed neutrino transport schemes.}.

This success, however, is accompanying further new question.
The explosion energies obtained in
some 2D models are underpowered by up to a factor of 10
compared to the canonical supernova kinetic energy
($\sim 10^{51}$ erg, see table 1 in \citet{Kotake11} for a current
summary).  What on earth is missing furthermore ?
3D hydrodynamics has been
pointed out to boost the onset of neutrino-driven explosions compared to 2D
\citep{nordhaus10}, although it
 is still under considerable debate \citep{hanke,hanke13,Takiwaki11,couch12}.
Very recently, general relativity has been reported
to help the onset of multi-D neutrino-driven explosions by
 \citet{bernhard11,bernhard12b} in 2D simulations with detailed neutrino transport and by
\citet{kuroda12,kuroda13} in 3D simulations but with approximate neutrino transport.
Impacts of nuclear equations of state (EOSes) have been
investigated in multi-D simulations by \citet{Marek09,marek09b,suwa12} and  \citet{couch13}.
However, there
may still remain further room to study more detailed nuclear physical
impacts in these first principle multi-D simulations, such as the
density dependence of symmetry energy and the skewness of compressibility
\citep{steiner,lattimer12} and influences of light nuclei
\citep[e.g.,][]{sumi08,arcones,nakamura}
and of inelastic neutrino-nucleus scattering
\citep[e.g.,][]{haxton,ohnishi07,langanke08}
on enhancing the neutrino heating rates in the gain region.
More recently, impacts of improved neutrino interactions based on
 the 1D full Boltzmann simulations have been elaborately investigated
 \citep{lentz11, lentz12}.
The neutrino-driven mechanism would be assisted by
other candidate mechanisms such as the acoustic mechanism
\citep[e.g.,][]{burr06}
or the magnetohydrodynamic mechanism (e.g.,
\citet{kota04a,kota04b,taki04,taki09,burr07,fogli_B,martin11,taki_kota},
see also \citet{kota06} for collective references therein).
Other possibilities include QCD phase transitions
in the core of the protoneutron star
\citep[e.g.,][]{takahara88,sage09}
viscous heating by the
magnetorotational instability \citep{thomp05},
or energy
dissipation via Alfv\'en waves \citep{suzu08}.

Joining in these efforts to look for some possible ingredients to
foster explosions,
we pay attention to the roles of nuclear burning in this study.
To the best of our knowledge, \citet{janka01a} were
the first to clearly point out
that an additional energy released by nuclear burning of
infalling material behind the shock could make a significant
contribution to affect the explosion  energy (see their Eq.(5)).
The mass in the silicon (Si) layer, depending sensitively on the
progenitor masses and structures, is in the range of
$\sim 0.3 - 0.6 M_{\sun}$ \citep{WW95,woos02,limongi}.
Since the release of nuclear energy
in Si burning is $\approx 10^{18}~{\rm erg \, g}^{-1}$,
a few $10^{50}$ erg are expected to be
deposited by the explosive nuclear burning.
It should be noted that nuclear burning
has been included in the full-scale simulations by the Garching group
 \citep{rampp02,Buras06a,
Buras06b,Marek09}, in which composition changes of silicon, oxygen
(and similarly neon and magnesium), and carbon
and their nuclear energy release are computed by a ``flashing" treatment
 \citep[see Appendix \ref{app-flash}, and also Appendix B.2 in ][]{rampp02}. In a series of
 multi-D simulations in which neutrino transport is treated by a
 more approximative way to follow a long-term postbounce
evolution in the context
 of the neutrino-driven mechanism, nuclear burning
 is included by a small network calculation \citep[e.g.,][]{kifo,scheck06,annop,hammer,arcones_2011,ugliano}.
However in
these literatures, impacts of nuclear
burning on the supernova dynamics have not been unambiguously
investigated so far.
 In conference proceedings, the Oak Ridge group reported
2D explosion models based on their radiation-hydrodynamic simulations
\citep{bruenn06,mezza07} for 11.2$~M_{\odot} $ and 15.0$~M_{\odot} $ stars,
only when an alpha network calculation was included, but not when
they applied the flashing treatment.
They pointed out that oxygen burning
 assists the (weak) shock
to move farther out due to the additional pressure support
in the vicinity of the weak shock. These situations motivate
us to revisit the impacts of nuclear burning on assisting
the shock propagation by performing hydrodynamic simulations
including a network calculation.

 In the present work, we take the following strategy to clearly
see the roles of nuclear burning. Firstly
we try, in the spirit of
\citet{burogoshy} and \citet{Janka01},
to find a critical condition in 1D, in which nuclear burning affects
the criteria of explosion. Instead of performing full-scale
radiation-hydrodynamic simulations which are computationally expensive,
we employ a light-bulb scheme to trigger explosions
\citep[e.g.,][]{Janka96} for the sake of our systematic
survey.
Previously the role of nuclear burning seems to be considered as
negligible using a very limited set of progenitor models
but we will show that for a previously untested progenitor model, nuclear burning
can really push the weak shock farther out to help explosions.

This paper opens with the description of numerical setup including
 information about our hydrodynamic code with nuclear network and
about initial models (Section 2). Results are given in section 3.
After giving a detailed explanation in 1D models
how nuclear burning could affect the postbounce dynamics
(section \ref{sec-1d}, \ref{sec-prog}),
we move on to discuss our 2D models to study how nuclear burning
interacts with multi-D hydrodynamics (section \ref{sec-2d}).
We summarize our results and discuss their implications in Section 4.

\section{Numerical Setup}

\subsection{Hydrodynamics with Nuclear Network}
We solve the hydrodynamic equations corresponding to the conservation of mass,
momentum, and energy,
\begin{equation}\label{eq-mass}
\frac{d \rho}{d t} + \rho \nabla \cdot \mathbf{v} = 0,
\end{equation}
\begin{equation}\label{eq-momentum}
\rho \frac{d \mathbf{v}}{d t} = - \nabla p - \rho \nabla \Phi,
\end{equation}
\begin{equation}\label{eq-energy}
\frac{\partial e}{\partial t} + \nabla \cdot \left[ (e+p)\mathbf{v} \right] = - p \mathbf{v} \cdot \nabla \Phi + \rho (H - C + Q),
\end{equation}
where $\rho$ is the mass density, $\mathbf{v}$ the fluid velocity, $p$ the pressure,
$\Phi$ the gravitational potential, and $e$ the total energy density, respectively.
The Lagrangian derivative is denoted by $d/dt \equiv \partial / \partial t + \mbox{\boldmath$v$} \cdot \nabla$. To treat Newtonian self-gravity, a monopole approximation is employed. The tabulated realistic equation of state based on the relativistic mean field theory \citep{Shen98} is
implemented according to the prescription in \citet{kotake}.
The term $Q$ in Eq. (\ref{eq-energy}) denotes the net energy deposition rate by nuclear burning.
The goal of this paper is to explore the effect of this term on shock revival. We compare two cases:
(a) For {\it burning} case, we estimate $Q$ by calculating a simple nuclear reaction network, and
(b) for {\it non-burning} case,
we do not solve the nuclear network ($Q=0$) but adopt Shen EOS throughout simulations.

