text:
\section{\label{sec:Intro} Introduction}
One of the primary goals of heavy-ion collision experiments at ultra-relativistic energies  is to study the
thermodynamic aspects of strongly interacting matter at high temperature and density. While at low density
and high temperature, present experimental as well as lattice data seem to indicate a smooth cross over~\cite{nature05120_Aoki, PRL65_2491_Brown} from
hadronic to a quark gluon matter, at high density and low temperature the system is expected to have a first order
transition~\cite{PRD78_074507_Ejiri, PRD29_Pisarski, NPA504_Asakawa, PRD58_096007_Halasz, PRD67_014028_Hatta, PRC79_Bowman}.
So the first order phase transition at high densities and low temperature should end at a critical end point (CEP) - a second order phase transition point - as one moves towards high temperature and low density region, in the phase diagram of
strongly interacting matter~\cite{JHEP_Fodor, PTPS_Stephanov, PRD71_114014_Gavai, PRD75_Schaefer}.

Several experimental programmes have been launched to study the phase transition of strongly interacting matter.
At present, Relativistic Heavy-Ion Collider (RHIC) at Brookhaven National Laboratory and the Large Hadron Collider (LHC) at CERN are
providing us plethora of data. In near future the Facility for Anti-proton and Ion Research (FAIR) at GSI will also provide us a large
amount of information. The low temperature and high $\mu_B$ region will be studied
in Beam Energy Scan (BES) programme of RHIC and the Compressed Baryonic Matter (CBM) programme at FAIR.
Those experiments would also explore the first order line of the phase diagram along with the location of the CEP.

The unveiling of the nature of phase transition requires a proper understanding of Quantum Chromo Dynamics (QCD),
the theory of strong interactions. Unfortunately, the non-perturbative nature of the phenomena inhibits the use of
first principle QCD for the study of
strongly interacting matter at extreme conditions. In this regard Lattice QCD (LQCD) provides the
most direct approach to study QCD at high temperature ~\cite{PRD78_114503_Gavai, PRD79_074505_Cheng,
boyd, engels, fodor1, fodor2, allton1,
allton2,allton3,forcrand, aoki1, nature05120_Aoki, Bazavov, Borsanyi, Borsanyi_JHEP_11_77, PRD77_014511_Cheng}. However LQCD
has its own restrictions due to the discretization of space-time. Furthermore,
at finite chemical potential, LQCD faces the well known sign problem.

In contrast, effective models~\cite{Ray, Bhattacharyya, PRL102_032301_Stephanov} provide
a simpler alternative for the study of the strongly interacting matter in the non-perturbative domain. Some of these
models have been quite successful in describing physics of strongly interacting matter. For example,
Polyakov loop extended Nambu-Jona-Lasinio model (PNJL) has been used to study various aspects of physics of
strongly interacting matter at high temperatures  and found to reproduce the zero density lattice data quite
successfully~\cite{Ray, Bhattacharyya}. On the other hand, hadron resonance gas (HRG) model
\cite{HRG_Braun-Munzinger} has been very successful in describing the hadron yields in central
heavy ion collisions from AGS up to RHIC energies~\cite{PLB344_Braun-Munzinge, arXiv:nucl-th/9603004_Cleymans,
PLB465_Braun-Munzinge, PRC60_054908_Cleymans, PRC73_Becattini, PLB518_Braun-Munzinger, NPA772_Andronic, PLB673_Andronic}.

A reliable way to understand the physics of the phase transition of strongly interacting matter is to study the
correlations and fluctuations of conserved charges. Susceptibilities
are related to fluctuations via the fluctuation-dissipation theorem. A measure of the intrinsic
statistical fluctuations in a system close to thermal equilibrium is provided
by the corresponding susceptibilities. At finite temperature and chemical potential fluctuations of conserved charges are
sensitive indicators of the transition from hadronic matter to quark-gluon plasma (QGP). Moreover, the existence of the CEP can be
signalled by the divergent fluctuations. For the small net baryon number, which
can be met at different experiments, the transition from hadronic to QGP phase
is continuous and the fluctuations are not expected to lead to any singular behaviour.
Computations on the lattice have been performed for many of these susceptibilities at zero chemical potentials
\cite{gottlieb,gavai,bernard1,bernard2}. It has been shown that at vanishing chemical potential the susceptibilities
rise rapidly around the continuous crossover transition region.

Since the prediction of HRG model for the system at freeze-out is in very good agreement with
the experiments, it would be interesting to study the susceptibilities as well as higher moments
using this model and its interacting version {\it i.e.} Excluded Volume Hadron resonance gas (EVHRG)
model~\cite{PLB97_Hagedorn, ZPC51_Rischke, PS48_277_Cleymans, Singh, PRC56_Yen, PRC77_Gorenstein, PLB718_Andronic, PRC85_Fu,
begunprc88, PLB722_Fu, PRC88_Tawfik}. In fact as the higher moments are
expected to be more sensitive to the phase transition, any deviation of experimental observation
from the model results may be taken as an indication of new phenomena.

HRG model is based on the Dashen, Ma and Bernstein theorem~\cite{dashen} which shows that a dilute system of strongly
interacting matter can be described by a gas of free resonances. The attractive part of the hadron interactions is taken
care of by these resonances. On the other hand, both the long range attraction as well as the short range repulsion are
important for the description of strongly interacting matter~\cite{begunprc88}. Moreover, near critical temperature HRG
calculations tends towards Hagedorn divergence which may be due to the
absence of repulsive interaction~\cite{PLB718_Andronic}. This repulsive part is incorporated through the excluded volume
effects in the HRG~\cite{ZPC51_Rischke} and is commonly known as EVHRG model.
EVHRG equation of states have also been used for the hydrodynamical models of Nucleus-nucleus collision~\cite{hama,werner,satarov}.
In the present work we will be discussing our results of susceptibilities and correlations using EVHRG model.

Recently fluctuations of conserved charges, using HRG model, have been studied
in Ref.~\cite{Mohanty} where actual experimental acceptances in terms of pseudo-rapidity and transverse momentum are considered.
In Ref.~\cite{PLB722_Fu}, higher moments of net-proton multiplicity have been studied using EVHRG model.

Our aim in the present work is twofold. Firstly we would like to have a physical understanding of the EVHRG model results
vis-a-vis HRG, lattice and experimental data. Secondly, we would like to study the high density sector to be explored in beam
energy scan at RHIC and CBM experiment at FAIR.

Here we present the temperature ($T$) and baryonic chemical potential ($\mu_B$) dependence of
susceptibilities of different conserved
quantities such as net-baryon number, net-strangeness and net-charge up to order four using EVHRG model.
Baryon-strangeness and charge-strangeness correlation functions have been evaluated at different $T$ and $\mu_B$.
Different values of baryon and meson radii have been used to study their effect on susceptibilities and correlations.
We have discussed experimental observables in the framework of HRG as well as EVHRG models. The product of moments
of distribution of conserved quantities are related to the ratio of different order of susceptibilities
\cite{PLB633_275_Ejiri, PLB695_Karsch, PRL105_022302_Aggarwal}
such as $\sigma^2/M=\chi^{2}/\chi^{1}$, $S \sigma=\chi^{3}/\chi^{2}$ and
$\kappa \sigma^2=\chi^{4}/\chi^{2}$ where $M$ is the mean, $\sigma$ is the standard deviation,
$S$ is the skewness, $\kappa$ is the  kurtosis of the distribution of conserved quantities and
$\chi^{n}$ are the $n^{th}$ order susceptibilities. In general, higher order susceptibilities are more sensitive to the
large correlation length and hence the critical point~\cite{PRL102_032301_Stephanov}. This implies that any memory
of the large correlation length retained in the thermal system at freeze-out would be reflected in the behaviour of higher moments.
We have studied the energy dependence of product of moments for
net-proton, net-kaon and net-charge and compare our result for
net-proton and net-charge with experimental data of fluctuation
along with the transverse
momentum and pseudo-rapidity acceptance.

The paper is organized as follows. HRG model and its extension to EVHRG are introduced in sec. \ref{sec:HRG}. In sec. \ref{sec:Fluctuation}
we have first discussed the
fluctuations of different conserved charges and correlations among them at zero $\mu_B$ (finite $T$) and compared them with the
lattice data. Then we have discussed the finite density scenario along with a comparison with the experimental data. Finally we have
summarized our results in sec. \ref{sec:Conclusion}.

