text:
\section{\label{introduction}Introduction}

 The excited states close to particle emission threshold in doubly-magic $^{16}$O have been of much interest due to the formation of $\alpha$ clustering structure, which is different from the spherical ground state with shell-like picture. In particular, the possible existence of 4$\alpha$ linear-chain structure (LCS) in highly excited states of $^{16}$O has been under intensive discussion. About half-century ago, Chevallier {\em et al}. observed resonant $2^+, 4^+$, and $6^+$ states in the reaction $^{12}$C($\alpha$, $^{8}$Be)$^{8}$Be and proposed that these states may correspond to the rotating states with 4$\alpha$ LCS. The moment of inertia (MOI) was estimated as $\hbar^2/(2{\mathscr J})$ = 64 keV with band-head excitation energy of $16.8$ MeV~\cite{Chevallier67}. This proposal was supported by the analysis of decay widths for the states~\cite{Suzuki72}. Later, Freer {\em et al.} performed the $^{12}$C($^{16}$O, 4$\alpha$)$^{12}$C reaction, and obtained a slightly smaller MOI ($96\pm20$ keV) with bandhead excitation energy of $17.0\pm0.7$ MeV~\cite{Freer95}. The calculation by Bauhoff {\em et al.}\cite{Bauhoff84} using the Brink's $\alpha$ cluster model (ACM) supported the existence of 4$\alpha$ LCS state in low-spin states of $^{16}$O, which predicted the MOI to be 64 keV and the band-head excitation energy of 16.3 MeV, in excellent agreement with the data~\cite{Chevallier67}. Most recently, a new measurement of the $^{12}$C($\alpha$, $^{8}$Be)$^{8}$Be excitation function was carried out. Unfortunately, this experiment did not provide any evidence to support the existence of $4\alpha$ LCS in $^{16}$O~\cite{Curtis13}.

 The formation of cluster structure in finite quantum many-body systems in itself is an interesting phenomenon. In nuclear physics, the cluster structure is essential to understand many problems of nuclear structure and reactions. A fully microscopic understanding of cluster formation necessitates the treatment of the individual nucleons as the fundamental ingredients, with the clusters and their properties emerging automatically from the calculations, instead of assuming a priori certain geometrical arrangements for the clusters. Self-consistent mean-field approaches with all nucleons treated on the same footing provide us good tools for understanding these phenomena from this aspect. The previous studies in this context have shown that the nucleons are prone to form cluster structure in the nuclear system with either high excitation energy and high spin with large deformation~\cite{Zhang2010Chin.Phys.Lett.4,Ichikawa11}, deep confining nuclear potential~\cite{Ebran13nature,Ebran13PhysRevC.87.044307}, or expansion with low density~\cite{Girod13PhysRevLett.111.132503}.

 In the recent decade, several studies based on selfconsistent mean-field approaches have been carried out for the $4\alpha$ LCS in $^{16}$O. The relativistic mean-field (RMF) calculations with a constraint on nuclear quadrupole moment demonstrated the existence of 4$\alpha$ LCS in hyperdeformed mean-field state with deformation parameter $\beta\simeq3.6$ and excitation energy of 37 MeV~\cite{Arumugam05,Liu12}. It can be understood that the degeneracy of single-nucleon levels is reduced by deformation since the spherical symmetry is lost, but can be recovered at some specific deformations, for example, with the long-short axis ratio around 2:1 (superdeformed shape) or 3:1 (hyperdeformed shape), which favors the formation of clusters~\cite{vonOertzen200643}. The stability of this state against quadrupole shape fluctuation in $^{16}$O has been studied with a generator coordinate method implemented with particle-number and angular-momentum projection (GCM+PNAMP) based on a non-relativistic Skyrme-Hartree-Fock (SHF)+BCS calculation with SLy4 force~\cite{Bender03NPA}. It was found that the $0^+_6$ state with dominated $8p$-$8h$ character and excitation energy of 32 MeV is close to the 4$\alpha$ LCS. A more recent calculation by Ichikawa {\em et al}.~\cite{Ichikawa11} using a cranking SHF method suggested that a rapidly rotating $^{16}$O can deform into the 4$\alpha$ LCS in the region of angular momentum ($13-18\hbar$). The MOI was estimated to be around $60-80$ keV with a very high band-head energy 38 MeV. The formation of LCS in high-spin state was regarded as a result of the competition between nuclear attractive and centrifugal forces due to rapid rotation. It means that even without taking into account the orthogonality condition to the low-lying state, which can enhance the stability of LCS and was considered in Refs.~\cite{Itagaki06PhysRevC.74.067304,Furutachi2011PhysRevC.83.021303,Suhara11PhysRevC.84.024328}, one finds a region of angular momenta for the formation of LCS in high-spin states.

 In recent years, the structure of the proposed 4$\alpha$ LCS rotational states in Ref.~\cite{Chevallier67} has been mainly interpreted in two different ways. A study of the structure and scattering of $\alpha+^{12}$C system using a double folding model in the coupled-channel method~\cite{Ohkubo10PLB} and a calculation with 4$\alpha$ orthogonality condition model (OCM)~\cite{Funaki12-PTP} suggest that the rotational states have the $^{12}$C($0^+_2$)+$\alpha$ cluster structure. On the other hand, most recently, the 4$\alpha$ LCS in $^{16}$O was investigated with the Brink model wave function by Suhara {\em et al}.~\cite{Suhara14PhysRevLett.112.062501}, suggesting that the 4$\alpha$ LCS has the one-dimensional  $\alpha$ condensate character, where the $\alpha$ clusters are trapped into a one-dimensional potential in a nonlocal manner, like a gas.

 The aim of this work is to search for the 4$\alpha$ LCS in $^{16}$O with a covariant density functional theory (CDFT), which has already achieved great success in describing variety aspects in nuclear physics~\cite{Ring96,Vretenar05,Meng06,Meng13}. On one hand, it has been pointed out in Ref.~\cite{Ebran13nature} that relativistic energy density functionals (EDF) are characterized by deep single-nucleon potentials and therefore are prone to predict the occurrence of much more pronounced cluster structures in nuclear ground state than the non-relativistic EDF. On the other hand, most clustering states appear in light nuclei and are deformed in the intrinsic frame. The effects from shape fluctuations and restoration of rotational symmetry need to be examined. Moreover, the cluster structure in nuclear excited states has not been studied with a relativistic functional. Therefore, the search for the 4$\alpha$ LCS in both low-spin and high-spin excited states of $^{16}$O and the investigation of the structure properties of these exotic states based on a relativistic EDF are very interesting. To this end, both the GCM+PNAMP and cranking methods on top of the CDFT are adopted.

 The paper is organized as follows. In Sec.~\ref{framework}, we introduce the basic formulae of the CDFT and its extension for nuclear collective excitation states briefly. The results from both GCM calculation for nuclear low-spin states and cranking calculation for nuclear high-spin states based on the CDFT are presented and discussed in Sec.~\ref{results}. Finally, a summary and outlook are given in Sec.~\ref{concluson}.

 \section{Theoretical framework}
 \label{framework}

 The starting point of the point-coupling type of CDFT is an EDF which has the following form~\cite{Burvenich02,Zhao10},
 \begin{eqnarray}\label{EDF}
 &&E_{\rm DF}[\rho_i, \nabla\rho_i, j^\mu_i, \nabla j^\mu_i]\nonumber \\
 &=&{\rm Tr}[(\mathbf{\alpha}\cdot\mathbf{p}+\beta m)\rho_V]\nonumber \\
 &+& \int d{\bm r }~{\left(\frac{\alpha_S}{2}\rho_S^2+\frac{\beta_S}{3}\rho_S^3 +
    \frac{\gamma_S}{4}\rho_S^4+\frac{\delta_S}{2}\rho_S\triangle \rho_S \right.}\nonumber \\
 &+&  {\left.\frac{\alpha_V}{2}j_\mu j^\mu + \frac{\gamma_V}{4}(j_\mu j^\mu)^2 +
     \frac{\delta_V}{2}j_\mu\triangle j^\mu \right.} \nonumber \\
 &+& \left. \frac{\alpha_{TV}}{2}j^{\mu}_{TV}(j_{TV})_\mu+\frac{\delta_{TV}}{2}
    j^\mu_{TV}\triangle  (j_{TV})_{\mu}\right.\nonumber \\
   &+& \left.\frac{1}{4}F_{\mu\nu}F^{\mu\nu}-F^{0\mu}\partial_0A_\mu+e\frac{1-\tau_3}{2}j_\mu
   A^\mu
 \right),
\end{eqnarray}
where  densities $\rho_i$ and currents  $j^\mu_i$ are bilinear combinations of Dirac spinors, namely $\bar\psi\Gamma_i\psi$ with $i=S, V, TV$ representing the symmetry of the coupling. The subscript $S$ stands for isoscalar-scalar ($\Gamma_S = 1$), $V$ for isoscalar-vector  ($\Gamma_V = \gamma^\mu$), and $TV$ for isovector-vector ($\Gamma_{TV} =\gamma^\mu t_3$) type of coupling characterized by their transformation properties in isospin and in space-time. $A^\mu$ is the four-component electromagnetic field. The coupling constants  $\alpha_i, \beta_i, \gamma_i, \delta_i$ are determined in the optimization of the EDF for the properties of several finite nuclei and nuclear matter~\cite{Burvenich02,Zhao10}.

In the following, we will introduce the extensions of the CDFT for low-spin and high-spin states separately in a brief way.
More detailed description can be found in Refs.~\cite{Yao10,Yao11,Niksic11,Yao13,Yao14} and Refs.~\cite{Peng08,Zhao11,Meng13} respectively.

 \subsection{The GCM calculation for low-spin states}

 The wave function of nuclear low-spin state is given by the superposition of a set of both particle-number and angular-momentum  projected (PNAMP) quadrupole deformed mean-field states in the framework of GCM~\cite{Yao14},
 \begin{equation}
 \label{GCMwf}
 \vert JNZ;\alpha\rangle
 =\sum_{q, K} f^{JNZK}_\alpha(q) \hat P^J_{MK} \hat P^N\hat P^Z\vert q (\beta,\gamma) \rangle.
 \end{equation}
where $\alpha=1,2,\ldots$ distinguishes different collective states with the same angular momentum $J$.  The operators $\hat{P}^{N}$, $\hat{P}^{Z}$, and $\hat P^J_{MK}$ project onto good neutron and proton numbers and onto good angular momentum. The mean-field states $\vert q(\beta,\gamma)\rangle$ are Slater determinants of single-(quasi)particle states from the RMF+BCS calculation with constraints on the mass quadrupole moments $Q_{20}= \sqrt{\dfrac{5}{16\pi}}\langle 2 z^2 - x^2 - y^2\rangle$ and $Q_{22} =\sqrt{\dfrac{15}{32\pi}}\langle x^2-y^2\rangle$, where the deformation parameters $\beta, \gamma$ are related to the quadrupole moments by $\beta= \dfrac{4\pi}{3AR^2}\sqrt{Q^2_{20}+2Q^2_{22}}$, $\gamma=\tan^{-1}(\sqrt{2}\dfrac{Q_{22}}{Q_{20}})$, respectively, with $R=1.2A^{1/3}$ and $A$ being the mass number. For simplicity, the mean-field states $\vert q(\beta,\gamma)\rangle$ are restricted to axially deformed, namely, $\gamma=0^\circ$ (prolate) and $180^\circ$ (oblate). In this case, $K=0$, and the $f^{JNZK}_\alpha$ is replaced with $f^{JNZ}_\alpha$. Moreover, $q(\beta,\gamma)$ is abbreviated with $\beta$ subsequently.