For {\it burning} case we are keeping track of 13 species of $\alpha$ network
(from $^4$He to $^{56}$Ni) by solving a separate advection equation for each species.
The nuclear reaction network is mainly based on the REACLIB database \citep{rauscher00}.
Experimentally determined masses \citep{audi} and reactions \citep{angulo} are adopted
if available. It should be noted that our network does not include the
photodissociation of iron elements because Shen EOS adopted in this study
takes account of these endothermic effects.
Note also that we solve the reaction network only for the grids
where $T<5 \times 10^9$ K, assuming that above this temperature
the local chemical composition is in nuclear statistical
equilibrium (NSE).

In this study, we employ the so-called light-bulb scheme \citep{Janka96},
in which neutrino heating and cooling is adjusted parametrically to trigger explosions.
Following \citet{Janka01} and \citet{nordhaus10},
the neutrino heating ($H$) and cooling rates ($C$)
in Eq. (\ref{eq-energy})
are given by,
\begin{equation}\label{eq-heating}
\begin{split}
H = 1.544 \times 10^{20}
& \left( \frac{L_{\nu_{\rm e}}}{10^{52} \, {\rm erg \, s^{-1}}}\right) \left( \frac{T_{\nu_{\rm e}}}{4 \, {\rm MeV}} \right)^2 \\
& \times  \left( \frac{r}{100 \, {\rm km}} \right)^{-2} (Y_{\rm n} + Y_{\rm p}) \, e^{-\tau_{\nu_{\rm e}}}~[{\rm erg}~{\rm g}^{-1}~{\rm s}^{-1}],
\end{split}
\end{equation}
\begin{equation}\label{eq-cooling}
C = 1.399 \times 10^{20} \left( \frac{T}{2 \, {\rm MeV}} \right)^6 (Y_{\rm n} + Y_{\rm p}) \, e^{-\tau_{\nu_{\rm e}}}, [{\rm erg}~{\rm g}^{-1}~{\rm s}^{-1}],
\end{equation}
where $L_{\nu_{\rm e}}$ is the electron-neutrino luminosity that is
assumed to be equal to the anti-electron neutrino luminosity
($L_{\bar{\nu}_{\rm e}} = L_{\nu_{\rm e}}$), $T_{\nu_{\rm e}}$ is
the electron neutrino temperature assumed to be kept constant as $4$ MeV, $r$
is the distance from the center, $T$ is the local fluid temperature, $Y_n$ and $Y_p$
are the neutron and proton fractions, and $\tau_{\nu_e}$ is the electron neutrino
optical depth that we estimate according to Eq. (7) in \citet{hanke}.

Note in this study that neutrino luminosity is assumed to evolve
exponentially with time \citep{kifo}
as
\begin{equation}
L_{\nu_{\rm e}} = L_{\bar{\nu}_{\rm e}} = L_{\nu0} \, {\rm exp}
(- t_{\rm pb}
/t_{d}),
\label{nuL}
\end{equation}
where $L_{\nu0}$ denotes the initial luminosity,
$t_{\rm pb}$ is the time measured after core bounce
$t_{d}$ is the decay time, respectively.
$L_{\nu0}$ and $t_{d}$ are treated as free parameters. Note that
neutrino heating
and cooling are switched on only after core bounce.

Only after core bounce, neutrino heating and cooling is switched on,
according to the prescriptions (Equations (\ref{eq-heating}) and
(\ref{eq-cooling}))
assuming $L_{\nu_{\rm e}} = L_{\bar{\nu}_{\rm e}}$ and $T_{\nu_{\rm e}} = T_{\bar{\nu}_{\rm e}}$. Before bounce, we employ the $Y_e$
prescription proposed by \citet{simple}, in which $Y_e$ is given simply
as a function of density, and after that, we
refrain from solving the change of $Y_e$ following
\citet{Murphy08,nordhaus10} and \citet{hanke}
(see, however, \citet{Ohnishi06}). As for the hydro-solver,
we employ the ZEUS-MP code \citep{hayes} which has been modified for
core-collapse simulations \citep[e.g.,][]{iwakami1,iwakami2}.
The computational grid is comprised of 300 logarithmically spaced, radial zones
from the center up to 5000 km.
For 2D models we adopt coarse mesh points ($n_{\theta} = 32$ uniform grids) in the polar direction to make it possible to perform 174 models
 in 2D covering a wide range of the parameter region. For some selected
models, a finer resolution ($n_{\theta} = 128$) is taken.

In order to induce non-spherical instability after the stall of the prompt
bounce shock,
we have added a radial velocity perturbation, $\delta v_r(r, \theta, \phi)$, to
the steady spherically symmetric flow according to the following equation,
\begin{equation}
v_r(r, \theta, \phi) = v_r^{0}(r) +\delta v_r(\theta, \phi),
\end{equation}
with
\begin{equation}
\delta v_r = 0.01 \times {\rm rnum} \times \, v_r^0 (r,\theta) \, ,
\end{equation}
where $v_r^0 (r,\theta)$ is the unperturbed radial velocity and $\delta v_r$ is the random multi-mode perturbation with a random number $-1 < {\rm rnum} < 1$.

\begin{figure}[htpb]
\begin{center}
\includegraphics[scale=0.6]{Figure1a.eps}
\includegraphics[scale=0.6]{Figure1b.eps}
\includegraphics[scale=0.6]{Figure1c.eps}
\includegraphics[scale=0.6]{Figure1d.eps}
\end{center}
\caption{Precollapse composition distributions for the 15 $M_{\sun}$ stars
of \citet{limongi} (labeled by LC15, {\it top left}),
\citet{WW95} (WW15, {\it bottom left}), and
\citet{woos02} (WHW15, {\it top right}) and for the $11.2 ~M_{\odot} $ star
of \citet{woos02} (WHW11, {\it bottom right}).}
\label{fig-pmodel}
\end{figure}

\subsection{Progenitor models}
In this study, we employ four progenitor models;
three for $15.0 ~M_{\odot} $ stars of
\citet[][hereafter LC15]{limongi}, \citet[][WW15]{WW95},
and  \citet[][WHW15]{woos02} and one for an $11.2 ~M_{\odot} $ star of
\citet[][WHW11]{woos02}.
For all the models, Figure \ref{fig-pmodel}
shows the precollapse composition profiles near from the outer edge of
the iron core to outside. As we will
explain in the next section, burning of the oxygen shell behind
the (weakly propagating) shock plays an important
role in assisting the shock expansion.
Therefore, the earlier the oxygen layer touches the (stalling)
shock after bounce, the better it could work.
Among the three variants of the
15 $M_{\odot}$ progenitors, the inner edge of the oxygen layer
(seen as a sharp decline in solid red lines of Figure \ref{fig-pmodel})
is positioned much closer to the center for models LC15 (closest, top
left panel) and WHW15 (next closest,
top right panel) compared to model WW15 (bottom left panel).
Table 1 shows a summary of the precollapse abundance distributions,
 in which each quantity from the left to right column corresponds to
 the different progenitor models, the progenitor
mass, the mass of the iron core,
 the outer edge of the iron core, the mass of the
  silicon layer, the outer edge of the silicon layer, and the mass of
the oxygen layer, respectively.
The edge between each layer is defined as the radius where the most abundant element shifts to one another (see, Figure \ref{fig-pmodel}).
The mass of oxygen layer for the 15
$M_{\odot}$ models of LC15 and WHW15 ($M_{O}$ in the table) is larger
than the other progenitors (i.e., WW15 and WHW11) and their oxygen layers
(denoted by $R_{{\rm Si}/{\rm O}}$) are positioned much
closer to the center, so that they can touch the supernova shock
in a shorter timescale after bounce
(before the neutrino luminosity gets smaller with time).
As one would anticipate, the impacts of nuclear burning are most
remarkable for the LC15 progenitor as we will show in the later sections.