\section{\label{sec:HRG} Hadron resonance gas model}
In this section we are going to discuss HRG and EVHRG model very briefly. The detailed
discussions can be found in Refs.~\cite{HRG_Braun-Munzinger, PLB344_Braun-Munzinge, arXiv:nucl-th/9603004_Cleymans,
PLB465_Braun-Munzinge, PRC60_054908_Cleymans, PRC73_Becattini, PLB518_Braun-Munzinger, NPA772_Andronic,
PLB673_Andronic, PLB97_Hagedorn, ZPC51_Rischke, PS48_277_Cleymans,  Singh, PRC56_Yen, PLB718_Andronic}.
The grand canonical partition function of a hadron resonance gas~\cite{HRG_Braun-Munzinger, PLB718_Andronic} can be written as
\begin {equation}
 \ln Z^{id}=\sum_i \ln Z_i^{id},
\end{equation}
where sum is over all the hadrons. $id$ refers to ideal {\it i.e.}, non-interacting HRG.
For particle $i$,
\begin{equation}
 \ln Z_i^{id}=\pm \frac{Vg_i}{2\pi^2}\int_0^\infty p^2\,dp \ln[1\pm\exp(-(E_i-\mu_i)/T)],
\end{equation}
where $V$ is the volume of the system, $g_i$ is the degeneracy factor, $T$ is the temperature, $E_i=\sqrt{{p}^2+m^2_i}$
is the single particle energy, $m_i$ is the mass and $\mu_i=B_i\mu_B+S_i\mu_S+Q_i\mu_Q$ is the
chemical potential. $B_i,S_i,Q_i$ are respectively the baryon number, strangeness
and charge of the particle, $\mu^,s$ being corresponding chemical potentials. The $(+)$ and $(-)$ sign corresponds to fermions and bosons
respectively.
Partition function depends in general on five parameters. However, only three are independent, since $\mu_Q$ and $\mu_S$
can be found from conservation of different quantum numbers like baryon number,
charge and strangeness~\cite{HRG_Braun-Munzinger, PLB718_Andronic}.

The partition function is the basic quantity from which one can calculate various thermodynamic quantities of the
thermal system created in heavy ion collisions. The partial pressure $P_i$, the particle density $n_i$, the energy density
$\varepsilon_i$, and the entropy density $s_i$ can be calculated using the standard definitions,

\begin{align}\label{eq:p}
 \begin{split}
  P_i^{id}&=\frac{T}{V}\ln Z_i^{id}
  =\pm\frac{g_iT}{2\pi^2}\int_0^\infty p^2\,dp \ln[1\pm\exp(-(E_i-\mu_i)/T)],
 \end{split}
\end{align}

\begin{equation}\label{eq:n}
 n_i^{id}=\frac{T}{V} \left(\frac{\partial \ln Z_i^{id}}{\partial\mu_i}\right)_{V,T}
 =\frac{g_i}{2\pi^2}\int_0^\infty\frac{p^2\,dp}{\exp[(E_i-\mu_i)/T]\pm1},
\end{equation}

\begin{align}
\begin{split}
\varepsilon_i^{id}&=\frac{E_i^{id}}{V}=-\frac{1}{V} \left(\frac{\partial \ln Z_i^{id}}{\partial\frac{1}{T}}\right)_{\frac{\mu}{T}}
=\frac{g_i}{2\pi^2}\int_0^\infty\frac{p^2\,dp}{\exp[(E_i-\mu_i)/T]\pm1}E_i,
\end{split}
\end{align}

\begin{align}\label{eq:s}
 \begin{split}
  s_i^{id}&=\frac{S_i^{id}}{V}=\frac{1}{V}\left(\frac{\partial\left({T \ln Z_i^{id}}\right)}{\partial T}\right)_{V,\mu}
 = \pm\frac{g_i}{2\pi^2}\int_0^\infty p^2\,dp \left[ \ln\left(1\pm\exp(-\frac{(E_i-\mu_i)}{T})\right)\right.
 \left.\pm\frac{(E_i-\mu_i)}{T(\exp((E_i-\mu_i)/T)\pm1)}\right].
 \end{split}
\end{align}

Since Eqs. \ref{eq:p} - \ref{eq:s} determine the thermodynamic properties of the system, those are called equations of state
(EOS) of the system.

\begin{figure}[]
\centering
 \subfigure {\includegraphics[scale=0.34,angle=-90]{energy_mub_a_new.eps}\label {energy_mub}}
 \subfigure {\includegraphics[scale=0.34,angle=-90]{pressure_mub_b_new.eps}\label {pressure_mub}}
 \subfigure {\includegraphics[scale=0.34,angle=-90]{entropy_mub_c_new.eps}\label {entropy_mub}}
 \subfigure {\includegraphics[scale=0.34,angle=-90]{number_mub_d_new.eps}\label {number_mub}}
 \caption{(Color online). \label{fig:EOS_mub}Equations of state  as a function of $\mu_B$ at constant $T$ keeping
 $\mu_S=\mu_Q=0$. Non interacting means non interacting HRG model {\it i.e.} without
 excluded volume correction and interacting refers to EVHRG. $R_m$ refers to radius of mesons and $R_b$ refers to radius of baryons.}
\end{figure}

Let us now discuss the interacting HRG or EVHRG model.
In contrast to the point like hadrons in HRG, in EVHRG model, hadronic phase
is modelled by a gas of interacting hadrons, where the geometrical size of the hadrons are explicitly incorporated
as the excluded volume correction~\cite{ZPC51_Rischke, PS48_277_Cleymans, PRC56_Yen} to approximate the short-range
repulsive hadron-hadron interaction.

Excluded volume corrections were first introduced in~\cite{PLB97_Hagedorn} but it was thermodynamically inconsistent. A thermodynamically consistent
excluded volume correction  was first proposed in~\cite{ZPC51_Rischke}.

In EVHRG model pressure can be written as
\begin{equation}\label{eq:p_new}
 P(T,\mu_1,\mu_2,..)=\sum_i P_i^{id}(T,\hat{\mu}_1,\hat{\mu}_2,..),
\end{equation}
where for $i$'th particle the chemical potential is
\begin{equation}\label{eq:mu}
 \hat{\mu_i}=\mu_i-V_{ev,i}P(T,\mu_1,\mu_2,..)
\end{equation}
where
$V_{ev,i}=4 \, \frac{4}{3} \, \pi R_i^3$ is the volume excluded for
 the $i$ th hadron with hard core radius $R_i$.

In an iterative procedure one can get the total pressure. Pressure $P(T,\mu_1,\mu_2,..)$ is suppressed compared to
the ideal gas pressure $P^{id}$ because of the smaller value of effective chemical potential. The other
thermodynamic quantities like $n_i$, $s$ , $\varepsilon$
can be calculated from Eqs. \ref{eq:p_new} - \ref{eq:mu} as

\begin{align}
 \begin{split}
   n_i=n_i(T,\mu_1,\mu_2,..)&=\frac{\partial P}{\partial\mu_i}
  =\frac{n_i^{id}(T,\hat{\mu_i})}{1+\sum_k V_{ev,k}n_k^{id}(T,\hat{\mu_k})},
 \end{split}
\end{align}

\begin{align}
 \begin{split}
  s=s(T,\mu_1,\mu_2,..)&=\left(\frac{\partial P}{\partial T}\right)_{\mu_1,\mu_2,..}
 =\frac{\sum_i s_i^{id}(T,\hat{\mu_i})}{1+\sum_k V_{ev,k}n_k^{id}(T,\hat{\mu_k})},
 \end{split}
\end{align}

\begin{equation}
 \varepsilon=\varepsilon(T,\mu_1,\mu_2,..)=\frac{\sum_i \varepsilon_i^{id}(T,\hat{\mu_i})}{1+\sum_k V_{ev,k}n_k^{id}(T,\hat{\mu_k})},
\end{equation}
This correction scheme is thermodynamically consistent {\it i.e.} EOS after corrections obey the relation

\begin{equation}
 s=\frac{\varepsilon+P-\sum_i \mu_i n_i}{T}.
 \end{equation}

In this work we have incorporated all the hadrons listed in the particle data book~\cite{PDG} up to mass of $3$ GeV.
In Fig. \ref{fig:EOS_mub} we have shown $\varepsilon, P, s$ and $n$ as a function of $\mu_B$ at fixed $T$. For
completeness one should also plot these quantities as a function of $T$ at fixed $\mu_B$. However such relations
are already given in Ref.~\cite{PLB718_Andronic, PRC88_Tawfik} and we do not repeat those here.
Our results show that there is almost
no effect of interaction till $\mu_B=0.4$ GeV in EOS. Beyond $\mu_B=0.4$ GeV we see quite a substantial change in
these quantities. The change is more pronounced at higher temperatures. One can see from this figure that at large
$\mu_B$ the energy, entropy and number density in EVHRG model  are suppressed by a factor of $2$, compared to HRG, if we take the radii of all the hadrons to be $0.2$ fm. This is expected as the finite radius acts as repulsive interaction between hadrons. If we increase the size of the baryons further to $0.3$ fm the suppression is even more. However
the thermodynamic quantities are less sensitive to the mesonic radii as can be seen from Fig. \ref{fig:EOS_mub}.
The plot for $R_b= R_m=0.3$ fm is almost same as that for $R_b=0.3$ fm, $R_m=0.2$ fm and is suppressed compared to $R_b=R_m=0.2$ fm.
This is an expected result as the system is dominated by baryons at high $\mu_B$.