Minimization of nuclear total energy with respect to the coefficient $f^{JNZ}_\alpha$ leads to the Hill-Wheeler-Griffin (HWG) equation~\cite{Ring80},
  \begin{equation}
   \sum_{\beta^\prime} [{\cal H}^J(\beta, \beta^\prime)-E^J_\alpha {\cal N}^J(\beta, \beta^\prime)] f^{JNZ}_{\alpha} (\beta^\prime) =0,
 \end{equation}
 where ${\cal N}^J(\beta, \beta^\prime)$ and ${\cal H}^J(\beta, \beta^\prime)$ are the norm kernel and the energy kernel, respectively. The solution of HWG equation provides the energy spectrum and all the information needed for calculating the electric multipole transition strengths in low-spin excited states.

 \subsection{The cranking RMF calculation for high-spin states}

 The GCM+PNAMP method can provide nuclear excited states with good quantum numbers, which are essential
for spectroscopic study. However, it is currently limited to low-spin states due to the computation difficulty.
To obtain nuclear high-spin states, we are restricted to the semiclassic cranking method on top of the CDFT, in which
the nucleus is cranked along $x$-axis with a constant rotational frequency $\omega$. The wave function of single-particle (s.p.) state is the solution of the Dirac equation in body-fixed rotating frame, which turns out to have the following form~\cite{Koepf89,Meng13},
 \begin{equation}
   \label{Eq.Dirac}
   (h_0 - \omega J_x)\psi_k(\mathbf{r},s,t)=\varepsilon_k\psi_k(\mathbf{r},s,t),
    \end{equation}
   where the single-particle Hamiltonian in non-rotating frame $h_0$ is
 \begin{equation}
   h_0= \mathbf{\alpha}\cdot[-i\mathbf{\nabla}-\mathbf{V}(\mathbf{r})]+\beta(m+S (\mathbf{r}))
    +V_0(\mathbf{r}).
    \end{equation}
 The $\varepsilon_k$ and $\psi_k$ are the energy and wave function of single-particle (s.p.) state in rotating frame, respectively. $m$ is bare nucleon mass. The $S(\mathbf{r}), V_\mu(\mathbf{r})$ represent the scalar potential and vector potentials. The $\mathbf{V}(\mathbf{r})$ is the space-like (time-odd) component of vector potential, which is often called {\em nuclear magnetism}~\cite{Ring96} and is nonzero only in time-reversal invariance violated systems. In the cranking RMF approach for a rapidly rotating nucleus, the Coriolis term $\omega J_x$ violates the time-reversal invariance in the intrinsic frame and therefore generates the nonzero {\em nuclear magnetism} term $\bm{V}(\bm{r})$.

 \subsection{Expansion of Dirac spinor on a basis}

The Dirac equation in both deformation constrained
RMF+BCS and cranking RMF calculations is solved by
expanding the Dirac spinor $\psi_k$ on a three-dimensional
harmonic oscillator (HO) basis in Cartesian coordinates,
 \beqn
 \psi_k(\mathbf{r},s,t) =
 \begin{pmatrix}
 f_k(\mathbf{r},s) \\
 ig_k(\mathbf{r},s)
 \end{pmatrix}\chi_k (t),
 \eeqn
 where  $\chi_k(t)$ is the isospin part and
 \bsub
 \label{expansion}\beqn
 f_k(\mathbf{r},s) &=& \sum_\alpha f_{\alpha k} \vert \alpha\rangle + \sum_{\bar\alpha} f_{\bar\alpha k} \vert \bar\alpha\rangle,\\
 g_k(\mathbf{r},s) &=& \sum_{\tilde\alpha} g_{\tilde\alpha k} \vert \tilde\alpha\rangle + \sum_{\bar{\tilde\alpha}} g_{\bar{\tilde\alpha} k} \vert \bar{\tilde\alpha}\rangle.
 \eeqn
 \esub
 The HO basis $\{\alpha, \bar\alpha\}$ are chosen as eigenstates of the $x$-simplex operator $\hat S_x=\hat Pe^{-i\pi \hat J_x}$ with positive and negative eigenvalues
   \beqn
    \displaystyle
  \label{Basis}
   \left\{
    \begin{array}{lclcl}
     \vert \alpha\rangle &=&
      \vert n_x n_y n_z\rangle
      \displaystyle \frac{i^{n_y}} {\sqrt{2}}
       \left(
        \begin{array}{c}
        1\\
        (-1)^{n_x+1}
        \end{array}
       \right),   \\
       \vert \bar {\tilde \alpha}\rangle &=&
      \vert \tilde n_x  \tilde n_y  \tilde n_z\rangle \displaystyle\frac{i^{\tilde n_y}}{\sqrt{2}}(-1)^{\tilde n_x+\tilde n_y+1}
      \left(
       \begin{array}{c}
       1\\
       (-1)^{\tilde n_x}
       \end{array}
      \right),
   \end{array}
  \right.
 \eeqn
 where $\vert n_x n_y n_z\rangle$ is the space part of the three-dimensional HO  wave function.
The phase factor $i^{n_y}$ is chosen in order to have a real matrix elements for the Dirac equation~\cite{Yao06PhysRevC.74.024307}.

In the deformation constrained RMF+BCS calculation for generating mean-field reference states as inputs of
GCM calculation, the symmetries associated with parity, $x$-simplex, and time-reversal invariance are imposed.
In this case, one has to expand the Dirac spinor only in half of the full basis with positive or negative simplex
eigenvalue. Therefore, we expand the large $f_k$ and small $g_k$ component in Eq.~(\ref{expansion}) only on the basis with positive and negative $x$-simplex values, respectively. In the cranking RMF calculation for high-spin states,
we adopt the tilde-cranking code developed in Refs.~\cite{Peng08,Zhao11,Meng13}  and restrict the rotation along $x$-axis. In this code, only the symmetries associated with parity ($P$) and the combination of time reversal ($T$) and space reflection with respect to $x$-$z$ plane ( $\hat P_y: y\to -y)$ are imposed. Since the time-reversal invariance is violated by the coriolis term, the time-reversal partner states are not degenerate in energy. The Dirac equation has to be solved in the full basis with both positive and negative $x$-simplex values, cf. Eq.~(\ref{expansion}). More details are also introduced in the review paper~\cite{Meng13}.

 \section{Results and discussions}
 \label{results}

In both the deformation constrained RMF+BCS and cranking RMF calculations, 12 major HO shells are adopted,
which turns out to give difference in total energy within 1 MeV compared with the value by 14 major shells
for the configurations with deformation parameter $\beta$ up to 4.0. We note that the GCM+PNAMP calculation with 14 major HO shells for the expansion of Dirac spinor is very time-consuming. In particular, as we will see in the results, this energy difference is marginal and will not have much influence on our conclusions, compared with the excitation energy of LCS candidate states. To implement the AMP for the deformed states, the oscillator lengths for HO basis are chosen to be isotropic $b_x=b_y=b_z=\sqrt{\hbar/m\omega_0}$ to keep the basis closed under rotation~\cite{Yao09amp}, where the oscillator frequency is given by $\hbar\omega_0=41A^{-1/3}$. There is no parameters in our study other than those in the EDF, for which the relativistic point-coupling parametrization PC-PK1~\cite{Zhao10} is used throughout this work. In the deformation constrained RMF+BCS calculation, a density-independent $\delta$ force implemented with an energy-dependent smooth cutoff factor~\cite{Bender00p} is adopted in the same way as the PC-PK1 was parameterized. In the cranking RMF calculation, pairing correlations between nucleons are neglected due to the anti-pairing effect of the Coriolis term.

 \subsection{Low-spin states}

 Figure~\ref{pes}(b) displays the mean-field and both particle-number and angular-momentum (PNAMP) projected energy as a function of the intrinsic quadrupole deformation $\beta$ in $^{16}$O. To search for the LCS in the mean-field state, we also plot the density profiles for some configurations on the curve. It is shown that there is a shoulder on the energy curve around $\beta=3.6$, at which an evident $4\alpha$ LCS is found. The excitation energy of this state is 39.1 MeV. After restoration of rotational symmetry, this energy is reduced to 31.5 MeV. The configuration mixing calculation predicts the excitation energy of $0^+$ state with the $4\alpha$ LCS to be 29.6 MeV. The result is consistent with the value of 32.0 MeV obtained by the previous GCM+PN1DAMP calculation using the SLy4 force~\cite{Bender03NPA}, which suggests a $8p$-$8h$ character for this state. However, these values are still much higher than the suggested value of 16.8 MeV in Ref.~\cite{Chevallier67}. This might be attributed to the spurious center-of-mass motion of each alpha particle not being correctly treated in the mean-field approaches~\cite{Ichikawa11,Girod13PhysRevLett.111.132503}.

 It is well known that bending motion is the main path for the breaking of linear chain configuration, which allows the structure change to other low-lying states~\cite{Umar10,Maruhn10}. This bending motion can be investigated by allowing triaxial deformation. To check the stability of the LCS against the distortion of triaxial deformation, we have calculated the total energy of mean-field states in the $\beta$-$\gamma$ plane for $^{16}$O, as shown in Fig.~\ref{PES2}. It is seen that the energy of mean-field configurations with $\beta\in[2.8, 4.0]$ increases rapidly when the $\gamma$ deformation increases from zero to $5^\circ$. For $\beta=2.8$ the increase is about 3 MeV, and the increase gets larger for more deformed states; about 12 MeV for $\beta=4.0$. \jmy{To examine further the influence of restoration of rotation symmetry, we carry out AMP calculation for some triaxial states with $\beta=3.2$. After projected onto $J=0$, the energy of state  is $-95.2$ MeV for $\gamma=5^\circ$  and $-89.8$ MeV for $\gamma=10^\circ$, which is much higher than the energy of axial state ($\gamma=0^\circ$) $-96.8$ MeV. In other words, the LCS should be stable against the $\gamma$-vibration.}

 Besides the rotational band with $4\alpha$ LCS (with $\beta\in[2.8, 4.0]$), an oblate deformed rotational band (with $\beta\in[-1.0, -0.5]$), together with a prolate deformed rotational band  (with $\beta\in[1.0, 2.0]$), which is similar to the ``kite" structure found in Ref.~\cite{Arumugam05}, is displayed in Fig.~\ref{pes}. \jmy{In what follows, the states dominated by the mean-field configurations with $\beta\in[1.0, 2.0]$ are labeled with ``prolate" states.} Moreover, when the deformation parameter $\beta$ is increased up to $\beta=4.8$, a structure of $^{8}$Be+$^{8}$Be appears in $^{16}$O, which is beyond the scope of the present study.