\begin{table}[htbp]
\caption{Summary of progenitor models and their composition features
(see
 text for the definition of each quantity).}
\begin{tabular}{ccccccl}
\hline
Model & $M_{\rm total}$   & $M_{\rm Fe}$ & $R_{\rm Fe/Si}$ & $M_{\rm Si}$ & $R_{\rm Si/O}$ & $M_{\rm O}$\\
          & $(~M_{\odot} )$           & $(~M_{\odot} )$       & $(10^3 \,{\rm km})$ & $(~M_{\odot} )$& $(10^3 \,{\rm km})$ & $(~M_{\odot} )$\\
\hline
LC15     & 13.4                   & 1.44              & 1.31                    & 0.221         & 2.22               & 0.814 \\
WHW15 & 12.6                  & 1.55               & 1.96                    & 0.124            & 2.97                & 0.943   \\
WW15 & 15.0                    & 1.42                & 1.31                   & 0.436           & 7.44                & 0.649 \\
WHW11& 10.8                  & 1.24                & 1.00                   & 0.168             & 3.74                & 0.289    \\
\hline
\\
\\
\end{tabular}
\label{tbl-model}
\end{table}

\clearpage
\section{Results}

\begin{figure}[htpb]
\begin{center}
\includegraphics[scale=0.4]{Figure2.eps}
\end{center}
\caption{Time evolution of the shock radii for model LC15
with different initial neutrino luminosities ($L_{\nu0, 52}$ in unit of
 $10^{52}$ erg s$^{-1}$) and the decay time
 ($t_d$ in unit of s). The red and blue line corresponds to the
 results with
  and
  without the energy feedback from nuclear
reactions, respectively.}
\label{fig-rsh1d}
\end{figure}

In section 3.1, we start to investigate how the energy feedback from
nuclear burning could affect the postbounce dynamics in 1D simulations.
 Then we study how the nuclear-burning impacts are sensitive to the progenitor models,
namely by the precollapse structures and their composition profiles
   (section 3.2). In section 3.3, we then move on to discuss how
nuclear burning would affect the 2D dynamics.

\subsection{Impact of Nuclear Burning in 1D simulations}\label{sec-1d}

Relying on the light-bulb scheme in this study, the destiny of the
stalling bounce shock (whether it will revive or not) depends simply
on the two parameters; the input neutrino
luminosity $L_{\nu0}$ and the decay time $t_{d}$
(see Equation (\ref{nuL}))\footnote{Without seeing a shock revival in $\sim$ 1 s
postbounce, we call it as ''non-exploding'' in this study}. Note in the
following that we characterize models as ($L_{\nu0,52}, t_{d}) = (x, y)$ for
convenience, in which the luminosity and the decay time is $x \times
10^{52}$ (erg/s) and $y$ (s), respectively.

Figure \ref{fig-rsh1d} shows comparisons of the postbounce shock evolution in 1D LC15 models
depending on the two parameters ($L_{\nu0,52}, t_{d}$)
and nuclear energy feedback from $\alpha$ network calculation.
Chosen three sets of parameters: ($L_{\nu0,52}, t_{d}$) = (2.2, 5.0), (2.0, 5.0), and (2.2, 2.0),
are shown as a solid line, a dotted line, and a dash-dotted line, respectively.
All of the models with nuclear burning, marked with red lines in Figure \ref{fig-rsh1d},
present a shock expansion leading to explosions, while among three models without nuclear burning
(blue lines) only the model with relatively higher luminosity and longer decay time
(($L_{\nu0,52}$, $t_d$) = (2.2, 5.0), solid blue line) exhibits a shock revival.
Note that in all the six cases
in Figure \ref{fig-rsh1d}, the bounce shock
stalls and then transits to a passive shock
which presents negative radial velocity behind the shock.
And only after that, the additional energy gain due to
nuclear burning acts to bifurcate the path of the passive shock, namely
whether the shock experiences recession afterward
(for all the blue lines in Figure \ref{fig-rsh1d}) or expansion (for red lines)
with different revival timescales depending on the input neutrino
parameters.

As seen from Figure \ref{fig-rsh1d}, larger input neutrino luminosity and shorter
decay timescale unsurprisingly leads to easier explosions.
More importantly, by comparing dotted red with dotted blue line
(($L_{\nu0,52}$, $t_d$)
= (2.0, 5.0)), the shock is shown to shift from recession to
expansion by the inclusion of nuclear burning.
In the case of higher neutrino luminosity ($L_{\nu0,52}$ = 2.2),
the trajectories of the shock are observed to be rather similar when the effect of nuclear burning is taken into account
(compare solid red with dashed red line).

In the following, we elaborate on how and why the
shock expansion is affected by nuclear burning as observed in Figure \ref{fig-rsh1d}.
Figure \ref{mshell-m15-2220} and \ref{mshell-m15-2050} show
the
mass-shell trajectory of models LC15 with the different parameter set of
$(L_{\nu 0,52}, t_{d}) = (2.2, 2.0)$ and $(L_{\nu 0, 52}, t_{d}) = (2.0, 5.0)$, respectively.
Note here that the former and latter case corresponds to the dashed and
dotted line in Figure \ref{fig-rsh1d}. Without nuclear burning
(left panels in Figure \ref{mshell-m15-2220} and \ref{mshell-m15-2050}),
the stalled shock oscillates, but
does not turn into expansion (see also Figure \ref{fig-rsh1d}).
With nuclear burning,
right panels of Figures \ref{mshell-m15-2220} and \ref{mshell-m15-2050},
the shock expansion can be seen to take place
when
the shock front passes through
the Si-rich layer (see the behavior of the thick red line in the
green region in
the right panel of Figure \ref{mshell-m15-2220})
or later it touches the O-rich layer (e,g., the shock in the red
region in the right panel of Figure
\ref{mshell-m15-2050}). For the latter case, the bounce shock firstly stalls as
in the non-burning model (compare the left with the right panel in
Figure \ref{mshell-m15-2050}), but then the shock front
deviates from
the non-burning case when it encounters with the
O-rich layer.