The difference of the EVHRG model, as compared to HRG, is governed by the radius parameter. The electromagnetic charge radii of
hadrons have been measured by different groups~\cite{amnedolia}.  For example, the radii for $p$, $\Sigma^-$, $\pi^-$ and $K^-$
are around 0.8 fm, 0.9 fm, 0.7 fm and 0.6 fm respectively. One can also define a strong interaction radii~\cite{povh} which comes
out to be around the same values. In accordance with these results, a value of 0.8 fm for baryons and 0.62 fm for mesons were proposed
earlier~\cite{PRC56_Yen}. On the other hand, Braun-Munzinger {\it {et al.}}~\cite{PLB465_Braun-Munzinge} argued that a more
realistic approach is to incorporate repulsive behaviour of the NN potential using hard-core radius ($\sim$ 0.3 fm) as obtained
from  nucleon-nucleon scattering~\cite{bohr}. The corresponding meson radius should not exceed that of baryons.
A similar hard-core radius of 0.2-0.3 fm has also been proposed in Ref.~\cite{giltinan} to explain the proton-proton scattering
data. It has also been shown earlier that to justify a
hydrodynamic approach to heavy ion collisions within the hadron phase the hard-core hadron radius should be $r \ge 0.2$ fm in
EVHRG model~\cite{PRC77_Gorenstein}. In the present study we have taken an approach similar to~\cite{PLB465_Braun-Munzinge} and
have used different baryon ($R_b$) and meson ($R_m$) radii between 0.2-0.3 fm.

\section{\label{sec:Fluctuation}Fluctuation and Correlation: Lattice vs. EVHRG }

\begin{figure}[]
\centering
  \subfigure {\includegraphics[scale=0.34,angle=-90]{p_t4_temp_a_new.eps}\label {press_temp}}
   \subfigure {\includegraphics[scale=0.34,angle=-90]{chi_B2_temp_b_new.eps}\label {chi_B2_temp}}
    \subfigure {\includegraphics[scale=0.34,angle=-90]{chi_S2_temp_c_new.eps}\label {chi_S2_temp}}
     \subfigure {\includegraphics[scale=0.34,angle=-90]{chi_Q2_temp_d_new.eps}\label {chi_Q2_temp}}
 \caption{(Color online). \label{fig:chi^2_temp}Variation of pressure and second order susceptibilities
 $\chi_B^2$, $\chi_S^2$ and $\chi_Q^2$
 with temperature at $\mu=0$. Lattice data for pressure are taken from
Bazavov {\it et.al}~\cite{Bazavov_eos_contm} and
Bors\'{a}nyi {\it et.al}~\cite{Borsanyi_JHEP_11_77} whereas
those for $\chi^2$ are taken from Bazavov {\it et.al}~\cite{Bazavov} and Bors\'{a}nyi {\it et.al} ~\cite{Borsanyi}}.
 \end{figure}

\begin{figure}
\centering
  \subfigure {\includegraphics[scale=0.34,angle=-90]{chi_B4_temp_a_new.eps}\label {chi_B4_temp}}
   \subfigure {\includegraphics[scale=0.34,angle=-90]{chi_S4_temp_b_new.eps}\label {chi_S4_temp}}
    \subfigure {\includegraphics[scale=0.34,angle=-90]{chi_Q4_temp_c_new.eps}\label {chi_Q4_temp}}
 \caption{(Color online). \label{fig:chi^4_temp}Variation of fourth order susceptibilities $\chi_B^4$, $\chi_S^4$, $\chi_Q^4$
 with temperature ($\mu=0$). Lattice data is taken from Ref.~\cite{Schmidt}.}
\end{figure}

Fluctuations and correlations of conserved charges such as net electric charge, baryon number and strangeness
have been considered
as probes of  hadronization and thermalization of the system created in nuclear collisions
\cite{Asakawa, Bower, Aziz}.
Fluctuation are considered to be important signatures for
the existence of CEP on the phase diagram as it would lead to large fluctuations in the thermodynamic quantities. Moreover, fluctuations are expected to show distinctly different
behaviour in a hadron resonance gas and a QGP.

\subsection{Fluctuations of conserved charges}
Derivatives of the grand canonical partition function ($Z$) with respect to chemical potential define
susceptibilities which experimentally become accessible through event-by-event analysis of fluctuations in observable quantities
such as baryon number, electric charge, strangeness and others.

The $n^{th}$ order susceptibility is defined as
\begin{equation}\label{eq:chi}
 \chi^n_x=\frac{1}{V T^3}\frac{\partial^n {(ln Z)}}{\partial {(\frac{\mu_x}{T})}^n},
\end{equation}
where $\mu_x$ is the chemical potential for conserved charge $x$. For our purpose $x=B$ (baryon),
$S$ (strangeness) and $Q$ (electric charge).

In Fig. \ref{fig:chi^2_temp} we have shown temperature dependence of pressure and second
order susceptibilities for various conserved charges at zero chemical potentials ($\mu_B=\mu_S=\mu_Q=0$).
From Fig. \ref{press_temp}, where we plot pressure as a function of temperature, one can see that
the continuum limit lattice data from~\cite{Borsanyi_JHEP_11_77, Bazavov_eos_contm} agrees within error-bar with HRG
and EVHRG model upto $T \sim 0.17$ GeV.
The second order susceptibilities are found to increase rapidly with increase of temperature.
Near $T=0.1$ GeV magnitude of $\chi_Q^2$ is almost double compared to $\chi_S^2$ and the
magnitude of $\chi_B^2$ is almost zero at this temperature.
As at low temperature fluctuations of
a particular charge are dominated by  lightest hadrons carrying that charge.
The dominant contribution to $\chi_B^2$ at low temperatures comes from protons (lightest baryon), while $\chi_S^2$
receives leading
contribution from kaons (lightest strange hadron) and $\chi_Q^2$ from pions (lightest charged hadron).
Since pion is lighter compared to proton and kaon,
magnitude of $\chi_Q^2$ is more than that of $\chi_B^2$ and $\chi_S^2$.
In EVHRG we have considered different values of $R_b$ and $R_m$ as shown in Fig. \ref{fig:chi^2_temp}.
It can be seen that there is almost no effect of interaction till $T=0.13$ GeV in fluctuations.
The reason for this is that the effective degree of freedom does not increase much up to this temperature
and therefore correction due to excluded volume is small.
Above $T=0.13$ GeV we find quite a substantial change in second order susceptibilities.
It can be seen from this figure that at large $T$, second order fluctuations are reduced by almost $30 \%$ compared to
the non-interacting hadrons, if we
take radii of all the hadrons to be $0.2$ fm.
If we increase radii of hadrons further to $0.3$ fm, the suppression is even more.
We have compared our result with LQCD data~\cite{Bazavov, Borsanyi}. It can be seen that up to $T=0.18$ GeV,
$\chi_B^2$ is in good agreement with LQCD if we consider radii of all hadrons to be $0.2$ fm whereas
$\chi_Q^2$ is in good agreement with LQCD for $R_m=0.2$ fm and $R_b=0.3$ fm.
The meson radius plays an important role for $\chi_S^2$ and $\chi_Q^2$ but not for $\chi_B^2$ which can be
seen from the figure. This is an expected result since in $\chi_S^2$ and $\chi_Q^2$ both the baryons and mesons contribute
whereas in $\chi_B^2$ only baryons contribute. One should, however, note that the dependence of $\chi_B^2$ on $R_m$ is not
completely negligible. We will address the issue later.

In non-interacting HRG model, under Boltzmann approximation, $\chi_B^4 \approx \chi_B^2$ and $\chi_B^1 \approx \chi_B^3$ as only baryons
with baryon number one contribute to
various susceptibilities~\cite{PLB695_Karsch}. In contrast, in case of higher order susceptibilities, electric charge and strangeness is
expected to show larger values as hadrons with multiple charge/strangeness get larger weight. A similar behaviour is expected for EVRHG
model as well. In Fig. \ref{fig:chi^4_temp} we have shown variation of fourth order susceptibilities with temperature at $\mu=0$.
The nature of all the fourth order susceptibilities is similar to second order susceptibilities. As expected,
magnitudes of fourth order susceptibilities are larger compared to that of second order susceptibilities
for strangeness and electric charge. However this is not true for baryon number fluctuations.
Although contributions in  $\chi_B$  are only from baryons, these quantities also depend on size of mesons
as can be seen from Fig. \ref{chi_B2_temp} and Fig. \ref{chi_B4_temp}. This dependence can be understood from Eqs. (\ref{eq:p_new})
and (\ref{eq:mu}) which shows the
dependence of chemical potential on hadronic radii through pressure. Hence, even for baryon number susceptibilities there may be
small difference in magnitudes of susceptibilities at different $R_m$ for EVHRG.
We compare our result with LQCD data ($N_\tau = 6, 8$) \cite{Schmidt}.
The LQCD data for $\chi_B^4$ and $\chi_S^4$ are in good agreement with HRG model up to $T=0.16$ GeV.
Whereas for $\chi_Q^4$, LQCD data is lower compared to both HRG and EVHRG.