\begin{figure}[t]
\includegraphics[width=8.5cm]{fig1.eps}
\caption{\label{pes}(Color online) (a) Spin-orbit interaction energy $SO1$ (\ref{SO1}) and sum of spin-orbit splitting energy $SO2$ (\ref{SO2}) and (b) total energy of the mean-field and PNAMP states (normalized to the energy of $0^+_1$ state) in $^{16}$O as a function of the intrinsic quadrupole deformation $\beta$. The horizontal
short lines with bullets are the GCM solutions. Only the states with similar dominated configurations (oblate, prolate, and LCS respectively) are plotted and placed at their ``average"
deformation $\bar\beta = \sum_\beta \vert g^J_\alpha\vert^2 \beta$, cf.(\ref{gg}). The insets are the contours
of intrinsic total density on $y$-$z$ ($x$-$y$) plane at $x = 0.3$ ($z=0.3$) fm for some typical prolate (oblate) configurations along the curve.}
\end{figure}

\begin{figure}[]
\centering
\includegraphics[width=8cm]{fig2.eps}
\caption{\label{PES2}(Color online) Mean-field energy surface in the $\beta$-$\gamma$ plane for $^{16}$O. Two neighboring contour lines are separated by 2.0 MeV.}
\end{figure}

\begin{figure}[]
\centering
\includegraphics[width=8cm]{fig3.eps}
\caption{\label{spin_orbit}(Color online) Comparison of the spin-orbit interaction matrix element $\langle k\vert V_{\rm s.o.} \vert k\rangle $, cf. (\ref{spinorbit}), for the $k$-th occupied s.p. state in the mean-field states of $^{16}$O
with $\beta = 0.0$ and $\beta = 3.6$.}
\end{figure}

 \jmy{In the following, we will study the structure of the $4\alpha$ LCS candidate states in details. First, we examine the spin-orbit interaction in the dominated configuration of the LCS candidate states.} Fig.~\ref{pes}(a) displays the spin-orbit interaction energy
 \begin{eqnarray}
 \label{SO1}
   SO1
   =-\sum_k v^2_k  \langle k\vert V_{\rm s.o.} \vert k\rangle,
   \end{eqnarray}
    and the sum of the matrix elements with its absolute values
   \begin{eqnarray}
   \label{SO2}
   SO2
   =\sum_k v^2_k  \Big\vert \langle k\vert   V_{\rm  s.o.} \vert k\rangle  \Big\vert.
   \end{eqnarray}
   for each mean-field state $\vert\beta\rangle$,  where a ``$-$" sign is introduced in defining $SO1$  to have positive values because the spin-orbit interaction is attractive,  $v^2_k$ is the occupation probability of the $k$-th s.p. state in the mean-field state $\vert\beta\rangle$ and the matrix element is given by~\cite{Koepf1991ZPhyA.339.81,Ring96}
    \beqn
    \label{spinorbit}
   \langle k\vert   V_{\rm s.o.} \vert k\rangle  =   \langle k\vert  \dfrac{1}{4m^2}(\nabla V_{\ell s})\cdot (\bp\times\sigma)\vert k\rangle,
   \eeqn
   with $V_{\ell s}=\dfrac{m}{m_{\rm eff.}}(V_0-S)(\bm{r})$, and $m_{\rm eff.} = m-\dfrac{1}{2} (V_0-S)(\bm{r})$. As in Ref.~\cite{Song2011CPL}, only the large component in the Dirac spinor $\psi_k$ is used in the calculation of quantity $\langle k\vert V_{\rm s.o.} \vert k\rangle$. One finds that for the spherical state the $SO1$ is very small due to shell closure (not exact zero because of the elimination of small component in the Dirac spinor), while the $SO2$ is very large, which reflects the size of spin-orbit splitting energies. Moreover, it is shown that the $SO2$ decreases with the deformation $\vert\beta\vert$ in both oblate and prolate sides. In particular, the values of $SO1$ and $SO2$ become close to each other in the configurations with $\vert\beta\vert>1.0$, \jmy{which is a sequence of immigration of nucleons from spin-orbit anti-parallel states to spin-orbit parallel states} with the increasing of quadrupole deformation $\beta$. The $SO1$ value turns out to be about 3.8 MeV for the configuration at $\beta = 3.6$ with $4\alpha$ LCS. Figure~\ref{spin_orbit} shows the comparison of matrix element $\langle k\vert  V_{\rm s.o.} \vert k\rangle$ for each occupied s.p. state in the mean-field states with $\beta= 0.0$ and $\beta = 3.6$. We note that the $\langle k\vert  V_{\rm s.o.} \vert k\rangle$  values at $\beta = 3.6$ are much smaller than those at the spherical shell-like state.  In particular, the values of the matrix elements for  $\beta = 3.6$ are always negative, which indicates that the spin and orbital angular momenta of all nucleons are parallel to each other. The spin-orbit interaction energy $SO1$ is not exactly zero, which may indicate that there exists a small mixture of non $\alpha$-cluster components in the configuration.   \jmy{However, we note that the values of $SO1$ and $SO2$ in the oblate state with $\beta=-1.2$ are also very small, about 3 MeV. It means that small spin-orbit energy is a necessary condition for the cluster (spin saturated) state and can be regard as a measure, but this is not exactly a sufficient condition.}

\begin{figure}[]
\centering
\includegraphics[width=8cm]{fig4.eps}
\caption{\label{spectra}(Color online) (a) Experimental and (b) calculated
low-spin spectra for $^{16}$O.  The data are taken from Refs.~\cite{nndc,Wakasa07}.}
\end{figure}

\begin{figure}[]
\centering \includegraphics[width=8.5cm]{fig5.eps}
\caption{\label{wfs}(Color online)  Collective wave functions of the oblate, ``SD", and LCS candidate states with $J=0, 2, 4, 6$ from the GCM+PNAMP calculation.}
\end{figure}

\begin{table}[b]
 \caption{\label{tab:kite} The rms charge radius $R^J_c$ (fm), spectroscopic quadrupole moment $Q_s$ ($e$ fm$^2$) and $E2$ transition strength $B(E2\downarrow)$ (e$^2$fm$^4$) for the low-spin states \jmy{labeled with ``prolate"} from the GCM+PN1DAMP calculation using the PC-PK1 force. The results are compared with other calculations~\cite{Bender03NPA,Suzuki76-2,Kanada14PhysRevC.89.024302} and the experimental data~\cite{Tilley1993}. See text for more details.}
 \begin{tabular}{cccccccc}
   \hline\hline
        &      &      &  \multicolumn{5}{c}{$B(E2\downarrow)$}    \\
   \cline{4-8}
    $J^\pi$    &   $R^J_c$    & $Q_{s}$     & Present & Ref.~\cite{Bender03NPA} &   Ref.~\cite{Kanada14PhysRevC.89.024302} & Ref.~\cite{Suzuki76-2} & Exp.~\cite{Tilley1993}  \\
     \hline
    $0^+$     &      3.01            &     0                &        &       &   &      &           \\
    $2^+$     &      3.05            &     -23.0            &  97.9  & 48.2  &177& 60.1 & $65\pm7$   \\
    $4^+$     &      3.07            &     -29.6            &  192.1 &       &290& 96.2 & $156\pm14$ \\
    $6^+$     &      3.11            &     -34.5            &  226.9 &       &   & 81.6 &            \\
   \hline\hline
 \end{tabular}
 \end{table}

 Figure~\ref{spectra} displays the calculated low-spin spectra of $^{16}$O in comparison with experimental data. Following Ref.~\cite{Bauhoff84}, the level sequences with similar structure are connected with dotted lines. Even though the calculated excitation energies are systematically higher than the data, three rotational bands based on different configurations are shown. The excitation energies of ``prolate" rotational states are in qualitative agreement with the measured levels connected with dotted lines, the band-head state of which ($0^+_2$) has been a mysterious state and was suggested to have $^{12}$C($0^+_1$)+$\alpha$ structure in Refs.~\cite{Suzuki76,Suzuki76-2,Libert1980,Ikeda80,Kanada14PhysRevC.89.024302}. Table~\ref{tab:kite} presents the detailed properties of these states. The calculated intraband $E2$ transition strengths are in rather good agreement with the data~\cite{Tilley1993}. However, we obtain the interband $E2$ transition strengths $B(E2\downarrow; 2^+_1 \to 0^+_1) = 0.16$ e$^2$fm$^4$, which is more than one order of magnitude smaller than the data $8.1\pm0.8$ e$^2$ fm$^4$~\cite{nndc}. \jmy{The intraband $E2$ transition strength $B(2^+_1 \to 0^+_2)$ is overestimated in the GCM calculation based on the extended $^{12}$C+$\alpha$ model~\cite{Kanada14PhysRevC.89.024302} and the present study, but is underestimated in the GCM+PNAMP study based on the Skyrme force~\cite{Bender03NPA}.}

\begin{table}[]
\tabcolsep=12pt
 \caption{\label{tab1:GCM} The excitation energy $E_x$ (MeV), rms charge radius $R^J_c$ (fm), spectroscopic quadrupole moment $Q_s$ ($e$ fm$^2$) and $E2$ transition strength $B(E2\downarrow)$ (e$^2$fm$^4$) for the low-spin states with dominated $4\alpha$ LCS from the GCM+PN1DAMP calculation using the PC-PK1 force. The calculated rms charge radius for the ground state is 2.76 fm. The ratio $R^J_c/R^{\rm g.s.}_c$ is around 1.4.}
 \begin{tabular}{ccccc}
   \hline\hline
    $J^\pi$ & $E_x$    & $R^J_c$    & $Q_{s}$   & $B(E2\downarrow)$      \\
     \hline
    $0^+$     &    29.6       &   3.88            &     0                &     \\
    $2^+$     &    30.4       &   3.95            &     -50.4            &  561  \\
    $4^+$     &    32.0       &   3.99            &     -66.5            &  874  \\
    $6^+$     &    34.8       &   4.02            &     -74.4            &  663  \\
   \hline\hline
 \end{tabular}
 \end{table}

Figure~\ref{wfs} displays the square of collective wave functions $\vert g^J_\alpha(\beta)\vert^2$ as a function of deformation $\beta$ for the states with oblate, prolate and LCS characters, where the $ g^J_\alpha(\beta)$s are related to the weight function $f^{JNZ}_\alpha$ in Eq.(\ref{GCMwf}) by the following relation,
\beq
\label{gg}
g^J_\alpha(\beta) = \sum_{\beta^\prime} ({\cal N}^J(\beta,\beta^\prime))^{1/2} f^{JNZ}_\alpha (\beta^\prime),
\eeq
and are orthonormal to each other. It is shown in Fig.~\ref{wfs} that the collective wave functions of $0^+, 2^+, 4^+$ LCS candidate states are very similar with a sharp peak at $\beta = 3.2$, while the $6^+$ state is fragmented. Moreover, the LCS candidate states are isolated from the low-lying states, which is consistent with the findings in the GCM calculation within a microscopic $N\alpha$-cluster model~\cite{Itagaki96}.