\begin{figure}[htbp]
\begin{center}
   \begin{tabular}{cc}
\resizebox{75mm}{!}{\includegraphics{Figure3a.eps}} &
\resizebox{75mm}{!}{\includegraphics{Figure3b.eps}}  \\
   \end{tabular}
\end{center}
\caption{Evolution of model LC15
with a parameter set of $(L_{\nu 0,52}, t_{d}) = (2.2, 2.0)$ visualized by the mass-shell
trajectories. The thick red line starting at $t=0$ denotes the position
of the shock.  Both cases either without ({\it left}) or with
({\it right}) the energy feedback from nuclear reactions are shown.
The regions colored by gray, green, and red correspond to
 the iron, silicon, and oxygen layers, respectively.
Thick gray lines correspond to the mass coordinates from 1.3 to 1.8$~M_{\odot} $ with every 0.1 $M_{\odot}$
(thin gray lines with every $0.02 M_{\odot}$).}
\label{mshell-m15-2220}
\end{figure}

\begin{figure}[htbp]
\begin{center}
   \begin{tabular}{cc}
\resizebox{75mm}{!}{\includegraphics{Figure4a.eps}} &
\resizebox{75mm}{!}{\includegraphics{Figure4b.eps}}  \\
   \end{tabular}
\end{center}
\caption{Same as Figure \ref{mshell-m15-2220} but for
the parameter set of $(L_{\nu 0,52}, t_d) = (2.0, 5.0)$.}
\label{mshell-m15-2050}
\end{figure}

\clearpage
To look more in detail how the nuclear burning contributes to the shock
acceleration, Figure \ref{snap1dm15_2220} shows the radial velocity profiles and the
composition distributions for model LC15 with the parameter set
$(L_{\nu 0,52}, t_{d}) = (2.2, 2.0)$ (the same parameter set as in Figure \ref{mshell-m15-2220}).
At $t_{\rm pb} = 150$ ms (top left panel), the shock front
is in the progenitor silicon-rich layer.
Behind the shock front,
heavier elements are synthesized as shown.
The nuclear energy released by silicon burning
heats the material behind the shock,
making it have a small positive velocity there
(compare the velocity profiles with and without nuclear burning in the top left panel).
The difference between the velocity profiles with versus without nuclear
burning becomes outstanding when
the oxygen-rich layer starts to touch the shock front ($t_{\rm pb} > 250$ ms).
Figure \ref{eex1d_m15_2220} shows the evolution of
the {\it diagnostic} (explosion) energy
for burning (red line) and non-burning (blue line) cases
and also the net energy released via nuclear reactions (green
line). As in \citet{Suwa10}, we define a {\it diagnostic} energy
that refers to the integral of the energy over all zones that
have a positive sum of the specific internal, kinetic, and gravitational energy.
It is impossible to calculate the final energy of the explosion that is still occurring at this early post-bounce stage.
After silicon burning starts to feed energy behind the
shock in addition to
neutrino heating (in the gain region, e.g., $t_{\rm pb}
= 150 $ ms, see the top left panel in Figure \ref{snap1dm15_2220}),
the diagnostic energy deviates from the one without burning
(compare red with blue line
in Figure \ref{eex1d_m15_2220}),
which is also clearly visible in the shock evolution
(Figure \ref{mshell-m15-2220}).
From
Figure \ref{eex1d_m15_2220}, the total amount of $3.1 \times 10^{50}$ erg
is shown to be released through nuclear burning in this case,
lifting up the diagnostic energy to be $5.0 \times 10^{50}$ erg.

\begin{figure}[htbp]
\begin{center}
\includegraphics[scale=0.7]{Figure5.eps}
\end{center}
\caption{Snapshots of velocity profile ({\it top}) and composition
distribution ({\it bottom}) for model LC15 with
$(L_{\nu 0,52}, t_d) = (2.2, 2.0)$
at selected postbounce epochs ($t_{\rm pb} =
150, 250, 350,$ and $400$ ms). Solid and dotted line
in the top of each panel shows the velocity profile with or without
nuclear burning, respectively. In the bottom part, distributions of
representative elements of the burning model are shown.
Note that the abundances of neutron
(n) and proton (p) are estimated from Shen EOS and the others are
calculated from the nuclear network calculation.
Nucleon-rich region in the abundance plot is separated by a vertical dashed line.
}
\label{snap1dm15_2220}
\end{figure}

\begin{figure}[htbp]
\includegraphics{Figure6.eps}
\caption{
Time evolution of diagnostic energy is shown for the same model as Figure \ref{snap1dm15_2220}.
The green line is the energy released by
nuclear burning and the diagnostic energy without nuclear
burning ({\it blue}) is also shown. Here the diagnostic energy is
defined as the sum of the kinetic,
thermal, and gravitational energy of fluid elements with positive radial velocity.}
\label{eex1d_m15_2220}
\end{figure}

As we already mentioned, oxygen burning predominantly
triggers the shock
expansion for the parameter set taken for Figure \ref{mshell-m15-2050}. But also in this case, the silicon layer is shown to be burned as a heating source
(top left panel of Figure \ref{snap1dm15_2050}),
which is the reason that the shock position becomes larger
compared to the non-burning model
(Figure \ref{mshell-m15-2050}).
When the shock front begins to swallow the oxygen layer
at $\sim 400$ ms postbounce
(the right panel of Figure \ref{mshell-m15-2050}),
the fresh fuel supplies energy to assist the shock expansion
(see, from top right, bottom left, to bottom right panels of Figure \ref{snap1dm15_2050}).
If not for the energy gain,
the stalled shock does not revive earlier than $t=750$ ms
as seen from
the left panel of Figure \ref{mshell-m15-2050}.
Even with the aid of nuclear burning, the explosion for this model
(Figure \ref{eex1d_m15_2050})
is weaker ($\lesssim 10^{50}$ erg) compared to the more luminous models
(Figures \ref{eex1d_m15_2220} and \ref{eex1d_m15_2250}).
This suggests that nuclear burning has a secondary impact on the
explosion mechanism
--- it can assist explosions only when neutrino heating is working enough
strong to push the weak shock to the fuel layers.

\begin{figure}[htbp]
\begin{center}
\includegraphics[scale=0.8]{Figure7.eps}
\end{center}
\caption{Same as Figure \ref{snap1dm15_2220} but for the parameter set of
$(L_{\nu 0,52}, t_d) = (2.0, 5.0)$.}
\label{snap1dm15_2050}
\end{figure}

\begin{figure}[htbp]
\includegraphics{Figure8.eps}
\caption{Same as Figure \ref{eex1d_m15_2220} but for the parameter set of
$(L_{\nu 0,52}, t_d) = (2.0, 5.0)$.}
\label{eex1d_m15_2050}
\end{figure}

\begin{figure}[htbp]
\includegraphics{Figure9.eps}
\caption{Same as Figure \ref{eex1d_m15_2220} but
for the most energetic case, ($L_{\nu 0,52}, t_d) = (2.2, 5.0$),
among the three examples shown
in Figure \ref{fig-rsh1d}. The diagnostic energy with nuclear burning is
about $ 8.0 \times
10^{50}$ ergs at $t_{\rm pb} = 465$ ms and still keeps rising.
The net energy released via nuclear reactions at this time is
$\sim 3.0 \times 10^{50}$ erg, occupying a significant fraction ($\sim$
40\%) of the diagnostic energy. For the model without nuclear burning,
the diagnostic energy is $\sim 0.8 \times 10^{50}$ erg at that time
and closely saturates to be $E_{\rm dia} \sim 2.3 \times 10^{50}$ erg
afterward.}
\label{eex1d_m15_2250}
\end{figure}