It has been argued in~\cite{PLB718_Andronic} that for $\epsilon$, $P$ and $s$, though lattice QCD results agree at lower temperatures,
they are expected to becomes larger than those in HRG at higher temperatures due to deconfinement. On the other hand, the difference
between lattice and HRG for the higher susceptibilities may have effects due to the difference in hadronic masses. It has also been
reported that the thermodynamic quantities calculated in lattice QCD may agree well with the HRG model if the masses of the hadrons
in the model are tuned appropriately to take into account the discretization errors in the hadron spectrum present in the lattice
calculations~\cite{huovinen_2010, borsanyi_2011}. In the present study EVHRG is found to show a better agreement with the lattice
data in the continuum limit.

 \subsection{\label{sec:Correlations}Correlations among different conserved charges}

Correlations among different conserved charges may act as probes of the structure of QCD at finite temperature.
In QGP, as baryon number as well as electric charge  are carried by different flavours of quarks, a strong correlation is
expected between B-Q, Q-S as well as B-S. On the other hand, in the hadronic sector presence of baryons and mesons would generate
an entirely different type of correlations between these quantities.
Hence, these correlations are expected to show changes across the phase transition which are characteristics of the changes
in the relevant degrees of freedom.

  \begin{figure}[]
   \subfigure {\includegraphics[scale=0.34,angle=-90]{chi_BS11_temp_a_new.eps}\label {chi_BS11_temp}}
    \subfigure {\includegraphics[scale=0.34,angle=-90]{chi_QS11_temp_b_new.eps}\label {chi_QS11_temp}}
     \subfigure {\includegraphics[scale=0.34,angle=-90]{chi_BQ11_temp_c.eps}\label {chi_BQ11_temp}}
 \caption{(Color online). \label{fig:chi_BSQ11_temp}Variation of $\chi_{BS}^{11}$, $\chi_{BQ}^{11}$ and $\chi_{QS}^{11}$
 with temperature at $\mu=0$. Lattice data for continuum extrapolation is taken from Ref.~\cite{Bazavov}.}
 \end{figure}
\begin{figure}[]
  \subfigure {\includegraphics[scale=0.34,angle=-90]{cbs_temp_a_new.eps}\label {cbs_temp}}
   \subfigure {\includegraphics[scale=0.34,angle=-90]{cqs_temp_b_new.eps}\label {cqs_temp}}
    \subfigure {\includegraphics[scale=0.34,angle=-90]{cbq_temp_c_new.eps}\label {c_bq_temp}}
 \caption{(Color online). \label{fig:C_BS_QS_temp}Variation of $C_{BS}$, $C_{QS}$ and $C_{BQ}$ with temperature at $\mu=0$.
 Lattice data for continuum extrapolation is taken from Ref.~\cite{Bazavov}.}
 \end{figure}

Correlation functions, $\chi^{ij}_{xx'}$, are defined by
 \begin{equation}\label{eq:corr}
 \chi^{ij}_{xx'}=\frac{1}{V T^3}\frac{\partial^{i+j} {(ln Z)}}{(\partial {(\frac{\mu_x}{T})}^i)(\partial {(\frac{\mu_{x'}}{T})}^j)},
\end{equation}
where {$x$} and {$x'$} correspond to conserved charges {\it B,S,Q} and $\mu$'s are chemical potentials of
corresponding conserved charges.
 In this section we show temperature dependence of various correlation functions at $\mu_B=0$. We also compare our result with LQCD
data~\cite{Bazavov}.

Fig. \ref{fig:chi_BSQ11_temp} shows the variation of correlations between conserved charges with temperature around $\mu_x=\mu_{x'}=0$.
Since at very low temperature main contribution comes from pions (baryon number as well as strange quantum number $=0$),
all the correlations remain zero.
The next particle to be excited is kaon and as a result $\chi_{QS}^{11}$ becomes non zero around $T=0.075$ GeV. The leading contribution to
$\chi_{QS}^{11}$ in the hadronic sector is due to charge kaons which has same sign for charge and strange quantum number. So
it remains positive and increases with temperature.
Other correlations pick up non-zero values above $T=0.1$ GeV when baryons
start populating the system.
 $\chi_{BS}^{11}$ is proportional to the product of baryon number and
strange quantum number. So here most of the contribution is due to lightest baryon $\varLambda^{}$ which
has baryon number $+1$ and strange quantum number $-1$.  Other contributing particles,
such as, $\Sigma$, $\Xi$ etc. also have relative negative sign between baryon number and strange quantum number.
As a result $\chi_{BS}^{11}$ remains negative. This negative value increases with $T$ due to the increase in the population
of the strange baryons. Again, HRG results show sharp increase compared to those from EVHRG model. Due to the contribution
from mesons (mainly kaons)
in $\chi_{QS}^{11}$, meson radius plays a dominating role and an increase in meson radius produces larger suppression in EVHRG model.
On the other hand, baryon radius plays a major role for both $\chi_{BS}^{11}$ as well as $\chi_{BQ}^{11}$. The dominant contribution in
$\chi_{BQ}^{11}$ at low temperature is due to proton and antiproton and for both of those  baryon
number as well as charge carry the same sign. So the value of $\chi_{BQ}^{11}$ remains positive and shows a sharp increase
with temperature in HRG, EVHRG being suppressed due to the effect of hard core radius.
In the quark sector strange quarks (antiquarks) carry $1/3$ (-$1/3$) baryon number and the relative sign between $B$ and $S$ is
always negative. As a result lattice result for $\chi_{BS}^{11}$ show a similar trend as that of HRG. On the other hand, $\chi_{QS}^{11}$
is always positive as charge as well as strangeness for strange quark is negative. Though the lattice values at lower temperature
($0.15$ GeV) is close to HRG and EVHRG, $\chi_{BS}^{11}$ as well $\chi_{QS}^{11}$ for lattice increase faster than
those for HRG as strange quark mass is much smaller
compared to strange baryons.
At high temperature quark masses decrease (which will eventually become zero at Stefan-Boltzmann limit) and lattice results
would start saturating whereas HRG results would keep on increasing. As a result lattice values
are suppressed compared to HRG values  both for $\chi_{QS}^{11}$ and $\chi_{BS}^{11}$.
In the case of $\chi_{BQ}^{11}$, EVHRG ($R_m$=0.2 fm and $R_b$=0.3 fm) results agree well with the lattice data for $T < 0.17$ GeV.
But at higher temperatures, the weighted sum of charges of massless quarks vanishes so the lattice results would start saturating with the
further increase in temperature whereas HRG results would keep on increasing similar like $\chi_{QS}^{11}$ and $\chi_{BS}^{11}$.

The LQCD results of charge correlations has been found to deviate from the ideal gas limit even at twice the transition temperature and
the large contributions of flavour fluctuations are expected to be the cause of these deviations~\cite{Bazavov}.
In order to analyse the experimental results, suitable ratios have been proposed to eliminate these contributions~\cite{PRL95_182301_Majumder}.
Three ratios, namely, baryon-strangeness correlation coefficient $C_{BS}$~\cite{PRL95_182301_Majumder}, electric charge-strangeness
correlation coefficient $C_{QS}$ and baryon-electric charge correlation coefficient $C_{BQ}$ can be written as~\cite{Bazavov}
\begin{equation}
 C_{BS}=-3\frac{\chi_{BS}^{11}}{\chi_S^2}, ~~~~~     C_{QS}=3\frac{\chi_{QS}^{11}}{\chi_S^2}, ~~~~~
 C_{BQ}=\frac{\chi_{BQ}^{11}}{\chi_B^2}.
\end{equation}

Figure \ref{fig:C_BS_QS_temp} shows variation of $C_{BS}$, $C_{QS}$ and $C_{BQ}$ with temperature at $\mu=0$.
We compare our result with LQCD data~\cite{Bazavov}.
At low temperature $C_{BS}$ is much lower than one because denominator contains mostly kaon whereas contribution to numerator comes
from baryons, mostly $\varLambda$, which is less populated than kaon. It increases with temperature but remains below 1 due to
larger contribution from mesons.  If all the hadronic radii are same, the interaction effect gets cancelled. On the other hand,
for larger baryonic radii, baryon population gets suppressed and $C_{BS}$ value for EVHRG becomes lower than HRG. In case of
simple QGP, or more generally, for a system where the quark flavours
are uncorrelated, this value will be unity. Since lattice $\chi_{BS}^{11}$ is higher,
lattice $C_{BS}$ values remain above the HRG (and EVHRG) and saturates at high temperature.