Table~\ref{tab1:GCM} presents the properties of the low-spin $4\alpha$ LCS candidate states.  The rms charge radii $R^J_c$ of these states are around 3.9 fm.  The ratio to the rms charge radii of ground state $R^J_c/R^{\rm g.s.}_c$ is around 1.4, in surprised agreement with the theoretical threshold value of $\sim1.45$ for $\alpha$ formation~\cite{Girod13PhysRevLett.111.132503}.

\begin{figure}[]
\centering
\includegraphics[width=8.2cm]{fig6.eps}
\caption{\label{density1}(Color online) The total density distribution (in fm$^{-3}$) of intrinsic states
with deformation parameter $\beta = 2.8$ (a), 3.2 (b), 3.6 (c), and 4.0 (d). }
\end{figure}

\begin{figure}[]
\centering
\includegraphics[width=8.2cm]{fig7.eps}
\caption{\label{density2}(Color online) The density distribution (in fm$^{-3}$) of each s.p. state corresponding to the mean-field configuration with $\beta=3.2$ in $^{16}$O. The s.p. states are labeled with the quantum numbers [$n_xn_yn_z$] of the largest component in the HO basis for the large component of Dirac spinor, cf. Eq.(\ref{expansion}).}
\end{figure}

\begin{figure}[]
\centering
\includegraphics[width=8.2cm]{fig8.eps}
\caption{\label{weight}(Color online) The weight $\vert f_{\alpha k}\vert^2$ [cf.(\ref{expansion})] of the most dominated components $[n_xn_yn_z]$ in the HO basis for the large component of Dirac spinors in the mean-field configuration with $\beta= 3.2$ in $^{16}$O as a function of quantum number $n_z$. }
\end{figure}

Figure~\ref{density1} displays the density of the dominated mean-field configurations in the $4\alpha$ LCS candidate states with deformation parameter $\beta= 2.8, 3.2, 3.6$ and 4.0. The $4\alpha$ LCS is shown clearly in these configurations, especially at $\beta = 3.6$. The distribution of the collective wave functions of $0^+, 2^+, 4^+$ LCS candidate states in Fig.~\ref{wfs} shows that the configuration with $\beta=3.2$ is the most dominated component, although the total energy curve exhibits a shoulder at $\beta=3.6$. It indicates that the GCM+PN1DAMP calculation gives a less $4\alpha$ LCS. To understand the nature of the $4\alpha$ LCS candidate states, the total intrinsic density of mean-field state at $\beta = 3.2$ is decomposed into the densities of the four lowest occupied s.p. states, as shown in Fig.~\ref{density2}. Our main findings are as follows:

\begin{itemize}
\item[i)] Integration of the densities in panel (a), (b), (c) and (d) of Fig.~\ref{density2} over the coordinate gives 4.00, 3.98, 4.00, 2.65, respectively, which turns out to be 4.00, 3.99, 4.00, 3.51, respectively for the configuration with $\beta=3.6$. Due to pairing correlation, the missing $\sim1.35$ particles  ($\sim0.70$ neutrons and $\sim0.65$ protons) at $\beta=3.2$ or $\sim0.5$ particles ($\sim0.25$ neutrons and $\sim0.25$ protons) at $\beta=3.6$ are scattered to a higher neutron and proton negative-parity state.
\item[ii)] To study the localization of nucleons in these s.p. states, following Ref.~\cite{Ebran13PhysRevC.87.044307} we calculate the localization parameter $\alpha =\sqrt{\langle r^2\rangle-\langle r\rangle^2}/\bar r$, where the average internucleon equilibrium distance is chosen as $\bar r = 0.9$. We obtain 1.2 for Fig.~\ref{density2}(a) and Fig.~\ref{density2}(c) and 1.8 for Fig.~\ref{density2}(b) and Fig.~\ref{density2}(d), all of which are much larger than the typical value $\sim1.0$ of localized clustering state.

    For the configuration at $\beta=3.6$, which has the most evident $4\alpha$ LCS, the localization parameter $\alpha$ becomes 1.4 and 2.1, respectively, slightly larger than those at $\beta=3.2$.
\item[iii)] The weight of the most dominated HO components [$n_x, n_y, n_z$] in the  four lowest s.p. states [cf. Fig.~\ref{density2}] is displayed in Fig.~\ref{weight}, where $n_x, n_y$ turn out to be zero in all the dominant HO components. The composition of s.p. wave function indicates the one-dimensional character of the $4\alpha$ LCS in the mean-field state at $\beta= 3.2$.  We note that the s.p. states labeled with the [004] and [001] in Fig.~\ref{density2}(b) and (d) actually have other competing HO components, as a consequence of large deformation.
 \end{itemize}

 \subsection{High-spin states}

To search for the 4$\alpha$ LCS in high-spin states, we perform cranked RMF calculations with various rotational
frequencies. We choose the $x$-axis as the cranking axis and start the calculations from a triaxially deformed
Woods-saxon potential~\cite{Koepf1991ZPhyA.339.81}. Table~\ref{tab2:crank} lists the properties of convergent solutions with the rotational frequencies $\omega$ in between 2.75 and 4.00 MeV.  These solutions correspond to the 4$\alpha$ LCS states found in the cranking SHF calculation, but with the cranking frequency $\omega$ higher than the value in between 1.9 (2.0) and 2.2 (2.1) MeV using SkI4 (SLy6) force~\cite{Ichikawa11}. The angular momentum for these states ranges from 12.6$\hbar$ to 18.0$\hbar$, which is almost the same as that by the cranking SHF calculation~\cite{Ichikawa11} as a consequence of its quantum nature. According to the definition of angular momentum $\sqrt{J_{\rm cra}(J_{\rm cra} + 1)} = \langle \hat J_x\rangle^2$, where $\langle \hat J_x\rangle = \sum^A_{k=1} \langle k\vert \hat j_x\vert k\rangle$, one finds that the angular momentum $J$ is defined by the spin direction of all nucleons, different from the classic quantities (such as radius and MOI) which are much dependent on the nuclear density distribution. The difference in the cranking frequency comes from the different MOI of the states. The MOI ${\mathscr J}$ in the present relativistic calculation is smaller than that in the non-relativistic calculation. The angular momentum deduced from the rigid-body MOI can be calculated as $J_{\rm rid} = {\mathscr J} \omega$, and this value is found to be similar to the cranking value $J_{\rm cra.}$. The deformation $\beta$ of these states ranges from 2.1 to 2.6, which is much smaller than that of the dominated mean-field states in the GCM states with LCS. Moreover, these states deviates slightly from axial symmetry with $\gamma=356^\circ$. It is shown that the spin-orbit interaction energy $SO1$ is very close to the sum of spin-orbit splittings $SO2$, which has been also found in the mean-field configurations of low-spin LCS states, cf. Fig.~\ref{pes}. However, this value is about 1.5 times of that in the dominated configurations of low-spin LCS states, indicating the larger mixing of $\alpha$-breaking component in high-spin states. We note that the spin-orbit interaction energy is decreasing with cranking frequency, which is also found in the cranking SHF calculation~\cite{Iwata14}.

\begin{table}[]
\tabcolsep=4pt
 \caption{\label{tab2:crank} The rotational frequency $\hbar\omega$ (MeV), angular momentum $J(\hbar)$, total energy $E_{\rm tot}$ (MeV), deformations ($\beta,\gamma$),  charge radius (fm), and the spin-orbit energies $SO1$ and $SO2$ (MeV). The angular momentum with the rigid-body MOI is calculated as $J_{\rm rid} = {\mathscr J} \omega$, where the MOI $1/(2{\mathscr J}) = 0.11$ (MeV$\hbar^{-2}$) is obtained from the parametrization of the energy from the cranking RMF calculations to the rotational formula $E_{\rm tot}(J_{\rm cra}) = J_{\rm cra}(J_{\rm cra} + 1)/(2{\mathscr J})$.}
 \begin{tabular}{c|ccccccc}
   \hline
   ($\hbar\omega$)& $J_{\rm cra}$   & $J_{\rm rid}$    & $E_{\rm tot}$ & $(\beta,\gamma)$  & $R_{\rm ch}$   & $SO1$   & $SO2$  \\
   \hline
   0.00 & 0 & 0 & $-127.2$ & ($0.0, 0^\circ$)  & 2.76 & 0.8  & 16.2 \\
   \hline
   2.75 & 12.63 & 12.73 & $-78.3$ & ($2.13, 357^\circ$)  & 3.55 & 6.9  & 6.9\\
   3.00 & 13.55 & 13.89 & $-75.6$ & ($2.16, 356^\circ$)  & 3.57 & 6.4  & 6.5 \\
   3.25 & 14.46 & 15.05 & $-72.8$ & ($2.20, 356^\circ$)  & 3.61 & 5.9  & 6.0 \\
   3.50 & 15.39 & 16.20 & $-69.7$ & ($2.27, 356^\circ$)  & 3.64 & 5.5  & 5.6 \\
   3.75 & 16.43 & 17.36 & $-65.9$ & ($2.39, 356^\circ$)  & 3.70 & 5.0  & 5.1 \\
   4.00 & 17.96 & 18.52 & $-60.1$ & ($2.65, 356^\circ$)  & 3.82 & 4.3  & 4.6 \\
   \hline
 \end{tabular}
 \end{table}

\begin{figure}[]
\centering
\includegraphics[width=8.6cm]{fig9.eps}
\caption{\label{densityomega}(Color online) The total density distribution (in fm$^{-3}$) at $x = 0.3$ fm in $^{16}$O corresponding to LCS by the cranking RMF calculation with rotational frequency $\hbar\omega= 3.0, 3.5, 4.0$ MeV, respectively. The rms radii of (long, mediate, short) axis are (a) ($3.0$,$1.3$,$1.1$) fm, (b) ($3.1$, $1.4$, $1.1$)  fm, and (c) ($3.3$, $1.4$, $1.1$) fm, respectively.}
\end{figure}

\begin{figure}[]
\centering
\includegraphics[width=8.6cm]{fig10.eps}\vspace{-0.5cm}
\caption{\label{speomega}(Color online) Energy ($\varepsilon_k$) of occupied s.p. states in $^{16}$O by the cranking RMF calculation as a function of cranking frequency $\hbar\omega$.  Each s.p. state is labeled with the quantum number of the largest HO component [$n_xn_yn_z$] in the large component of Dirac spinor, cf.~(\ref{expansion}).}
\end{figure}

Figure~\ref{densityomega} displays the density distribution of the states at the rotational frequency $\omega =
3.0, 3.5, 4.0$ MeV, respectively. It is shown that the $4\alpha$ LCS is less obvious than that shown in the mean-field configurations illustrated in Fig.~\ref{density1} and that by the cranking HF calculation based on the non-relativistic Skyrme EDF~\cite{Ichikawa11}. The length of the longest $z$-axis with total nucleon density $\rho\leq0.02$ fm$^{-3}$ is $\sim13$ fm, much shorter than that ($\sim16$ fm) in the non-relativistic Skyrme calculation~\cite{Ichikawa11}. It provides a simple explanation for the smaller MOI ${\mathscr J}$ (by a factor of $1.5-1.8$) in the present calculation.
Moreover, the density around the central (tip) region is decreasing (increasing)  as the rotational frequency increases due to the increase of the centrifugal force.