\clearpage

\subsection{Progenitor Dependence}\label{sec-prog}

\begin{figure}[htpb]
\begin{center}
\includegraphics[scale=0.8]{Figure10.eps}
\end{center}
\caption{Parameter maps of the initial neutrino luminosity $L_{\nu0,52}$
and its decay time $t_d$ that separates the non-exploding regime
(blue region) from the exploding one (red region) in 1D
simulations for the four different progenitors. A horizontal yellow
region in-between (clearly visible for the LC15 progenitor;{\it top left})
 shows the parameter region in which 1D explosions are obtained when
the network calculation is performed. }
\label{fig-para1d}
\end{figure}

Figure \ref{fig-para1d} shows a parameter map on the ($L_{\nu0,52}$, $t_d$)
plane for each progenitor. As can be seen, higher neutrino luminosity
and/or longer decay time leads to easier explosions
 (colored by red and denoted as "Explosion"), while is simply opposite
for smaller neutrino luminosity and/or shorter decay time
(colored by light-blue and denoted as "No explosion" in the figure).
For the LC15 progenitor model (top left panel),
 a parameter region colored by yellow can be seen between the
exploding and the non-exploding regime, in which
 an explosion is obtained only when nuclear burning is included
in the hydrodynamics simulations. The emergence of the yellow region
means that the minimum neutrino luminosity necessary to drive an
explosion is reduced by taking into account energy feedback form
nuclear burning.
The burning-mediated regime is clearly visible only for the LC15
progenitor. As already mentioned in section 2.2, this is because
 this model possesses a massive oxygen layer
and the oxygen shell is
positioned closest to the center among the progenitors taken in this study.

The area of the yellow region in Figure \ref{fig-para1d} is not so large even for the LC15 progenitor,
which suggests again that nuclear burning has a secondary importance.
In the case of energetic explosions, for example ($L_{\nu0,52}, t_d$) = (3.0, 0.8),
a difference of diagnostic energy between models with and without nuclear burning is
$\sim 5 \times 10^{49}$ erg (Table \ref{tbl-result}).
In the case of marginal weak explosions with $E_{\rm dia} \lesssim 10^{50}$ erg (which is often the case in recent first-principle CCSN simulations), however,
it should be emphasized that the inclusion of nuclear burning could
 increase the diagnostic energy up to about $\sim 0.6 \times 10^{51}$ erg.

\begin{figure}[htpb]
\begin{center}
\includegraphics[scale=0.8]{Figure11.eps}
\end{center}
\caption{
Time evolution of the mass accretion rates, evaluated at $R=500$ km for 4 non-exploding models.
}
\label{fig-macc}
\end{figure}

The critical luminosity for explosions can be read from the $y$-axis in
Figure \ref{fig-para1d} in the limit of long $t_d$ (namely, approaching to a constant neutrino
 luminosity), which corresponds to $2.7$ (WHW15), $2.0$ (LC15),
$1.9$ (WW15), and $1.2$ (WHW11) in unit of $10^{52}$ erg/s,
 respectively.
The WHW15 model shows the highest critical neutrino luminosity
among our models. This is because of the higher mass accretion
rate of the WHW15 model (blue solid line in Figure \ref{fig-macc}), which makes
 the impact of nuclear burning relatively smaller.
The critical luminosity becomes smallest for model WHW11,
mainly owing to a compactness of the precollapse core
and small mass accretion rate coming from its tenuous envelope
as shown in a blue dotted line in Figure \ref{fig-macc}.
The mass accretion rate averaged between 200 ms and 600 ms after bounce
for each model is
0.33 (WHW15), 0.23 (LC15), 0.21 (WW15), and 0.08 $~M_{\odot} ~{\rm s}^{-1}$ (WHW11), respectively,
which is roughly proportional to the critical luminosity except for
the WHW11 progenitor model.
When the input luminosity is taken below the critical curves,
nuclear burning cannot alone drive explosions
because the shock needs to expand far away from the central protoneutron star
firstly by neutrino heating
(i.e., the shock revival due to neutrino heating is
 preconditioned to enjoy the assistance from nuclear burning).

\begin{figure}[htb]
\begin{center}
\includegraphics[scale=1.2]{Figure12.eps}
\caption{
Diagnostic energy as a function of initial neutrino luminosity $L_{\nu0,52}$.
The shaded area shows energy difference between models with ({\it open circles}) and without nuclear burning ({\it crosses}) for some selected $t_{\rm d}$ sequences.
{\it left}: The case of LC 15 progenitor. It can be seen that energy difference
tends to be large for less energetic models.
{\it right}: The case of WW15 progenitor. The energy difference is small
even for less energetic models.
}
\label{fig-eddif}
\end{center}
\end{figure}

In Table  \ref{tbl-result} time of explosion, $t_{\rm exp}$, and diagnostic energy, $E_{\rm dia}$, are listed for some chosen sets of the neutrino parameters.
The time of explosion is defined as the moment when a shock reaches an average radius of 4500 km, while non-exploding models are denoted by a ``---'' symbol.
The diagnostic energy is plotted as a function of neutrino luminosity
for a various decay time scales in Figure \ref{fig-eddif}.
In fact, the diagnostic energy is shown to be remarkably enhanced in the case of marginal explosions (i.e., low neutrino luminosity $L_{\nu, 0}$ and/or short decay time $t_{d}$),
and the difference gets small for large $L_{\nu, 0}$ and $t_{d}$, in which explosions are predominantly triggered by neutrino heating. As repeatedly mentioned so far, these features due to nuclear burning are only remarkable in the LC15 progenitor. Nevertheless, it is worth mentioning that
the shock extent even for the WW95 progenitor, for which
 the impact of nuclear burning is relatively small
(see the bottom left panel of Figure \ref{fig-para1d}), becomes bigger for models with nuclear burning compared to those without (Figure \ref{rsh1d_w15}).

\begin{figure}[htbp]
\begin{center}
\includegraphics[scale=0.8]{Figure13.eps}
\end{center}
\caption{Time evolution of the shock radii for several 1D models employing the WW15
progenitor. The shock moves farther out for models including nuclear
burning
(red lines) compared to those without (blue).}
\label{rsh1d_w15}
\end{figure}

\clearpage

\subsection{2D Results}\label{sec-2d}
\begin{figure}[htpb]
\begin{center}
\includegraphics[scale=0.8]{Figure14.eps}
\end{center}
\caption{
2D distributions of entropy and silicon of LC15 model ($n_{\theta} = 128$).
Entropy in unit of $k_{\rm B}$ baryon$^{-1}$ is in the left-half sphere
and silicon mass fraction in the right-half.
Shown is the case of ($L_{\nu0,52}, t_d) = (2.4, 1.1)$ at $t_{\rm pb}$ = 100 ({\it left panel}) and 200 ms ({\it right}) postbounce, respectively.
}
\label{fig-snap2d-1}
\end{figure}

\begin{figure}
\begin{center}
\includegraphics[scale=0.8]{Figure15.eps}
\end{center}
\caption{Same as Figure \ref{fig-snap2d-1}
but of a 2D model with $(L_{\nu0,52}, t_d)  = (2.2, 1.1)$.}
\label{fig-snap2d-2}
\end{figure}

\begin{figure}[htpb]
\begin{center}
\includegraphics[scale=0.8]{Figure16.eps}
\end{center}
\caption{Time evolution of the diagnostic energy ({\it red line})
and net nuclear burning energy ({\it green}) for LC15 model in 2D ($n_{\theta} = 32$)
with $(L_{\nu 0,52}, t_d) = (2.4, 3.0)$.
The diagnostic energy of the case without nuclear burning ({\it blue}) is also shown.
}
\label{fig-eex2d}
\end{figure}

We move on to discuss axi-symmetric 2D models
and examine the effects of nuclear burning
in the same manner as in the previous section.
To see clearly the impacts of nuclear burning in our 2D simulations, we
choose to employ the LC15 in the following.