At very low temperature, contribution to numerator of $C_{QS}$ come from  charged kaons only while the contributions
to denominator
come from all the kaons. So $C_{QS}$ comes out to be around $1.5$.
With increase of temperature lambda starts populating the system and $C_{QS}$ becomes close to $1$.
There is no effect of interaction in most of the temperature range except at very high temperatures. Here, a higher baryonic radii
(compared to meson radii) induces a small increase in $C_{QS}$. Interaction effects get cancelled if radii are same for all hadrons.
$C_{BS}$ and $C_{QS}$ are related through the equation $C_{QS}=0.5(3-C_{BS})$~\cite{Bazavov}. So in lattice studies~\cite{Bazavov}
at low temperature, where $C_{BS}$ is very small $C_{QS}$ is near 1.5, same compared to HRG (and EVHRG)
and at high temperature tends to one.

At low temperatures, contribution to numerator of $C_{BQ}$ come from  protons only while the contributions to denominator
come from both protons and neutrons. As a result $C_{BQ}$ is close to $0.5$.
It decreases slowly with increase in $T$ as at high $T$ heavier
neutral baryons like $\varLambda$ start contributing to the denominator whereas only
charged baryons contribute to numerator. For both HRG and EVHRG $C_{BQ}$ is very close to each other due to the cancellation
of interaction effects. In lattice, $C_{BQ}$ approaches zero at high $T$ as the system is in QGP phase. However at lower
temperature it approaches the HRG/EVHRG values.

\subsection{\label{sec:mub}High density scenario}
  \begin{figure}[]
  \centering
  \subfigure {\includegraphics[scale=0.34,angle=-90]{chi_B1_mub_a.eps}\label {chi_B1_mub}}
  \subfigure {\includegraphics[scale=0.34,angle=-90]{chi_B2_mub_b.eps}\label {chi_B2_mub}}
   \subfigure {\includegraphics[scale=0.34,angle=-90]{chi_B3_mub_c.eps}\label {chi_B3_mub}}
    \subfigure {\includegraphics[scale=0.34,angle=-90]{chi_B4_mub_d.eps}\label {chi_B4_mub}}
 \caption{(Color online). \label{fig:chi_B_mub}Susceptibilities $\chi_B^1$, $\chi_B^2$, $\chi_B^3$, $\chi_B^4$ as a function of $\mu_B$ keeping $T$ fixed and $\mu_S=\mu_Q=0$.}
 \end{figure}
 \begin{figure}
 \centering
   \subfigure {\includegraphics[scale=0.34,angle=-90]{chi_S1_mub_a_new.eps}\label {chi_S1_mub}}
    \subfigure {\includegraphics[scale=0.34,angle=-90]{chi_S2_mub_b_new.eps}\label {chi_S2_mub}}
     \subfigure {\includegraphics[scale=0.34,angle=-90]{chi_S3_mub_c_new.eps}\label {chi_S3_mub}}
      \subfigure {\includegraphics[scale=0.34,angle=-90]{chi_S4_mub_d_new.eps}\label {chi_S4_mub}}
 \caption{(Color online). \label{fig:chi_S_mub}Susceptibilities $\chi_S^1$, $\chi_S^2$, $\chi_S^3$, $\chi_S^4$ as a
 function of $\mu_B$ keeping $T$ fixed and $\mu_S=\mu_Q=0$.}
 \end{figure}
 \begin{figure}
 \centering
   \subfigure {\includegraphics[scale=0.34,angle=-90]{chi_Q1_mub_a.eps}\label {chi_Q1_mub}}
    \subfigure {\includegraphics[scale=0.34,angle=-90]{chi_Q2_mub_b.eps}\label {chi_Q2_mub}}
     \subfigure {\includegraphics[scale=0.34,angle=-90]{chi_Q3_mub_c.eps}\label {chi_Q3_mub}}
      \subfigure {\includegraphics[scale=0.34,angle=-90]{chi_Q4_mub_d.eps}\label {chi_Q4_mub}}
 \caption{(Color online). \label{fig:chi_Q_mub}Susceptibilities $\chi_Q^1$, $\chi_Q^2$, $\chi_Q^3$, $\chi_Q^4$ as a function of $\mu_B$ keeping $T$
 fixed and $\mu_S=\mu_Q=0$.}
 \end{figure}

At very high densities and low temperatures, strongly interacting matter is expected to undergo a first order phase transition
which ends at CEP as one moves towards higher $T$ and lower $\mu_B$ along the phase boundary. At finite $\mu_B$ due to the
expected stronger divergence at the phase boundary and at CEP, study of higher order moments is extremely important at finite $\mu_B$.
In fact, not only the magnitude but the signs of third moments have also been proposed as a signature for CEP~\cite{asakawa_prl}.

In this section we have discussed the results of fluctuations and correlations at large $\mu_B$.
In Fig. \ref{fig:chi_B_mub} - \ref{fig:chi_Q_mub}. we show variation of $\chi_x^1$, $\chi_x^2$, $\chi_x^3$, $\chi_x^4$
with $\mu_B$ for a fixed temperature and at $\mu_S=\mu_Q=0$ where $x=B, S, Q$. Here we have considered
 $T=0.1$ GeV and $0.15$ GeV for the purpose of illustration. For each temperatures we show variation of the quantities with $\mu_B$ in
HRG and EVHRG model with different baryon ($R_b$) and meson ($R_m$) radii.
The effect of interaction is found to be more pronounced at
high temperatures. It can be seen from these figures that at high $T$ and large
$\mu_B$ the magnitude of fluctuations are suppressed by a factor of $2$ or more, compared to HRG, if we take the radii of all
the hadrons to be $0.2$ fm.
At high $\mu_B$  fluctuations are very sensitive to $R_b$ but not to $R_m$ as in this region system is dominated
by baryons. Similar behaviour was obtained in Fig. \ref{fig:EOS_mub} as well.
$\chi^1_S$ and $\chi^3_S$ are proportional to the odd power of strange quantum number of the particles.
Dominant contribution to $\chi_S$ comes from $\varLambda$, the lightest strange baryon
which has strange quantum number $-1$ (at $\mu_S=0$ strange mesons don't contribute to $\chi^1_S$ and $\chi^3_S$
because particle and anti-particle terms are equal in magnitude but opposite in sign).
As a result, $\chi^1_S$ and $\chi^3_S$ remain negative (Fig. \ref{chi_S1_mub} and Fig. \ref{chi_S3_mub}).

As mentioned earlier, there are contributions from multiple charged hadrons in electrical charge and strangeness sector only,
baryon number being always one. Hence, at high $\mu_B$ region magnitudes of $\chi_x^3$ and $\chi_x^4$ are found to be almost double compared
to that of $\chi_x^1$ and $\chi_x^2$ respectively for $x=S,Q$ (Fig. \ref{fig:chi_S_mub}
and Fig. \ref{fig:chi_Q_mub}), though the change in $\chi_B$ remains small as shown in Fig. \ref{fig:chi_B_mub}. At very small $\mu_B$ and given $T$ (0.1 or 0.15 GeV) system
is dominated by mesons and $\chi_B$ is small. With increase in $\mu_B$ system will be populated by proton, neutron as well as hyperons and $\chi_B$ will increase. This increase will be sharper for HRG due to the absence of repulsive interaction.