Figure~\ref{speomega} displays the energy of occupied s.p. states by the cranking RMF calculation as a function of rotational frequency $\omega$. Each state is labeled with the quantum number of the largest component $[n_xn_yn_z]$ in the large component of Dirac spinor. Time-reversal partner s.p. states are not degenerated due to the violation of time-reversal invariance by the time-odd fields. Therefore, one observes two s.p. states with the same quantum numbers $[n_xn_yn_z]$ but different energies. Moreover, it is shown that except the levels around the Fermi energy, all the s.p. levels are labeled with $n_x = n_y = 0$, just different from each other by the quantum number along $z$-direction, which illustrates the one-dimensional character of these states.

\begin{figure}[]
\centering
\includegraphics[width=8cm]{fig11.eps}
\caption{\label{E_I}(Color online) Excitation energy of the state in Tab.\ref{tab2:crank} as a function of angular momentum $J(J+1)$ predicted by the cranking RMF calculation. The dashed line is by the rotational formula $E(J_{\rm cra}) = J(J + 1)/(2{\mathscr J})$ with the MOI $\hbar^2/(2{\mathscr J}) = 0.11$ MeV}
\end{figure}

\jmy{The results of the cranking RMF calculation are plotted in Fig.~\ref{E_I}, which displays the excitation energy as a function of the angular momentum $J(J + 1)$.  The band-head excitation energy by the extrapolation from the cranking RMF results is 30.2 MeV at $J=0$, very close to the energy 29.6 MeV of $0^+$ state by the GCM+PN1DAMP calculation. The MOI is estimated to be $\hbar^2/(2{\mathscr J}) = 0.11$ MeV, larger than the value $0.06-0.08$ MeV obtained from the cranking SHF calculation. In other words, we obtain a smaller MOI ${\mathscr J}$ , which is multiplied with a higher rotational frequencies $\omega$ resulting the same angular momentum as the cranking SHF calculation for LCS candidate states.}

 \section{Summary}
 \label{concluson}

We have \jmy{searched for} the $4\alpha$ linear-chain structure in both low-spin and high-spin excited states of $^{16}$O within a covariant density functional theory. The low-spin states have been calculated by configuration mixing of particle-number and angular-momentum projected quadrupole deformed mean-field states from deformation constrained RMF+BCS calculation. The high-spin states have been determined by the cranking RMF calculation. Our conclusions for the linear-chain structure in high-lying low-spin and high-spin states are summarized as follows:
\begin{itemize}
\item[i)] For the low-spin candidate states, an evident $4\alpha$ LCS has been shown in the dominated intrinsic configurations. The analysis of the intrinsic configuration suggests that the $4\alpha$ clusters stay along a common axis. \jmy{Due to the mixing of $\alpha$-cluster breaking components, the spin-orbit energy is not zero but turns out to be much smaller than that of shell-like state. Moreover, the spin and orbital angular momenta are parallel in this alpha-cluster breaking components.} The dynamical correlation effects from restoration of rotational symmetry and configuration mixing play an important role in lowering ($\sim$9 MeV) the excitation energy of these exotic states. Besides, the energies and $B(E2)$ values of the rotational band built the second $0^+$ state has been reproduced  rather well in a fully microscopic way.

\item[ii)] For the rotational high-spin states, the MOI and band-head ($J = 0$) excitation energy are estimated to be around 0.11 MeV and 30 MeV, respectively, which are slightly different from the results ($0.06-0.08$ MeV and 38 MeV) of the $4\alpha$ LCS states found in the previous cranking SHF calculations.  However, the existence of $4\alpha$ LCS in the high-spin states found in the present work is less obvious due to the large mixing of $\alpha$-breaking components, even though these states are found at the same angular momentum region, i.e. $13-18\hbar$.
\end{itemize}

Finally, we point out that the present study demonstrates the ability of the projected GCM based on the CDFT for the cluster structures in nuclear low-spin states. The extension of the present study to the cluster structures in excited states of other light nuclei is also very interesting, such as the stability of clusters found in superdeformed states of Ar isotopes against the shape fluctuation~\cite{Lu2014PhysRevC.89.044307}. For some other exotic cluster states, however, the other shape degrees of freedom, such as octupole deformation might be required. Work along this direction is in progress. Moreover, we note that for the high-spin states the cranking solutions pertain to the intrinsic frame and therefore cannot directly be compared
to experiment. The implementation of AMP technique for time-reversal violated system is necessary to carry
out a detailed spectroscopic study for the high-spin states. Some efforts have recently been devoted along this
direction based on the non-relativistic Skyrme EDF~\cite{Zdunczuk07PhysRevC.76.044304,Bally12}. The
application of such methods for the clusters in nuclear high-spin states will also be very interesting.

\begin{acknowledgements}
The authors thank discussions with K. Hagino and Y. Funaki and the discussions during the YITP
workshop YITP-W-99-99 on ``International Molecule-type Workshop on New correlations in exotic nuclei and
advances of theoretical models", which are helpful to complete this work. This work was supported in part by the Tohoku
University Focused Research Project ``Understanding the origins for matters in universe", the Major State 973 Program 2013CB834400, the NSFC under Grant Nos. 11305134, 11175002, 11105111, and 10947013, and the Fundamental Research Funds for the Central Universities (XDJK2010B007 and XDJK2013C028).

\end{acknowledgements}

\bibliographystyle{apsrev4-1}

redpajama_set_name: RedPajamaArXiv


text:
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text:
Q: jQuery plugin not processing disabled property on option tags My .net website is using a jQuery plugin; I have the following code on a simple .aspx page:
<select id="Select2" name="categoryFilter">
    <option class="inactiveLabel" value="A" disabled="disabled">A</option>
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    <option class="inactiveLabel" value="B" disabled="disabled">B</option>
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When I load the page in a browser, the jquery plugin adds a style="display: none;" property on the < select > tag and converts the above code to the below, which in turn shows up on the page:

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Q: segmentation fault with memcpy (C) I encountered "segmentation fault" error when running the following code, but I am wondering why:
int main()
{
char *str = "abcdefghijklmn";
void *str_v;

memcpy(str_v, str, 14);

printf("str_v is %s \n", (char *) str_v);
return 0;
}

Thanks for help.

A: void *str_v;

defines str_v to be of type void *, i.e., it can store a pointer a variable of any type. However, you need memory space for the characters to be copied by memcpy from the source to the destination. Therefore, you need to allocate enough memory using malloc -
char *str_v = malloc(strlen(str) + 1);

strlen does not count the terminating null byte in the string pointed to by str. Therefore, you have to allocate one extra byte for the terminating null byte.
#include <stdio.h>
#include <stdlib.h>
#include <string.h>

int main(void) {
    // a string literal is read-only so make str
    // const so attempting to change will cause
    // compiler error
    const char *str = "abcdefghijklmn";

    // allocate memory dynamically to the
    // string pointed to by str. +1 is for the
    // terminating null byte since strlen does
    // not count the null byte
    char *str_v = malloc(strlen(str) + 1);

    // malloc can fail if there is not enough
    // memory to allocate. handle it
    if(str_v == NULL) {
        printf("error in memory allocation\n");
        return 1;
    }

    // copy all bytes in the string pointed to
    // by str to the buffer pointed to str_v.
    // number of bytes to be copied is strlen(str) + 1
    // +1 for copying the terminating byte as well
    memcpy(str_v, str, strlen(str) + 1);

    // print the copied string. It need not be
    // cast to (char *) since str_v is already
    // of type (char *)
    printf("str_v is %s \n", str_v);

    // free the dynamically allocated space
    free(str_v);
    return 0;
}

A: You need to first allocate memory for str_v:
void *str_v = malloc(14);

A: You are using uninitialized pointer in memcpy(str_v, str, 14);, to fix it, you could add the following statements before it:
str_v = malloc(14);
if (str_v == NULL) { /* malloc failed */ }

A: Because you have not allocated any memory for str_v

A: You can just do
char * str_v = strdup( str );

From http://linux.die.net/man/3/strdup:
#include <string.h>

char *strdup(const char *s);

The strdup() function returns a pointer to a new string
which is a duplicate of the string s.
Memory for the new string is obtained with malloc(3),
and can be freed with free(3).


text:
Q: Is momentum equivalent to a virtual shift in position? I have been reading a paper that offhandedly describes shifting the origin of a position term in a harmonic oscillator potential, as being equivalent to adding a momentum term in the Hamiltonian.
"This is a shift in the origin of the coordinates and, being a virtual shift in the position, produces a term in the dynamical equation for the position proportional to the rate at which the trap is being shifted."
So I am imagining the coordinate shift as,
$x \to x+\Delta x,$
but to produce the change described in the dynamical position equation, sounds like it requires this change in the Hamiltonian,
$H \to H + (\frac{\partial}{\partial t} \Delta x)\, p$
I can't see how these two things are equivelent?
A. C. Doherty, K. J. Feedback control of quantum systems using continuous state estimation. Phys. Rev. Lett. 60, (1999).

A: Disclaimer, I haven't read the paper.
In the paper [1] the author defines the following relationship:
$$
\dot x = \frac{p}{m}
$$
in eq (36). The author is defining an optimal control problem, whereby feedback terms are added to the Hamiltonian in both of the phase space variables $(x,p)$. It is stated that this is readily performed for $x$, but not so for $p$.
The author states that there are two possible approaches to achieve this.
In the first, the desired term in the Hamiltonian is proportional to the rate at which the position is shifted. He states this is a 'virtual shift' since it is a shift in the origin of the coordinates.
I would imagine the following transformation:
$$
x' = x + \dot x dt = x + \frac{p}{m}dt
$$
There is now a linear momentum term in the Hamiltonian; therefore, a degree of freedom for the feedback control.
The second method is to apply a large impulse $J$ to the system:
$$
J = \int F dt = \int \frac{dp}{dt} dt = \int dp = \delta p
$$
This creates a shift in $x$ and the feedback control is through the equal and opposite impulse on the 'reset momentum'.


Police have arrested 22 people working at one of Israel's biggest commercial banks over suspected money-laundering.
The Bank Hapoalim employees are thought to have been involved in an operation worth hundreds of millions of dollars.
Police chief Amichai Shai said the affair was one of the largest in Israeli history and involved funds from several other countries.
Investigators say employees helped customers move money without reporting the transfers.
"It appears they helped customers transfer funds without reporting it as required by law. We are talking about hundreds of millions of dollars," Mr Shai said at a press conference.
Police said that funds had passed through the bank from many countries but cited only France as one of them.
Police said they were examining more than 80 bank accounts linked to 170 customers.
All the employees arrested worked at a central Tel Aviv branch of Bank Hapoalim.
After introducing anti money-laundering legislation, Israel was removed from an OECD money-laundering blacklist in 2002.
In a statement the bank said it had ordered its employees to co-operate fully with the investigation and said it had taken several measures to prevent funds being laundering through the bank.