Figures \ref{fig-snap2d-1} and \ref{fig-snap2d-2} show entropy evolution
(left-hand-side in each panel) with the mass fraction of silicon (right-hand-side)
 for two sets of neutrino parameters
at selected postbounce epochs ($t_{\rm pb} = $100 and 200 ms postbounce).
Small- and large-scale
inhomogeneities in the entropy plots come from neutrino-driven
convection and
the SASI, both of which lead to more easier explosions in 2D than 1D
\citep[e.g.,][]{Marek09,Murphy08,Ohnishi06}.

Reflecting the stochastic motions of the expanding shocks, the way
how the (anisotropic) shock surfaces touch the nuclear fuel (in the
shape of spherical shells) changes from model to model in 2D.
In the case with $L_{\nu0,52}=2.4$ (Figure \ref{fig-snap2d-1}), the expanding
shock firstly reaches to the silicon layer near in the vicinity of the north pole
at $t_{\rm} \sim 150$ ms. Simultaneously, heavy elements like nickel
are synthesized there, which helps to
push the burning material preferentially along the direction for the moment.
In a less luminous case assuming smaller luminosity ($L_{\nu0,52}=2.2$), and the same decay time (Figure \ref{fig-snap2d-2}), the shock encounters the silicon layer closer to the center, where a mass accretion rate is effectively higher, resulting in the longer explosion time.

As shown from Figure \ref{fig-eex2d}, nuclear burning
does assist 2D explosions similar to 1D, but
 the energy difference (here $\sim 0.2 \times 10^{51}$ erg)
is generally smaller in 2D than in 1D
(compare with Figures \ref{eex1d_m15_2220}, and \ref{eex1d_m15_2250}).
The comparison of the energy gain due to nuclear burning
between 1D and 2D models is more clearly shown in
Table \ref{tbl-result} and Figure \ref{fig-eddif2d}.
The difference of the diagnostic energy with and without nuclear burning
is larger in 1D than that in 2D.
This may be because neutrino-driven convection and the SASI in 2D models (as
indicated by entropy distributions in Figures \ref{fig-snap2d-1} and \ref{fig-snap2d-2})
enhances
the neutrino heating efficiency,
which makes the contribution of nuclear burning relatively
smaller compare to 1D models.

Finally Figure \ref{fig-para2d} is the parameter map in 2D
for the LC15 progenitor.
As expected, 2D hydrodynamics leads to more easier explosions
compared to 1D (see the dashed lines which are the critical curves in 1D).
More importantly, the yellow region still exists in 2D models
for the LC15 progenitor.
Nuclear energy released in 2D models reduces the critical luminosity
by $0.1-0.5 \times 10^{52} {\rm erg~s^{-1}}$ depending on $t_{\rm d}$,
as well as 1D models,
although its impact on the diagnostic energy is weaker than for 1D models.
It would be interesting to perform multi-D (radiation-hydro)
simulations with
nuclear network calculation for the previously untested progenitor model.

\begin{figure}[htpb]
\begin{center}
\includegraphics{Figure17.eps}
\end{center}
\caption{
Same as Figure \ref{fig-eddif} but
for LC15 model in 2D ($n_{\theta} = 32$).
}
\label{fig-eddif2d}
\end{figure}

\begin{figure}[htpb]
\begin{center}
\includegraphics[scale=0.7]{Figure18.eps}
\end{center}
\caption{Same as Figure \ref{fig-para1d} but for 2D simulations. The
dashed lines represent the critical curves in 1D (compare Figure \ref{fig-para1d}).
 Note that we adopt coarse mesh points in the polar direction (32 uniform grids), so that we can perform 2D simulations for 174 models in total to make this parameter map.
}
\label{fig-para2d}
\end{figure}

\section{Conclusions}

We revisited the potential impacts of nuclear burning on
the onset of neutrino-driven explosions of core-collapse supernovae.
By changing the neutrino luminosity and its decay time
to obtain parametric explosions
in 1D and 2D models with or without a 13-isotope $\alpha$ network,
we studied how
the inclusion of nuclear burning could affect
 the postbounce dynamics for four progenitor models; three for $15.0
 ~M_{\odot} $ stars of
 \citet{limongi}, \citet{WW95}, and \citet{woos02},
 and one for an $11.2 ~M_{\odot} $ star of \citet{woos02}
 Our results showed that the energy gain due to nuclear burning of
infalling material behind the shock can energize the
shock expansion especially for models that produce only marginal explosions
 in the absence of nuclear burning. These models enjoy
the assistance from nuclear burning typically in the
following two ways, whether the shock front passes through the
 silicon-rich layer, or later it touches to the oxygen-rich layer.
 Depending on the neutrino luminosity and its decay time,
 the diagnostic energy of explosion was found to increase up to a few times $10^{50}$ erg
 for models with nuclear burning compared to the corresponding models without.
 The energy difference becomes generally smaller in 2D
than in 1D, because
neutrino-driven convection and the SASI in 2D models enhance the neutrino heating efficiency, making the contribution of nuclear burning relatively smaller compared to 1D models.
It was pointed out that these features are most remarkable for the LC15 progenitor,
which possesses a massive oxygen layer
with its inner-edge radius
being smallest among the employed progenitors,
which makes the timescale shorter for the shock to encounter the rich fuel.
Considering reduction of the critical luminosity
and increase of the diagnostic energy by nuclear burning,
and also uncertainties in the structure of progenitors,
our results indicate
that nuclear burning should still remain as one of the important
ingredients to foster the onset of neutrino-driven explosions.