\begin{figure}
  \subfigure {\includegraphics[scale=0.34,angle=-90]{chi_BS11_mub_a.eps}\label {chi_BS11_mub}}
   \subfigure {\includegraphics[scale=0.34,angle=-90]{chi_QS11_mub_b.eps}\label {chi_QS11_mub}}
    \subfigure {\includegraphics[scale=0.34,angle=-90]{chi_BQ11_mub_c.eps}\label {chi_BQ11_mub}}
 \caption{(Color online).  \label{fig:chi_BSQ11_mub}$\chi_{BS}^{11}$, $\chi_{BQ}^{11}$, $\chi_{QS}^{11}$ as a function of $\mu_B$ keeping $\mu_S=\mu_Q=0$.}
\end{figure}
 \begin{figure}
   \subfigure {\includegraphics[scale=0.34,angle=-90]{C_BS_mub_a_new.eps}\label {C_BS_mub}}
   \subfigure {\includegraphics[scale=0.34,angle=-90]{C_QS_mub_b_new.eps}\label {C_QS_mub}}
    \subfigure {\includegraphics[scale=0.34,angle=-90]{c_bq_mub_c_new.eps}\label {c_bq_mub}}
 \caption{(Color online). \label{fig:chi_C_BS_QS_mub}Variation of $C_{BS}$, $C_{QS}$ and $C_{BQ}$ with $\mu_B$ keeping $\mu_S=\mu_Q=0$.}
\end{figure}
At finite $\mu_B$ (fixed $T$) due to larger contribution from effective chemical potentials, the effect of interaction, compared to
zero $\mu_B$ case, is more
prominent on correlations as shown in Fig. \ref{fig:chi_BSQ11_mub}.
The plots are given for different $R_m$ and $R_b$.
It can be seen that at low $\mu_B$, $\chi_{BS}^{11}$  and $\chi_{BQ}^{11}$ are zero whereas $\chi_{QS}^{11}$
is non-zero as pions and kaons are main contributors in this range of parameters. At large $\mu_B$, baryons start populating the system
and both B-S and B-Q correlations increase more sharply compared to $\chi_{QS}$ as kaons remain the main contributor in $\chi_{QS}$
and charge hyperon population is much smaller. One can also see that there is no effect of interaction till $\mu_B=0.3$ GeV in
$\chi_{BS}^{11}$ and $\chi_{BQ}^{11}$. However at high $T$, $\chi_{QS}^{11}$ is affected by interaction even at low $\mu_B$.

In Fig. \ref{fig:chi_C_BS_QS_mub} we show variation of $C_{BS}$, $C_{QS}$ and $C_{BQ}$  with $\mu_B$ at a fixed
 $T$ and $\mu_S= \mu_Q =0$. At low $\mu_B$, kaon population is dominating in the denominator of $C_{BS}$
 and it is less than unity. On the other hand increase in $\mu_B$ facilitates the strange baryon population
 and $C_{BS}$ increases with increasing $\mu_B$. Moreover, the effect of large $\mu_B$ becomes more
 pronounced for lower $T$. So that $C_{BS}$ at $T$=0.1 GeV is larger than that at $T=0.15$ GeV for
large $\mu_B$ ($> 0.6$ GeV). Similarly at low $\mu_B$, $C_{QS}$ is around $1.5$ as it gets contribution from
mainly charged kaons in the numerator and both charged and neutral kaons in denominator.  With
increase in $\mu_B$, $\varLambda$ starts populating the system so that $C_{QS}$ keeps decreasing.
Since this effect is more pronounced for larger $T$, $C_{QS}$ is lower for larger $T$ at large  $\mu_B$ ($> 0.7$ GeV).

At low $\mu_B$, for small $T$, $C_{BQ}$ gets contribution from protons and neutrons in the denominator and only protons
in the numerator. So it is
close to $0.5$ as shown earlier in Fig. ~\ref{c_bq_temp}. At larger $T$ ($0.1$ or $0.15$ GeV), $\varLambda$ starts contributing in the
denominator and $C_{BQ}$ becomes
less than $0.5$.
Similarly as $\mu_B$ increases, population of protons, neutrons and lambda increases. As a result $C_{BQ}$ becomes less than $0.5$.
At high $\mu_B$, $C_{BQ}$ saturates as rate of increase becomes same for different species. For HRG and EVHRG
$C_{BQ}$ is close to each other due to cancellation of interaction effect.

\subsection{\label{sec:Experiment}Experimental scenario}
Experimentally measured moments such as mean ($M$), standard deviation ($\sigma$), skewness ($S$) and kurtosis ($\kappa$) of
conserved charges are used to characterize the shape of charge distribution.
The standard deviation corresponds to the width
of the distribution, the skewness is a measure of the asymmetry of the distribution and kurtosis describes
peakness of the distribution.
Products of moments are related to susceptibilities ($\chi_x$) by the following relations,
\begin{equation}\label{moment_product}
 \frac{\chi_x^2}{\chi_x^1}=\frac{\sigma_x^2}{M_x}, ~~~~ \frac{\chi_x^3}{\chi_x^2}=S_x\sigma_x, ~~~~
 \frac{\chi_x^4}{\chi_x^2}=\kappa_x\sigma_x^2.
\end{equation}

The advantage of using the above mentioned products of moments is that they are expected to be independent of the volume
of the system. On the other hand, our discussion on the variation of $\chi_x$ with $T$ (or $\mu_B$) shows that the cancellation of the volume effect, depending on the degrees of freedom involved, will become less as one increases the order of susceptibility
in the numerator (or denominator). In nucleus-nucleus collision experiments, beam energy ($\sqrt{s_{NN}}$) is varied to scan the
phase plane. At a particular $\sqrt{s_{NN}}$, if CEP is reached, the signature of CEP could survive during the
time evolution of the system. Hence along the freeze-out line one would expect a non-monotonic behaviour of the
quantities given in Eq. \ref{moment_product}~\cite{PRL105_022302_Aggarwal, AHEP_Tawfik}.
To compare the products of moments with experiment one has to know freeze-out $T$ and $\mu$
at a particular $\sqrt{s_{NN}}$.
Freeze-out curve $T(\mu_B)$ can be parametrized by~\cite{PRC73_Cleymans}
\begin{equation}
 T(\mu_B)=a-b\mu_B^2-c\mu_B^4,
 \end{equation}
where $a = 0.166 \pm 0.002$ GeV, $b =0.139 \pm 0.016$ GeV$^{-1}$, $c=0.053 \pm 0.021$ GeV$^{-3}$.
The energy dependence of the $\mu_q$ can be parametrized as~\cite{PLB695_Karsch}
\begin{equation}
 \mu_x(\sqrt{s_{NN}})=\frac{d_x}{1+e_x\sqrt{s_{NN}}},
\end{equation}
where $d_x$ and $e_x$ are listed in table \ref{tableLabel_muq}.

\begin{table}[h]
\centering
\begin{tabular}{|c|c|c|}
\hline
\it x&$d_x$ (\it GeV)&$e_x$ (\it GeV$^{-1}$)\\
\hline
\it B &$1.308 \pm 0.028$ &$0.273 \pm 0.008$ \\
\it S &$0.214$&$0.161 $\\
\it Q &$-0.0211$ &$0.106$\\
\hline
\end{tabular}
\caption{Parametrization of chemical potentials $\mu_x$ along the freeze-out curve.}
\label{tableLabel_muq}
\end{table}

\begin{figure}[]
   \subfigure {\includegraphics[scale=0.34,angle=-90]{chi_2_1_np_roots_a.eps}\label {chi_2_1_np_roots}}
    \subfigure {\includegraphics[scale=0.34,angle=-90]{chi_3_2_np_roots_b.eps}\label {chi_3_2_np_roots}}
     \subfigure {\includegraphics[scale=0.34,angle=-90]{chi_4_2_np_roots_c.eps}\label {chi_4_2_np_roots}}
 \caption{(Color online). \label{fig:np_roots}Energy dependence of $\sigma^2/M$, $S\sigma$ and $\kappa\sigma^2$
 for net-proton. Experimental data is taken from Ref. ~\cite{STAR_Luo}.}
 \end{figure}

The $T$ - $\mu_B$ parametrisation with $\sqrt{s_{NN}}$ is obtained by fitting the different particle ratios obtained
experimentally at different
$\sqrt{s_{NN}}$. So for EVHRG model, in general, the parameters are expected to be different for different hadronic radii.
In our study, considering all the particle ratios, we found the parameters to be same as
\cite{PRC73_Cleymans} for $R_b=R_m$. On the other hand, for $R_B \ne R_m$ case, for the radii used here, the parameter are
found to be within $\pm 0.005- 0.008$ GeV of the above fit.
Moreover, phenomenological freeze-out condition of fixed energy per nucleon about $1$ GeV, calculated in our model,
matches quite well with the above mentioned freeze-out parametrization.
Hence we have used the above mentioned freeze-out parametrization for comparison
with the experimental results. It may also be noted here that as $\sqrt{s_{NN}}$ increases from 7.7 GeV to 200 GeV, $T$ increases from
around $0.140 $ GeV to $0.166 $ GeV and corresponding $\mu_B$ varies between $0.421$ GeV to $0.023$ GeV. Corresponding $\mu_S$ and $\mu_Q$ are expected
to vary between $0.095$ GeV to $0.006$ GeV and $-0.011$ GeV to $-0.001$ GeV~\cite{PLB695_Karsch}.

In terms of transverse momentum ($p_T$) and rapidity ($y$) and azimuthal angle ($\phi$)
 $d^3p$ and $E_i$ can be written as
$d^3p=p_T \, m_{Ti} \, \cosh y \, dp_T \, dy \, d\phi$
and $E_i=m_{Ti} \, \cosh y$, where $m_{Ti}=\sqrt{(p_T^2+m_i^2)}$. One can write a similar expression in terms of $p_T$ and
pseudo-rapidity $\eta$ as well. These prescriptions have been used to set the momentum and rapidity acceptance range to
compare the present results with the experimental data.