TOTTENHAM manager Mauricio Pochettino admits he is worried VAR is going to change the "spirit" of the game and predicts fans will "see a different sport" in the future.
Pochettino made the comments after seeing his side seal a 1-0 victory against Manchester City in the first leg of their Champions League quarter-final tie.
The game saw several controversial issues, but it didn't take long for the video assistant referee to be involved.
VAR is set to be introduced into the Premier League next season and Pochettino believes there is concerned about how it will change the game of football.
The Argentine thinks there is still a lot of work to do in the off-season to get the system ready.
"I think there are many things that we need to try and make clear," Pochettino said.
Pochettino is calling for clear guidelines on how VAR going to be used next year.
"We need to be clear and set the protocol, so everyone knows or it is going to be a big problem," he said.
"It is going to be a tough summer, we need to be all involved to try to find the best way to work.
"It is going to be important if it is going to check everything, if it is only handball, it is aggression, I don't know.
VAR judged that Spurs defender Danny Rose had handled the ball in the box from a Raheem Sterling shot.
Sergio Aguero an opportunity to give City the lead from the penalty spot after 15 minutes but the penalty was saved by Hugo Lloris.
Harry Kane also suffered an injury in a challenge with Fabian Delph, which could rule out the Spurs striker for the rest of the season.
The 25-year-old suffered his injury as he slipped trying to block Delph's clearance on the right touchline.
Delph got to the ball first but his foot made contact with Kane's ankle on the follow through.
Pochettino believes if VAR was consulted Delph could have been given his marching orders.
"I said to [Delph] 'you were lucky'," Pochettino said.
"Because if checking on the VAR maybe, technically, it was a red card.
Pochettino feels the game at the Tottenham Hotspur Stadium shows there is still room for improvement with VAR.
"I think today shows that the system is still a lot of things to do, there is a lot of work to do," he said.
"You know there are many decisions where nobody knows if VAR is going to be in or not, if you are going to check or not.


text:
The 100 Season 4 Premiere, Marvel's RUNAWAYS Sets Start Date, and More TV News
Posted by Amy Ratcliffe on February 2, 2017
Season four of The 100 premiered last night, and the world is in trouble. Well, more trouble than usual. Read today's TV-Cap for our recap of the episode, as well as an interview with the creator and cast. You'll also find information on Marvel's Runaways, learn about a new A Song of Ice and Fire story from George R.R. Martin, and more.
A Wrecked World. Okay, Let's get into all things The 100. Don't worry–you won't find spoilers about the season four premiere, just about the end of season three. The last season ended with Clarke learning the world was about to fall apart because nuclear power plants were beginning to melt down. With only six months until the world will be destroyed, what's next for the gang? Sydney talked to series executive producer and creator Jason Rothenberg about the general plan and what he learned from last season. One big takeaway: "It was a little too dark. It was relentlessly dark." Read all his comments here at Nerdist.
And what's ahead for the characters? Cast members tease what's coming up for everyone in this Nerdist article. You won't find plot spoilers, but you will find information abut where all their heads are at.
Finally, how about the season four premiere? You can relive all the details by reading Sydney's recap (don't read it unless you've watched the episode, because spoilers).
Josie Sings. Here's what your morning needs: Josie and the Pussycats covering "Sugar, Sugar" on Riverdale. I like that even in moments of high school frivolity Riverdale manages to have a slightly creepy vibe–and it's not just because of the rain (is anyone else worried about the rain harming the musical instruments?). The next episode of Riverdale will air on February 2.
A New Story. George R.R. Martin has dropped the news he'll be writing another story set in the world of A Song of Ice and Fire. This is only tangentially related to TV news, but so many of y'all are Game of Thrones fans, so I'm including it just in case. Martin's new tale is another prequel story, and it's about Aegon the Conqueror's two sons. "The Sons of the Dragon" short will appear in the anthology title The Book of Swords; the book will be released on October 10. [Nerdist]
Names and More Names. Production of season two of The Shannara Chronicles is beginning in New Zealand, and the existing cast members are welcoming more names to the family. MTV has announced five additions to their line-up: Malese Jow will play Mareth, Vanessa Morgan will play Lyria, Gentry White is Garet, Caroline Chikezie is Tamlin, and Desmond Chiam will be Riga. Whew. Get more details about the characters at TVLine.
Look who'ssss back… Mark Gatiss has news regarding some old friends… #DoctorWho
A video posted by Doctor Who Official (@bbcdoctorwho) on Jan 31, 2017 at 9:01am PST
A Chilly Embrace. Doctor Who writer Mark Gatiss dropped by Instagram to announce the return of a familiar foe: Ice Warriors. Kyle A. points out the villains haven't been around much in the modern series–only once actually. Get more details on Ice Warriors here at Nerdist.
Lucky 13. Marvel's Runaways is headed to the TV series format for Hulu, and they've announced when production will kick off: February 13. The working titles for Runaways is "Rugrats." February 13 will also mark the beginning of filming for Cloak and Dagger. [CBR]
S'more Recaps. The 100 wasn't the only show that aired Wednesday night. Heck, no. We have recaps for the latest episodes of The Magicians, The Expanse, and Vikings.
What did you think of the premiere of The 100? Have any predictions about what's ahead? Sound off in the comments.
Featured Image: The CW
A Song of Ice and Fire, caroline chikezie, desmond chiam, Doctor Who, gentry white, george r.r. martin, jason rothenberg, Malese Jow, riverdale, runaways, television news, the 100, The Expanse, The Magicians, The Shannara Chronicles, TV news, TV-Cap, vanessa morgan, Vikings
SUPERNATURAL Stars Talk Seeing a New (or Old) Side to Castiel
VIKINGS Season Four Finale Recap: "The Reckoning"
THE 100 Creator, Cast Tease Their Characters' Season 4 Journeys
Take a Peek Inside GUARDIANS OF THE GALAXY: CREATING MARVEL'S SPACEFARING SUPER HEROES (Exclusive)

redpajama_set_name: RedPajamaCommonCrawl


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text:
Déc>
Postdoctoral fellow – University Pierre and Marie Curie, Paris
Subject: Formation of calcified roots in terrestrial sediments
Terrestrial sediments are commonly used for paleoenvironmental reconstructions. However such reconstructions may be biased by the presence of calcified roots (rhizoliths). These objects, which may be rather abundant (up to 20 000 per m2), are usually not syngenetic to the embedding sediment. A better knowledge of their formation mechanism appears crucial to better use terrestrial paleoenvironmental archives.
To this aim, the "Environmental Geochemistry" group of the "Biogeochemistry and Ecology" lab (BioEMCo) from UPMC and the "Mineralogy and Cosmochemistry" lab (LMCM) of the French National History Museum (MNHN) seek applications to a postdoc position in an interdisciplinary, young and dynamic team of organic geochemists and mineralogists.
The position will be funded through a Labex Matisse (Paris) fellowship for one year, with a starting date in mid-2013.
During the funded year, natural rhizolith samples will be characterized at a multiple length scale using a combination of organic geochemistry and mineralogy techniques, involving gas and liquid chromatography coupled to mass spectrometry, Raman microspectroscopy, scanning and transmission electron microscopy and synchrotron-based X-ray absorption microspectroscopy.
The ideal candidate should thus have a solid background in organic geochemistry and/or biogeochemistry and be interested in using recently-developed analytical techniques. Applicants must have the ability to work in a team, have good communication skills and should be highly motivated and committed to pursuing such interdisciplinary research. They must also have demonstrated record of presenting and publishing research results.
The post-doctoral fellow will benefit from the widely recognized expertise of the two involved labs in their respective area. The project will also rely on collaborations with Guido Wiesenberg (University of Zurich) and Martina Gocke (University of Bayreuth).
Applications including a detailed CV and a motivation letter should be sent by email to Dr Arnaud Huguet (arnaud.huguet[a]upmc.fr) or Dr Sylvain Bernard (sbernard[a]mnhn.fr)
Poste d'ingénieur de recherche à l'Université de Stockholm
Poste IR en analyses géochimiques à l'ISTO
Offre de thèse au LIEC-Nancy


text:
Q: How to find historically how many EC2 instances have been spun up by Elastic Beanstalk? I have an API powered by an Elastic Beanstalk setup with an instance count setting between 1 and 24. Historically when the load become heavier, it did has spun up additional EC2 instances.
We're planning to significantly increase the load to the API, I'm trying to explore current utilisation and scalability of the setup. I'm tackling this with following approach:

*

*Get hold of historical API call count & throughputs and I have managed to retrieve the data.

*Check out historically how many EC2 instances EB has spun up and what're the instance type/size used

*Workout the relationship between API call count/throughput and EC2 instance count/size.

*Project the required EC2 instance count/size for the future hence the cost as well.

I'm currently stuck with step 2. I found this link to identify EC2 instance that's currently used by EB but not sure how to find out the historical data.
Any advice would be appreciated.
Cheers

A: You can enable extra metrics on the Auto Scaling Group, which will allow you to display the count metrics you are looking for on the Elastic Beanstalk monitoring page.
From the EC2 console, click Auto Scaling Groups in the left-hand navigation and click on the autoscaling group associated with your Elastic Beanstalk application. (If you don't know the auto scaling group, you can find it by clicking on one of the EC2 instances, selecting the Tags tab, and finding the aws:autoscaling:groupName value.) After you have selected the correct auto scaling group, click the Monitoring tab, and check the "Auto Scaling group metrics collection: Enable" checkbox.