\acknowledgments
We thank H.T. Janka for stimulating discussions and we are also
grateful to T. Kuroda, Y. Suwa, T. Kajino for helpful exchanges.
KK and TT are thankful to S. Yamada and K. Sato for continuing encouragements.
NN was financially supported by the European Research Council under
EU-FP7-ERC-2012-St Grant 306901.
Numerical computations were carried out in part on XT4 and
general common use computer system at the Center for Computational Astrophysics, CfCA,
the National Astronomical Observatory of Japan.  This
study was supported in part by the Grants-in-Aid for the Scientific Research
from the Ministry of Education, Science and Culture of Japan
(Nos. 20740150, 23340069, and 23540323)
and by HPCI Strategic Program of Japanese MEXT.

\begin{table}[htbp]
\caption{Summary of results.}
\begin{tabular}{ccccccccc}
\hline \hline
                         &&&  & \multicolumn{2}{c}{without burning} && \multicolumn{2}{c}{with burning}\\
                          \cline{5-6}  \cline{8-9}
model & $L_{\nu 0,52}$ & $t_{\rm d}$ && $t_{\rm exp}$ & $E_{\rm dia}$ && $t_{\rm exp}$& $E_{\rm dia}$\\
       & ($10^{52}{\rm erg \, s}^{-1}$) & (s)   &&       (s)           & ($10^{51}$erg)  &&   (s)       & ($10^{51}$erg)\\
\hline
LC15             & 2.0 &    5.0           && ---                      & ---                         && 0.836      & 0.188                      \\
                     & 2.2 &    2.0            && ---                      & ---                         && 0.502      & 0.516            \\
                     & 2.2 &    5.0            && 0.819                & 0.234                     && 0.465      & 0.796             \\
                     & 2.5 &    0.8            && 0.811                & 0.065                     && 0.460      & 0.359              \\
                     & 2.5 &    1.6            && 0.462                & 0.832                     && 0.416      & 0.836                \\
                     & 3.0 &    0.4            && 0.498                & 0.140                     && 0.424      & 0.203                \\
                     & 3.0 &    0.8            && 0.394                & 1.017                     && 0.368      & 1.071                \\
WHW15      & 2.7 &    2.5            && 0.712                & 0.765                      && 0.598      & 0.906                      \\
                     & 3.0 &    1.0            && 0.556                & 0.613                    && 0.531      & 0.644                      \\
                     & 3.5 &    0.5            && 0.493                & 0.379                     && 0.477      & 0.403                      \\
                     & 4.0 &    0.4            && 0.455                & 0.622                    && 0.403      & 0.706                      \\
WW15         & 2.0 &    5.0            && 0.543                & 0.385                     && 0.527      & 0.388                      \\
                     & 3.0 &    1.0            && 0.360                & 1.058                     && 0.357      & 1.087                      \\
                     & 3.5 &    0.5            && 0.336                & 0.954                     && 0.333      & 1.005                      \\
                     & 4.0 &    0.3            && 0.325                & 0.651                     && 0.322      & 0.704                      \\
WHW11      & 1.5 &    5.0            && 0.472                & 0.195                      && 0.465      & 0.208                      \\
                     & 2.0 &    5.0            && 0.353                & 0.821                     && 0.349      & 0.845                      \\
                     & 2.5 &    0.7            && 0.319                & 0.800                     && 0.316      & 0.837                      \\
                     & 3.0 &    0.4            && 0.292                & 0.911                     && 0.289      & 0.951                      \\
\hline
LC15 (2D)  & 2.0 &    4.0            && ---                      & ---                            && 0.541      & 0.226                      \\
                     & 2.2 &    2.0            && 0.664                & 0.113                     && 0.491      & 0.301           \\
                     & 2.2 &    4.0            && 0.542                & 0.355                     && 0.488      & 0.534            \\
                     & 2.5 &    0.8            && 0.596                & 0.099                     && 0.461      & 0.237             \\
                     & 2.5 &    1.6            && 0.464                & 0.623                     && 0.425      & 0.692               \\
                     & 3.0 &    0.4            && 0.514                & 0.019                     && 0.437      & 0.151               \\
                     & 3.0 &    0.8            && 0.401                & 0.881                     && 0.372      & 0.947               \\
\hline \hline
\\
\\
\end{tabular}
\label{tbl-result}
\end{table}

redpajama_set_name: RedPajamaArXiv


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text:
Offensive Combat preview - Hands-on with the browser-based FPS
By Lorenzo Veloria published 22 June 12
Sasquatches, bananas and tea-bagging galore
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The experience can be distilled down into two parts: customization and gameplay. Once the game began, we had the option to customize our character in a variety of ways. Naturally, we began with our look. Offensive Combat's visual customization ranges from hardcore Call of Duty-esque military costumes to giant banana suits and lizard heads. Each part of the body – including the head, torso, legs and arms – can be modified however you want. Feel like creating an abominable snowman wearing a Hawaiian shirt, or a cowboy wearing banana pants? Go for it.
The weapons break down to primary, secondary, melee and grenades. The primary weapon slot houses assault and sniper-type weapons that range from modern M16-style assault rifles to space-age ray guns. Secondary slots consist of equally varied pistols and shotguns. Then again, if you want to give your opponents an extra dose of humiliation, equip a rubber chicken or the aptly named Ham-mer (a honey-glazed ham with a fork as a handle) to the melee slot and beat them to death with it. Getting kills earns experience for weapons, unlocking perks like faster reload times, quicker downsite aiming, or greater ammo capacity.
Once you do get the upper hand on a player and reduce them to a hole-riddled carcass, you have the option to engage in Offensive Combat's version of tea-bagging. This isn't the "victory crouch" made famous by the Halo community; instead, these are pre-chosen "pwn" animations that has your character humping air, flipping the bird, or riding a pony over your victim's body. Pwns can be purchased and equipped in the character customization screen before jumping into a match. Successfully completing a pwn will earn you additional coins which you can use to purchase more elaborate pwns or buy new weapons and costumes.
Surprisingly, for a browser-based game the shooting feels on par with a standard PC game loaded onto our hard drive. Control inputs are responsive, and we didn't experience any slowdown or graphical hitches the entire time we were in-game.
If you want to get your hands on Offensive Combat, the North American open beta starts in August. Be sure to check back for more information on Offensive Combat as we get closer to its full release.

redpajama_set_name: RedPajamaCommonCrawl


Coffee body scrubs have been all the rage in beauty recently thanks to companies like Frank Body (which I love—their scrubs are so luxurious). Caffeine is cellulite's biggest enemy. With regular use, it's shown to reduce the appearance of cellulite as well as provide antioxidant protection. My DIY version is very basic but effective! Not only was this so easy to make, but also, I knew right away it was working. My hands have never felt so smooth. I recommend scrubbing your whole body in the morning; it feels so energizing! I did smell a little like coffee, but that went away after washing with my favorite Rosewater Body Wash ($13) by Jason.
This DIY face mask was recommended to me by my facialist Ildi Pekar. There are so many benefits to using raw honey on your skin. It's full of antioxidants. It brightens, helps to promote cellular renewal, hydrates, and is also a natural antibacterial. So it's a great addition to face wash (I love the raw honey–based Facial Cleanser, $65, from Ildi's I Pekar line). The last time I was in for a facial Ildi recommended adding mango to my raw honey mask. Mango contains vitamin C, which helps to boost collagen production as well as fruit acids, which soften dead skin cells for a brightening effect. You can even just eat your mango, rub the soft yellow inside of the skin all over your face, wait 15 minutes, and rinse. Don't forget your daily SPF, especially after exfoliating.
I travel so much for work that I often don't know which time zone I'm in. I carry essential oils around with me on the plane and in my purse whenever I need a moment to just chill out and breath. One of my personal favorites is this Rose Oil($35), worn and inspired by Amma the hugging saint, called Amma's Rose.


Welcome to our new web page! It is short on content at the moment but we will fix that up. There are also probably quite a few bugs and issues as we transition from our old website. Please let us know if you find anything that doesn't work.
Max is the Director of the NetSmartz program provided by the Boys & Girls Clubs of Utah.