In Fig. \ref{fig:np_roots} we have shown energy dependence of $\sigma^2/M$, $S\sigma$ and $\kappa\sigma^2$
for net-proton. We compare our result with experimental data of net-proton fluctuations for $(0-5) \%$  central
Au-Au collisions measured at STAR~\cite{STAR_Luo}. Experimental data is measured at mid rapidity $(|y|<0.5)$ and within
the transverse momentum range $0.4<p_T<0.8$ GeV.
Same acceptances range has been used for different hadronic radii in the present manuscript.
At low energy, $\sigma^2/M$ is almost unity and its value
increases with increase of $\sqrt{s_{NN}}$ as can be seen from the Fig. \ref{chi_2_1_np_roots}.
Both HRG and EVHRG model give almost same result irrespective of the value of radii.
At low energy $S\sigma$ for HRG is almost unity and its value
decreases with increase of $\sqrt{s_{NN}}$ as can be seen from the Fig. \ref{chi_3_2_np_roots}.
At low $\sqrt{s_{NN}}$, $S\sigma$ for EVHRG is less than that
of HRG model and suppression increases with increase of radii. However, at high $\sqrt{s_{NN}}$, both HRG and EVHRG model give almost same
result. Experimental data of $S\sigma$ can be described well with EVHRG model for radii of hadrons between $0.3 - 0.4$ fm.
At low energy $\kappa\sigma^2$ (Fig. \ref{chi_4_2_np_roots}) in HRG model is slightly less than unity and its value
reaches to unity as we move to high energy. There is prominent suppression of $\kappa\sigma^2$ in EVHRG model at low $\sqrt{s_{NN}}$.
The $\kappa\sigma^2$ of net-proton matches within error-bar with EVHRG model at $\sqrt{s_{NN}} \geq 39$ GeV and  $\sqrt{s_{NN}} \leq 11.5$
GeV but at intermediate energies EVHRG model over estimates the experimental data. Deviation of experimental data of $S\sigma$ and
$\kappa\sigma^2$ for net-proton at intermediate energies ($\sqrt{s_{NN}}= 19$ GeV and $27$ GeV)
may be an indication of existence of quark degrees of freedom or different physics process which is not included
in HRG/EVHRG model.

In Ref.~\cite{PLB722_Fu}, STAR data for net-proton fluctuations is already compared with EVHRG model in full space.
Energy dependence of fluctuations for net-proton using LQCD can be found in Ref.~\cite{Mohanty_science, Karsch_PRD84_R}.
Though at high energies, where $\mu_B$ is small, LQCD agrees well with the experimental data, at low energies {\it i.e.} for
higher $\mu_B$ it fails.

\begin{figure}[]
   \subfigure {\includegraphics[scale=0.34,angle=-90]{chi_2_1_nk_roots_a.eps}\label{chi_2_1_nk_roots}}
    \subfigure {\includegraphics[scale=0.34,angle=-90]{chi_3_2_nk_roots_b.eps}\label{chi_3_2_nk_roots}}
     \subfigure {\includegraphics[scale=0.34,angle=-90]{chi_4_2_nk_roots_c.eps}\label{chi_4_2_nk_roots}}
 \caption{(Color online). \label{fig:nk_roots}Energy dependence of $\sigma^2/M$, $S\sigma$ and $\kappa\sigma^2$
 for net-kaon.}
 \end{figure}

In Fig. \ref{fig:nk_roots} we have shown energy dependence of $\sigma^2/M$, $S\sigma$ and $\kappa\sigma^2$
for net-kaon. We have chosen transverse momentum and pseudo-rapidity within the range $0.2 < p_T < 2.0$ GeV and $-0.5 < \eta < 0.5$
in our calculation.
At low energy $\sigma^2/M$ for net-kaon is slightly more than unity and its value increases rapidly with increase
of $\sqrt{s_{NN}}$ and result is almost same for both HRG and EVHRG model. Radii of hadrons
practically have no effect on the results as  shown in Fig. \ref{chi_2_1_nk_roots}.
$S\sigma$ for net-kaon decreases with increase of $\sqrt{s_{NN}}$ as can be seen from Fig. \ref{chi_3_2_nk_roots}.
Value of $S\sigma$ in EVHRG model is suppressed compared to HRG model and suppression increases with
increase of radii of hadrons.
In Fig. \ref{chi_4_2_nk_roots} energy dependence of $\kappa\sigma^2$ for net-kaon is shown. In this case, volume effect is more
prominent, as discussed earlier. $\kappa\sigma^2$ for net-kaon increases with increase of $\sqrt{s_{NN}}$ and then
saturates. Value of $\kappa\sigma^2$ is
suppressed in EVHRG model compared to HRG model and suppression increases with increase of radii of hadrons.
At all energies $\kappa\sigma^2$ for net-kaon lie between $0.9$ to $1.1$ in both HRG and EVHRG.

\begin{figure}[]
   \subfigure {\includegraphics[scale=0.34,angle=-90]{chi_2_1_nc_roots_a.eps}\label{chi_2_1_nc_roots}}
    \subfigure {\includegraphics[scale=0.34,angle=-90]{chi_3_2_nc_roots_b.eps}\label{chi_3_2_nc_roots}}
     \subfigure {\includegraphics[scale=0.34,angle=-90]{chi_4_2_nc_roots_c.eps}\label{chi_4_2_nc_roots}}
 \caption{(Color online). \label{fig:nc_roots_2}Energy dependence of $\sigma^2/M$, $S\sigma$ and $\kappa\sigma^2$
 for net-charge. Experimental data is taken from Ref. ~\cite{STAR_nihar}.}
 \end{figure}

In Fig. \ref{fig:nc_roots_2} we have shown energy dependence of $\sigma^2/M$, $S\sigma$ and $\kappa\sigma^2$
for net-charge.
We have chosen transverse momentum and pseudo-rapidity within the range $0.2 < p_T < 2.0$ GeV and $-0.5 < \eta < 0.5$
in our model calculation.
We have compared our results with experimental data of net-charge fluctuations for $(0-5) \%$ central
Au-Au collisions measured at STAR~\cite{STAR_nihar}.
Figure \ref{chi_2_1_nc_roots} shows $\sigma^2/M$, for net-charge, increases rapidly with increase of
$\sqrt{s_{NN}}$ and compared to experimental values our results are suppressed at higher energies.
$S\sigma$ for net-charge decreases with increase of $\sqrt{s_{NN}}$ as can be seen from Fig. \ref{chi_3_2_nc_roots}.
Experimental data of $S\sigma$ for net-charge matches within error-bar
with HRG/EVHRG model
at $\sqrt{s_{NN}} \leq 19.6 $ GeV
and $\sqrt{s_{NN}} \geq 62.4$ GeV but at other intermediate energies HRG/EVHRG model over estimate the experimental data.
Figure \ref{chi_4_2_nc_roots} shows $\kappa\sigma^2$ for net-charge slowly decreases with increase of $\sqrt{s_{NN}}$ and then saturates.
At all  $\sqrt{s_{NN}}$, $\kappa\sigma^2$ for net-charge lie between $1.4$ to $1.8$ in both HRG and
EVHRG model which is in agreement with experiment within error-bar at $\sqrt{s_{NN}} \geq 11.5$ GeV. Calculations
for ratios of higher order fluctuations of electric charge using LQCD can be found in Ref.~\cite{PRL_111_Borsanyi}.

\section{\label{sec:Conclusion} Discussion and Conclusion}
We have shown fluctuations ($\chi^i_x$; $i=1-4; x=B, S, Q$) of various conserved charges like net baryon number, net strangeness
and net charge at finite temperatures and chemical potentials using interacting and non-interacting hadron resonance gas model and compared them with the lattice as well as experimental data.

We can draw following inferences from the present study:
\begin{itemize}

\item In general HRG results are larger compared to EVHRG, difference being higher for higher temperatures and densities.

\item At high temperatures and $\mu_B = 0$, compared to HRG, second order fluctuations from EVHRG fits better to LQCD continuum data for radius of hadrons between $0.2-0.3$ fm.

\item The LQCD data ($N_\tau = 6, 8$) for $\chi^4_B$ and  $\chi^4_S$ are in good agreement with HRG/EVHRG model up to $T = 0.16$ GeV.
Whereas, both HRG and EVHRG model overestimates LQCD data for  $\chi^4_Q$.