Once that is enabled, go back to the Elastic Beanstalk console, select the environment, and click the Monitoring link in the left-side navigation. In the Monitoring section, click Edit, and in the Add Graph section, select "AWSEBAutoScalingGroup" for the resource. Under the "CloudWatch metric" options, you should now see some new metrics with the "Group" prefix (note that it may take up to 5 minutes for the new metrics to appear):

You can create a metric with "GroupMaxSize", selecting "Maximum" as the Statistic in order see the instance counts launched by the autoscaler over time.


text:
Sea Eagles v Roosters preview
Fri 27 Jun 2014, 05:31 PM
Sea Eagles v Roosters
Brookvale Oval
This tantalising Grand Final rematch-rematch and resumption of the 'Angry Birds Cup' sees the defending premiers head north over the Spit Bridge looking to avenge their shock 8-0 loss at Allianz Stadium back in Round 4.
The Chooks did get the better of the Sea Eagles four times from four in 2013, including the one that counted most on the first Sunday in October, but that's all behind us now as we look ahead to this top-four clash.
Both sides head into this week in good form and reasonably close to full strength. It's hard to know how much to read into Manly's 26-0 disposal of the hapless Sharks last week but their previous game (which was in Round 13, before their second bye) was a clinical 32-10 dismissal of a full-strength Bulldogs outfit at Brookvale.
Only Glenn Stewart, who is still on his way back from ankle surgery, and the suspended Anthony Watmough are unavailable from Manly's best 17, and Geoff Toovey has opted for the same squad that lapped the Sharks last week, although Jamie Buhrer and Dunamis Lui switch, with Lui going to lock and Buhrer to second row. Given Manly continued racking up wins with the likes of Daly Cherry-Evans, Kieran Foran, Brett Stewart and Jamie Lyon out injured it's still a formidable-looking side even with two Test back-rowers sitting out.
As ladder leaders and one of just two teams, along with the Panthers, on 22 competition points, it's important for Manly to chalk up one more home win before their glut of away games (seven of their last 10 away from Brookvale) kicks off with a trip to ANZ against the Bulldogs next week.
The Roosters are in a similar boat, racing up to fourth on the ladder just a win behind Manly on the back of four straight victories. They'll be well rested after their Round 15 bye, which followed big wins over the Knights and Storm in the previous two weeks. With Test back-rower Boyd Cordner returning from an ankle injury on the bench, Origin centre Michael Jennings (elbow) is the only notable absentee from their top 17.
He was missing from their last game, in Round 14, due to Origin commitments – meaning Mitch Aubusson stays in the centres, although Dan Tupou returns on the wing, displacing Nene McDonald. Aidan Guerra also returns from Origin pushing Dylan Napa to a five-man bench with Willis Meehan dropping off. Hooker Heath L'Estrange is named on the bench for the first time, in jersey 18, with utility Dan Mortimer having packed his bags and moved to the Gold Coast.
Unlike Manly, the Roosters have a fair run home with six of nine at Moore Park and a bye still up their sleeve. A win here, with a home match against the poor old Sharkies next week followed by a bye, could help the Roosters make a serious charge up towards top spot on the ladder.
Get your ticket to NRL Round 16
Watch Out Sea Eagles: The Roosters are one of the most dangerous ball-running sides in the competition, having broken 409 tackles so far this season (third most) while they have easily the most line breaks of any side. Their 82 line breaks in 14 games is well clear of the second-placed Eels (74). The danger men here, not surprisingly, are their halves. James Maloney has the equal-most line break assists in the competition with 16, and is just one ahead of his halves partner Mitchell Pearce, who has 15. The recipients have been their classy back three, with wingers Daniel Tupou and Roger Tuivasa-Sheck (both 12) and fullback Anthony Minichiello (10) all in the 10 best players in the competition for line breaks this year.
Watch Out Roosters: While we're on line breaks, Manly centre Steve Matai is the outright competition leader, with 14, and he's equal second when it comes to tries, with 11 four-pointers in 13 games. His outside man Jorge Taufua is racking them up too, with seven tries in his eight games. That left edge has been the go-to zone for Manly this year with dramatic effectiveness. Maybe it's because right-side specialist Glenn Stewart has been missing for most of the season, maybe it's because his in-form brother, fullback Brett (a staggering 14 try assists in 10 games) has been favouring the left, but for whatever reason, that zone has been devastating for Manly this year so the Roosters' right-edge pair of Tuivasa-Sheck and Shaun Kenny-Dowall will need to bring their defensive games.
Plays To Watch: Brett Stewart gliding into the above-mentioned formation with a cheeky grubber when he spots the opposition short at the back; the Roosters to make excellent use of decoy runners and second-man plays to give their halves a confusing array of ball-runners to send through half-gaps; Jamie Lyon to prove why the Sea Eagles shouldn't neglect their right-side attack with his effective draw-and-flick-pass; the Roosters' ex-Origin halves to show the incumbents exactly how you send towering 6'5" winger Dan Tupou on an aerial raid with some well-placed cross-field bombs.
Where It Will Be Won: Discipline. The Roosters, as we've come to expect, are one of the most penalised teams in the competition – their 107 infringements is third-worst in the competition behind Wests Tigers (111) and Gold Coast (109) while Manly, at just 70, have felt the referees' wrath fewer times than any other side. Given this match will be at Brooky, with a partisan home crowd just metres away to loudly remind the refs any time they feel the visitors are inside the 10, the Roosters can't expect any leg-ups and will be on the back foot quickly if they can't control their discipline. In particular, Jared Warea-Hargreaves (15 penalties conceded, equal-most) and Jake Friend (14 penalties, equal third most) have been too sloppy around the ruck and will need to tighten it up here.
The History: Played 134; Sea Eagles 85, Roosters 47; drawn 2. These two sides seem to go on some peculiar streaks – before Manly's Round 4 win the Chooks had won four straight. The previous four were split two apiece but before that it was Manly with six in a row, the Roosters won five of six before that, Manly five straight before that. Read into that what you will but with Manly having almost a two-to-one advantage overall and a close to 80 per cent advantage over the Tricolours at Brookvale the history is certainly on their side.
What Are The Odds: Punters at Sportsbet.com.au can't split the two teams with money running 50:50 in the head-to-head market. Better support though for the Roosters in line betting, getting 1.5 start. For latest odds and betting options go to Sportsbet.com.au.
Match Officials: Referees – Shayne Hayne & Gavin Morris; Touch Judges – Russell Turner & Brett Suttor; Video Referees – Bernard Sutton & Luke Patten.
Televised: Channel Nine, Live, 7.30pm (NSW); Channel Nine, Delayed, 9.30pm (Qld).
The Way We See It: A real mouth-watering clash of flying feathers, this is a tough one to pick. The Roosters will be well-rested after the bye, which may help or hinder them, although aside from Origin halfback Cherry-Evans the rest of the Manly squad had a week off prior to the low-intensity game against the Sharks. The home ground advantage may tip the scales slightly towards the northern beaches boys but we'll take the defending premiers to make it five in a row with a tight win. Roosters by two points.


text:
Q: Kafka consumer not getting a single message from partition I just noticed that when I produce a single message into a partition, my consumer is not receiving it. Only after I produce a few more messages into the same partition, the consumer receives them. My fetch.min.bytes is set to 1.
Is there some other config that could affect here?
I have a dedicated consumer for each partition.
Consumer code for the relevant part. My consumer starts several threads for different topics that are defined by the configs['stream']. Uses https://github.com/mmustala/rdkafka-ruby which is a fork from original consumer gem. I added a batch consuming method. And a method to shut down the consumer in a managed way.
key = configs['app_key']
consumer = Rdkafka::Config.new(config(configs)).consumer
topic = "#{topic_prefix}#{app_env}_#{configs['stream']}"
consumer.subscribe(topic)

logger.info "#{rand}| Starting consumer for #{key} with topic #{topic}"
begin
  retry_counter = 0
  retries_started_at = nil
  current_assignment = nil
  partitions = []
  consumer.each_batch(configs['max_messages_per_partition'] || 5, 100, rand) do |messages|
    partitions = messages.collect {|m| m.partition}.uniq.sort
    logger.info "#{rand}| Batch started. Received #{messages.length} messages from partitions #{partitions} for app #{key}"
    current_assignment = consumer.assignment.to_h
    values = messages.collect {|m| JSON.parse(m.payload)}
    skip_commit = false
    begin
      values.each_slice((values.length / ((retry_counter * 2) + 1).to_f).ceil) do |slice|
        logger.info "#{rand}| Sending #{slice.length} messages to lambda"
        result = invoke_lambda(key, slice)
        if result.status_code != 200 || result.function_error
          logger.info "#{rand}| Batch finished with error #{result.function_error}"
          raise LambdaError, result.function_error.to_s
        end
      end
    rescue LambdaError => e
      logger.warn "#{rand}| #{e}"
      if consumer.running? && current_assignment == consumer.assignment.to_h
        retry_counter += 1
        retries_started_at ||= Time.now
        if retry_counter <= 5 && Time.now - retries_started_at < 600
          logger.warn "#{rand}| Retrying from: #{e.cause}, app_key: #{key}"
          Rollbar.warning("Retrying from: #{e.cause}", app_key: key, thread: rand, partitions: partitions.join(', '))
          sleep 5
          retry if consumer.running? && current_assignment == consumer.assignment.to_h
        else
          raise e # Raise to exit the retry loop so that consumers are rebalanced.
        end
      end
      skip_commit = true
    end
    retry_counter = 0
    retries_started_at = nil
    if skip_commit
      logger.info "#{rand}| Commit skipped"
    else
      consumer.commit
      logger.info "#{rand}| Batch finished"
    end
  end
  consumer.close
  logger.info "#{rand}| Stopped #{key}"
rescue Rdkafka::RdkafkaError => e
  logger.warn "#{rand}| #{e}"
  logger.info "#{rand}| assignment: #{consumer.assignment.to_h}"
  if e.to_s.index('No offset stored')
    retry
  else
    raise e
  end
end

config
def config(app_config)
  {
      "bootstrap.servers": brokers,
      "group.id": app_configs['app_key'],
      "enable.auto.commit": false,
      "enable.partition.eof": false,
      "log.connection.close": false,
      "session.timeout.ms": 30*1000,
      "fetch.message.max.bytes": ['sources'].include?(app_configs['stream']) ? 102400 : 10240,
      "queued.max.messages.kbytes": ['sources'].include?(app_configs['stream']) ? 250 : 25,
      "queued.min.messages": (app_configs['max_messages_per_partition'] || 5) * 10,
      "fetch.min.bytes": 1,
      "partition.assignment.strategy": 'roundrobin'
  }
end

Producer code uses https://github.com/zendesk/ruby-kafka
def to_kafka(stream_name, data, batch_size)
  stream_name_with_env = "#{Rails.env}_#{stream_name}"
  topic = [Rails.application.secrets.kafka_topic_prefix, stream_name_with_env].compact.join
  partitions_count = KAFKA.partitions_for(topic)
  Rails.logger.info "Partition count for #{topic}: #{partitions_count}"
  if @job.active? && @job.partition.blank?
    @job.connect_to_partition
  end
  partition = @job.partition&.number.to_i % partitions_count
  producer = KAFKA.producer
  if data.is_a?(Array)
    data.each_slice(batch_size) do |slice|
      producer.produce(JSON.generate(slice), topic: topic, partition: partition)
    end
  else
    producer.produce(JSON.generate(data), topic: topic, partition: partition)
  end
  producer.deliver_messages
  Rails.logger.info "records sent to topic #{topic} partition #{partition}"
  producer.shutdown
end

UPDATE: It looks like the number of messages is irrelevant. I just produced over 100 messages into one partition and the consumer has not yet started to consume those.
UPDATE2: It didn't start consuming the messages during the night. But when I produced a new set of messages into the same partition this morning, it woke up and started to consume the new messages I just produced. It skipped over the messages produced last night.