Thinking about getting the skimz monzter sm-201 e series. Anyone know much about these good or bad?? Or any other recommendations??
I have one on my 120 gal. I switched from Vertex IN-180 and I am very happy with it.It has been about 2 months now.It is completely silent ,you can't hear the pump running at all and it pulls tons of dark skimmate.Very easy to adjust and with its unique output it doesn't produce microbubbles at all.
I have heard some bad things about these skimmers one guy has a bad pump and no C/S so he is looking for a new pump. SO I would do some searches for bad C/S faulty pumps.
I believe that the last one was the smallest skimmer they make.
An alternative would be the Warner Marine MF 201. Basically the same skimmer but customer service is good.
just looked at the warner, looks like thats what ill be getting, thanks!!


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Christmas Led Projector Lights, GOODAN 16 Pattern, Range 40ft Projection Distance Holiday Light Projector, IP65 Waterproof Landscape Garden LED Lights for Various Themes Halloween, Christmas, etc.


TRANSFERRED—Fred H. Vreeland to Helene Desmare, wife of Augustus C. Vreeland, portion Sixth district, Henry Clay avenue, Calhoun, Perrier, and Prytania streets, $9000.
So, she had remarried by then.
Reference "Augustus C. Vreeland". Genealogy at Pitard.net. https://ancestors.pitard.net/getperson.php?personID=I15666&tree=1sttree (accessed April 22, 2019).


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Sunday, 9/16: Daniel Radcliffe to Talk Live about Suicide Prevention on Google+ Hangout
On Sunday, September 16, 2012 at 2:00 p.m. E.D.T., Daniel Radcliffe will participate in a live online discussion to raise awareness about preventing suicide through The Trevor Project's "Talk to Me" campaign. The event will be broadcast through TrevorTalkToMe.org and on The Trevor Project's YouTube and Google+ pages.
Daniel Radcliffe Talks Live this Sunday, September 16, 2012 for National Suicide Prevention Month
The Trevor Project is full of amazing volunteers who work every day to save lives on the phone and online, but the 'Talk to Me' campaign is about how each one of us can help save a life, too. I am really proud to be a part of this extraordinary initiative
West Hollywood, CA (PRWEB) September 13, 2012
On Sunday, September 16, 2012 at 2:00 p.m. E.D.T., Daniel Radcliffe will participate in a live online discussion to raise awareness about preventing suicide through The Trevor Project's "Talk to Me" campaign. This live conversation on Google+ Hangout will feature questions submitted by young people online and posed by members of The Trevor Project's Youth Advisory Council. The event will be moderated by Shira Lazar of the Emmy®-nominated live, online interactive show, "What's Trending with Shira Lazar," and will be broadcast through TrevorTalkToMe.org and on The Trevor Project's YouTube and Google+ pages.
"Suicide is absolutely tragic, and it's also completely preventable, which is why it is so important to learn how to help during The Trevor Project's National Suicide Prevention Month," said Daniel Radcliffe, actor and 2011 Trevor Hero Award honoree. "The Trevor Project is full of amazing volunteers who work every day to save lives on the phone and online, but the 'Talk to Me' campaign is about how each one of us can help save a life, too. I am really proud to be a part of this extraordinary initiative with The Trevor Project."
"Talk to Me" is a public awareness campaign to prevent suicide and runs throughout the month of September. The campaign is grounded in research indicating improvements in help-seeking behaviors and access to care can have a dramatic effect on suicide prevention, a message emphasized in the new National Strategy for Suicide Prevention released on Monday by the Department of Health and Human Services.
The live chat on September 16 will feature Radcliffe, who will be answering questions from Google's office in Toronto, Ont., and Lazar will be moderating the event from Google's office in Venice, Calif. Trevor Youth Advisory Council members, Andii Viveros, 19, Brandon Robert White, and Shontay Richardson, 20 will be co-hosting the event from Fort Lauderdale, Fla., Oklahoma City, Okla., and Purchase, N.Y., respectively. Young people from around the world have been submitting questions for Radcliffe through TrevorTalkToMe.org all this week.
"The Trevor Project is very excited for this truly international event and grateful for Daniel Radcliffe's continued and unwavering support of our life-saving, life-affirming programs for lesbian, gay, bisexual, transgender and questioning youth. It really makes a difference to hear a straight ally and role model like Daniel empower young people to do something life-saving, like saying, 'talk to me' to a friend," said Abbe Land, Executive Director & CEO of The Trevor Project.
To learn more about "Talk to Me" and to get involved, visit TrevorTalkToMe.org.
ABOUT THE TREVOR PROJECT:
The Trevor Project is the leading national organization providing crisis intervention and suicide prevention services to lesbian, gay, bisexual, transgender and questioning young people under 24. Every day, The Trevor Project saves young lives through its free and confidential lifeline, in-school workshops, educational materials, online resources and advocacy. Honored by the White House as a "Champion of Change," The Trevor Project is a leader and innovator in suicide prevention. Learn more at TheTrevorProject.org.
Laura McGinnis


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Sakarya (grekiska: Σαγγάριος; latin: Sangarius) är en flod i västra Anatolien i Turkiet, i det landskap som under antiken kallades Frygien. Den utmynnar i Svarta havet. Floden har gett namn till den moderna provinsen Sakarya som den genomflyter. Även staden Adapazarı, som ligger vid floden, kallas ibland Sakarya.

Vid floden stod 1921 slaget vid Sakarya mellan turkiska och grekiska styrkor.

Externa länkar

Vattendrag i Turkiet
Svarta havets avrinningsområde

redpajama_set_name: RedPajamaWikipedia


June 19 - Family-owned Dutch shipping group Vroon has responded to negative articles published in the Dutch media concerning its financial state.
The Telegraaf reported on Friday that the Breda-based concern has debts totalling EUR1.1 billion (USD1.23 billion), and some activities will be trimmed down.
It added that Vroon's 22 creditors, which include the big Dutch banks and insurer Delta Lloyd, have agreed to a restructuring plan for Vroon.
In response, Vroon said that since late 2016, it has been in discussion with its banking and finance partners to address the financial consequences of this situation. These discussions have progressed in a constructive atmosphere and it expects to reach agreements over the summer.
It explained that other than in the offshore support vessel market, where it has a presence through its subsidiary Vroon Offshore Services, its other businesses are all performing in line with expectations.
Vroon's activities in the offshore wind energy sector operate under the MPI banner, where it is active in offshore wind turbine installation and maintenance markets with a range of vessels, equipment and service offerings.
In an official statement it said: "Despite the challenging market conditions during 2016, Vroon produced a positive cash flow, although did make various impairment charges on the book value of vessels that led to negative net results, for the first time in the company's history."
Pictured below, MPI Resolution was the world's first purpose-built vessel for installing offshore wind turbines, foundations and transitions pieces.


The Youth Team's fixture against Blackpool this weekend (Saturday 11th November) has been postponed.
This is due to Stalybridge Celtic playing a home match in the FA Trophy on the same day.
The fixture has been rearranged for Tuesday 12th December, 1pm kick-off, at Bower Fold.
The Youth Team's next match is at home (Bower Fold) against Wrexham on Saturday 18th November, 11am kick-off.