A: I believe the issue was that the partition had not received messages for a while and apparently it did not have an offset saved. When the offset was acquired it was set to the largest value which is the default. After I set auto.offset.reset: 'smallest' I have not seen such an issue where messages would have been skipped.


text:
What Music Means to Me?
I was trying to figure out a way to do some housekeeping without just blatantly pouring out a list of unconnected things aside from a glorified version of "what I did this past weekend." TJ was an inspiration to this solution, so props to his strange list. The irony is here that I'm going to get way more intimate than his little list will ever do to tell us about TJ_han.
I grew up mostly under the traditional, classical school of music, typical to East Asians. Fundamentally I am still heavily influenced by the lifestyle philosophy of my long-time piano teacher, who is this very nice but crazy piano woman that plays her art like…a crazy woman. In retrospect watching the Explosions in the Sky play last night (they were great, by the way) was not as crazy as how this shaggy, 5′ asian woman would pour all that she has upon the baby grand in her house during a usual practice session. Being a stereotypical motherly figure in the Faith she would hang the usual inspirational decorations on the walls of her house where she practices her trade. If you're unfamiliar with it, don't let it bother you. What stuck out in my memory after all these years was a plaque that said, simply and exactly as I still remember it today, "Music is the language of the soul."
It's a saying derived from the ideas of some dead people a long time ago, indeed, and one can question its worth in biblical truth. Nonetheless being the type of person who would choose to go blind rather than going deaf, if such a morbid selection I must make, I appreciate it. To me it's not merely just another form of art. It is a very special and unique mode to communicate.
Like a typical, sheltered Asian kid I didn't really have the freedom to explore music in my youth, especially since creating music wasn't my forte. What was available to me back in the day was what trickles out from the demoscene in the early 1990s–it was free, easily accessible (being the computer geek that I am), and it related to me much better than pop music. (Even though it was legal, it never bothered me to think along those lines.) And of course, mp3 piracy was barely in its infant stages then. In some way my "starvation" for this mode of expression only worsened in the space of a few years, in which exploded as I enrolled at my alma mater. It's no coincident that my appreciation for anime turned for the worse at around the same time mp3 piracy took off, as that became the decisive point in my life which the union of the two gave birth to my affection towards anime pop and soundtrack music. The catalyst was me having that kind of phat pipes during that turning point in internet history, at a premium geek school no less.
The marriage of visual and aural culture is partly what drives visual kei and the hard rock bands to their similar heights in popularity to some extent. Seeing Dir En Grey play last Friday was yet another testament to just how far things have come full circle. It was just a shame that the band before and after Diru's act were way better. Alas, my sense of classicism just doesn't slice the way popular trends do, sorry to all the fangirls who toughed the nasty tropical storm on the lawn like I did.
At least, it seems my sense of visual art kind of does slice the "popular" way. Being a new owner of Ugetsu Hakua's Flamboyant will put me in good company.
Maybe I'm slowly walking towards the deep end as my blog progress: putting words down to pin down songs and images, but sometimes that's the only way you can respond to these things, y'know? Nailing fansubbers down was a painful exercise because it pierced egos and people's mistaken beliefs, even if it may be cathartic. As fun as it could be, I'd rather dance to something much more anointed (and dare I say, progressive?).
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This entry was posted on Sunday, September 3rd, 2006 at 10:52 pm and is filed under Christian Living, Conventions and Concerts, Modern Visual Culture, Popular Culture, Seiyuu, Idol, Pop. You can follow any responses to this entry through the RSS 2.0 feed.
3 Responses	to "What Music Means to Me?"
September 4th, 2006 at 11:24 am
I give you mucho credit for sitting through a DeG concert. And yes, I feel similarly about music. I have mine playing at all times and take at least some form of it everywhere with me.
I do that too, take my music with me… but I'm probably a step short of saturating it in my living spaces all the time. Music I feel strongly about tend to get treated with more respect? I listen to them more, too, but there's a time and place for them. And there's also a time and place for silence…
TheBigN
September 8th, 2006 at 6:47 pm
Often, it is the absence of music which is more powerful than the music itself. And music is probably something that I will never forsake. It is something that I hope will always be with me, and it does really seem like the language of the soul at times. And then with others, it sounds like souls crying in agony. :3


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Steampunk is a magnificent movement that is, at once, a community, a visual aesthetic, and a subgenre of fiction.
While much of Steampunk fiction seems frivolous and glorifies colonialism and classism while denying the horrors and injustices of the Age of Steam, there is a wealth of texts that deal seriously with a variety of complex, contemporary social issues, some of which have obvious tie-ins to technology. Science, mathematics, psychology, sociology, economics and yes, even computer technology – and how mankind's use of these spheres of knowledge can lead to the best and worst of creations – are possible topics of discussion.
While the stories in the Steamfunk anthology are enjoyable reads – full of action, adventure, thrills and chills – they also pose important questions about the nature and the future of science, society, and commerce and issues of race, gender and class.
Most readers of Steamfunk will simply enjoy the courageous heroes and heroines, the bone-crushing battle scenes and the wondrous airships, aether weapons and mechanical monsters. Others, however, will consider the greatest virtue of Steamfunk to be its power as social commentary – which speaks, sometimes subtly and sometimes quite loudly, of the relation of technology to man, of what it means to be truly free and the ways in which industrialization affects how we relate to one another.
I knew, from the initial planning of Steamfunk to its release, that this book would be history making and world shaking; that the stories would be highly entertaining and deliver strong social commentary.
Because it's in the pedigree.
Steamfunk is a subgenre of Steampunk, which is a child of Cyberpunk – a subgenre of science fiction in which the future is one in which society is largely controlled by computers, at the expense of freedom, peace and social order.
In 1982, in his Science Fiction short story, Burning Chrome, William Gibson – the father of Cyberpunk – coined the word "cyberspace". At the time, few people had a concept of what such a term could come to truly mean. And yet, thanks to Gibson's use of it, especially in his epochal cyberpunk novel Neuromancer, "cyberspace" gradually gained enough cultural credence to become the de facto name for the emerging World Wide Web.
Science Fiction has always played an essential role in the dissemination and popularization of science's most nascent and speculative concepts. In the 1980s, when we were introduced to a fictional "cyberspace," we digested the idea until it became commonplace – a household word – and in the process, unwittingly prepared ourselves for massive cultural and technological change.
Since the Age of Steam and the scientific visions of Jules Verne and H.G. Wells, Science Fiction has been a future-changing medium. Although its role is not necessarily to be prophetic, it often fulfills its own predictions in surprising ways.
We literally live Science Fiction.
Ideas that seemed ludicrous in Science Fiction's "golden age" of the 1950s have long since become reality – geosynchronous communications satellites, famously dreamed up by Arthur C. Clarke; Karel Capek's "robots," first concocted in 1920; or cloning and neuro-enhancing pharmaceuticals, the subject of Aldous Huxley's Brave New World, penned in1931.
Science Fiction allows us to envision new realities; to feel invested in science even if we do not understand it. By seeing a version of the future in Science Fiction, we can begin to appreciate the myriad possibilities of science and also explore the potential negatives of its unintended consequences.
Imagining our future changes our perspective. As such, Science Fiction has long provided its writers remarkable leverage for political and social commentary, touching on practically every major sociopolitical theme throughout the history of man. When the writers Star Trek created conflicts between the crew of the Enterprise and alien life, they were using Science Fiction to deal with issues of race, Cold-War fears, and American imperialism. What kind of long-term effect this had on the political consciousness of its watchers is difficult to judge, but such engagement with complicated social issues is not a rarity in the genre; it's the norm.
True to its Science Fiction roots, Steamfunk takes our fears, hopes, and anxieties and frames them in a form that provides long-lasting meaning and value.
The authors of Steamfunk continue to create such climates. What will the next "cyberspace" be, or the next Moon landing, and who will invent it? Will "Steamfunk", "funktastic", or "Steamfunkateer" become household words in the next ten or twenty years?
Science Fiction writers in the year 2050 will be imagining the year 3000, and beyond, and so on. It is a living, breathing tradition that informs the very world it critiques, inventing new myths, words, worlds and realities.
In addition to Steamfunk's powerful expression as Science Fiction, just as powerful is its manifestation as Fantasy.
Fantasy, like Science Fiction, is a powerful tool for social commentary.
Loyalty, faith and identity may seem abstract to many, but in Fantasy, we do not experience these concepts in the abstract. They are, after all, real to the hero, in ways that evoke intense emotion in him or her and in the reader.
Our need to see the hero torn between loyalties, faiths and identities arises from a need to be torn ourselves – to do what we must; to believe as we do; to be who we are.
Fantasy stories, are fables of identity, set in a world where the demands of loyalty and faith are often absolute.
We writers are, indeed, some deep folks, ain't we?
So, yes, dear Steamfunkateers, as you peruse the pages of Steamfunk and lose yourself in all that funktasticality…realize that what you hold in your hands just might be the window to your future, or the keys that unlock the mysteries of your past.
So keep your goggles shined and your top-hats at the ready Steamfunkateers. The airship Sweet Chariot has landed and it's delivering uncut (Steam)funk!
Posted by Balogun on March 3, 2013 in Adventure, Afrofuturism, Dark Fantasy, Fantasy, Science Fiction, Speculative Fiction, Steampunk and tagged fantasy, science fiction, social commentary, steamfunk, steampunk.
I like the article, but I'm not sure of the connection between Steamfunk and my countryman riding the tchukudu and the people fleeing a vicious militia attack in the background. Its close to home.
Steamfunk deals with social issues that other subgenres of Science Fiction and Fantasy sweep under a rug. The connection is we authors of Steamfunk bring the hard issues to light, such as the plight of your countrymen, through well-crafted stories, more digestible and more powerful than any blurb in the news. Thanks, for your comment.
Excellent points made, I enjoyed this very much!
That was really beautiful. I only read the first two stories in Steamfunk! but they were fantastic. You got some great writers to work with there.
Thank you! I concur. The writers are absolutely funktastic!
First, thank you for producing such a fabulous blog. Is Steamfunk available in print? Or for Kindle? Either way I can't wait to read all the stories!
Thanks, so much, for your support!
As a black woman, I have been part of many genres of the Fantasy experience, whether in Renaissance England, or Italian City States, one thing is true This is not a Historical prospective. Steampunk is not real, it has never been based in reality and personally? I don't much need it to be so. My Character has money, as does my family because we worked hard and were able to be educated. I don't do Civil War Reenactment, because that is a Reenactment I don't do no ones laundry. But then I don't also base my life on the color of my skin, nor was I raised to do so. Instead I have Cosplay for fun. I don't reduce my experience to simply what nationality my forefathers were, but what COULD have been. That is what Steampunk is about, the sheer what if, and what would I have been….
I agree that one aspect of Steampunk is fantasy, but not pure fantasy. Remember, the tone of Steampunk as it is practiced is based on Victorian England culture and sensibilities. That is real history. The corsets, top hats, hoop skirts and derbies, social greeting and customs are real history. The steam technology has a non-fiction basis as well.
That being said, the beauty of the Steamfunk! anthology is that it presents Steampunk in all its aspects, from pure fantasy to steam/aether laced alternate history. Once you (hopefully) read it you'll see.
Well said, Milton! Thank you!
The post is very informative. I especially like the play on the Parliament Funkadelic in the title :).
Thanks, so much, for your feedback, Sheryse!
Sadly, I do not own a kindle. I would have loved to have purchased a hard copy of Steamfunk! The cover art by Marcellus Shane Jackson is gorgeous and your article 'MAKE MY FUNK THE STEAMFUNK, I WANT MY FUNK UNCUT: Steamfunk as Social Commentary' presents such a fascinating dimension to the steampunk movement. Really inspiring.
You can purchase a hard copy of Steamfunk here: http://www.mvmediaatl.com/. Hard copies will be available on Amazon and Barnes & Noble in a day or so.