\item Correlations at $T\ne 0$ and $\mu_B=0$ shows much stronger dependence on the degrees of freedom involved.
Lattice continuum data for both $\chi_{BS}^{11}$ and $\chi_{QS}^{11}$ are closer to HRG results (higher than EVHRG) at
lower $T$ but rises less sharply and becomes less than HRG for higher $T$.
On the other hand, $\chi_{BQ}^{11}$ calculated in lattice is close to EVHRG results at lower $T$. Initially it increases with $T$ but then
decreases beyond $T=0.165$GeV as discussed earlier.

\item The correlation ratios from both HRG and EVHRG disagree with LQCD continuum data though the trends are qualitatively similar.
This difference could be attributed to the fact that LQCD incorporates transition from hadronic to quark degrees of freedom, whereas
only hadronic degrees of freedom are present in HRG or EVHRG model. At high $\mu_B$, the magnitudes of susceptibilities as well
as correlations are higher correspond to $\mu=0$ case.

\item The susceptibilities as well as correlations are found to increase with $\mu_B$ at fixed temperatures for both HRG and EVHRG,
the effect of interaction being larger for higher $T$.

\item Since low energy collisions usually correspond to larger $\mu_B$, the effect of repulsive interaction, as present in EVHRG,
is distinguishable for lower energies. Moreover this difference is more pronounced for higher order susceptibilities.

\item With increase of $\sqrt{s_{NN}}$, chemical potential decreases sharply whereas temperature increases
slowly. Therefore, $\chi^1$ and $\chi^3$  decrease with increase
of $\sqrt{s_{NN}}$ whereas $\chi^2$ and $\chi^4$ decrease slowly and then saturate.
As a result $\sigma^2/M$ increases with increase of $\sqrt{s_{NN}}$
, $S\sigma$ decreases with increase of $\sqrt{s_{NN}}$ whereas $\kappa\sigma^2$ remains almost constant in all energies.

\item Although the variations of $\sigma^2/M$ and $S\sigma$ with $\sqrt{s_{NN}}$ seem to describe the experimental data well,
higher moment $\kappa\sigma^2$ shows large deviations.
It may be an indication of quark degrees of freedom.
It would be
interesting to look at the other higher moments as they are supposed to have stronger dependence on correlation length and hence
will be more sensitive to the critical fluctuations.

\end{itemize}
In general, EVHRG seems to have a better agreement with the LQCD continuum data at low $T$ and $\mu_B = 0$. But the
comparison with the experimental data does not provide us with a clear preference between HRG and EVHRG.

It may be noted that in figs.\ref{chi_S2_temp} and \ref{chi_BS11_temp} LQCD results are larger than all the HRG results in the
crossover temperature range of $0.14-0.15$ GeV. The LQCD may become closer to the HRG by the inclusion of non-PDG additional strange beryons
which, though not observed experimentally, are predicted by the quark-model and also observed in the LQCD spectrum \cite{14046511}.

Here we would like to mention that the, grand canonical (GC) description, as used for the present study is usually
considered as the relevant
description for the systems in heavy ion collision~\cite{jeon&koch-Hwa}. But if the conserved quanta, under
consideration, is small then one need to take care of the charge conservations and the present description will
not be appropriate. More specifically, it has been found that the results for scaled variances vary for different
ensembles though the mean multiplicities from different ensembles tend to agree with each other in the infinite
volume limit~\cite{begunprc76}. Moreover, micro canonical ensemble seems to give a better
agreement with the data~\cite{begunprc76}. These findings definitely suggest the importance of the conservation laws.
We plan to study these aspects in our future work.

\section *{Acknowledgement}
The work is funded by CSIR, UGC (DRS) and DST of the Government of India.
The authors thank STAR collaboration for providing the experimental data.
We would like to thank Anirban Lahiri, Sarbani Majumder, Xiaofeng Luo, Nihar Ranjan Sahoo and Swagato
Mukherjee for useful discussion.

redpajama_set_name: RedPajamaArXiv


WEST EARL TOWNSHIP, Pa. -- Route 222 in Lancaster County has been closed twice this summer because of flooding. Many folks are wondering what's being done to prevent this moving forward.
The good news is the problem is already on PennDOT's radar. The bad news is it will take at least eight years, if not longer, before any changes can be made.
In the last ten years, Route 222 south of Brownstown has closed three times because of flooding.
"It's highly unusual, to the point where many of us who work here cannot remember having a summer with these extended periods of rain and the amount of flooding that we've had," Fritzi Schreffler, a spokesperson with PennDOT, said.
PennDOT is already working on a project to reduce congestion and improve safety on another area of Route 222 at the interchange at Route 30.
It's a 20 million dollar project that is scheduled to happen over the next several years. Before it can look into this problem, phase 1 and 2 must be completed.
"When we looked at the amount of flooding, we were able to kind of tack something on to this project," Schreffler said. "So other part of the projects have to be completed first before we can look at it. And we'd have to assess, is there anything we can do? Is it strictly up to mother nature? In terms of maybe the road won't be flooded again for another ten to twenty years."
Right now, folks have to wait for the water to recede.
"There are some things that we can look at, in terms of 'can we somehow direct water away from that particular section from the roadway? Is there something we can do with the retaining walls?' but in the case like what we've had this summer, it's just one of those all you can do is wait until it recedes and hope for the best," Schreffler said.
Since the road hasn't sustained any damage PennDOT says it can't do anything.
"It's not that a roadway is not a priority when it floods it's just typically flooding is flooding and there really isn't anything we can do to prevent it. If we get several inches of rain, and the creeks rise, there's not a lot that we can do about that," Schreffler said.
Right now Route 222 is open. If the road were to close again because of flooding, PennDOT says the only thing it can do is wait for the water to go down.


The Park City Planning Department has published a list of refinements to Treasure crafted by the development partnership in recent months, a diverse set of changes that were presented as the partnership attempts to win support for the proposal during what are expected to be the final months of discussions after more than a decade of talks.
The Planning Department detailed the refinements in a report issued in anticipation of a meeting about Treasure scheduled on Wednesday. The Park City Planning Commission appears to be preparing to cast a vote on Treasure later in 2017. The list of refinements seems to be an important step by the developer at a time when the Planning Commission continues to have deep-rooted concerns about the project. The list covers nearly three pages and addresses refinements between the current plans and a 2009 version.
The list provides a building-by-building rundown of the refinements. Treasure is designed to appear as if it is a collection of separate buildings. They will be connected with an underground garage, however.
Converting one of the buildings to flats rather than the townhouses that had been planned. The building was also shifted to the west.
Eliminating a building for a pool and shifting the activities that were planned inside to another space in Treasure.
Eliminating a circular ramp that was designed to access a parking garage.
Adding a penthouse unit to a building, requiring another story.
Eliminating a story from a building.
Adding several stories at one location of a building, which changes the mass.
Eliminating one story from the west wing of a building and adding a partial story to the building's east wing.
The refinements were made to a 2009 version of Treasure that has largely been the basis for the talks since then. The 2009 version itself was a more detailed rendition of an earlier plan.


Leading edge luxury and state-of-the-art design is set to change the face of Main Ridge in this fully renovated and extended designer residence with a poolside pavilion set high on its seven acres approx. to frame panoramic rural views through to the bay and ocean.
A design masterpiece, the progressive combination of clever internal styling, buffering wharf style decking and organic natural materials blur the boundaries between art and architecture, while multiple open, light-filled living spaces combine dramatic beauty with sophisticated amenities and meticulous attention to detail.
With interiors that present straight from the pages of a magazine, towering walls of glass rise up from floor-to-ceiling emphasising the outdoors areas and voluminous sense of space and light. Storage solutions are prioritised to retain the streamlined presence in every room; while pendant lighting, engineered oak flooring, porcelain tiling in the wet areas with an earthy concrete look and the inspired use of Cyprus highlights provide uniformity.
This expertly-designed home puts the focus on family function with four bedrooms, three bathrooms and three clearly defined living zones. Soaring 3.3 metre ceilings and a fireplace wrapped in floor-to-ceiling Cyprus defines the family living and dining room which seamlessly extends to the solar heated pool and deck with glass balustrading for unimpeded views. A BBQ kitchen is matched with a superb pavilion with an integrated lounge, kitchenette with wine fridge, WC and huge cut out windows framing the magical outlook.
A second living area is a place of perfect peace with a wood combustion heater, day bed and deck access; while a lower-level retreat with study offers self-contained guest accommodation with a fourth bedroom with en suite. The luxurious main bedroom enjoys a dressing room and sublime en suite with a freestanding bath where you can lie back and soak up the water views.
The sophisticated kitchen matches stone benchtops with a broad island bench with breakfast bar, Smeg appliances, butler's pantry and an adjoining open study with concealed storage.
Comprehensive appointments include ducted air conditioning and heating underfloor heating in the top-floor bathrooms, mud room, ducted vacuum and family-wise laundry.
Positioned within close proximity to everything the Hinterland has to offer this outstanding holiday house sets the benchmark for fine design and family function.


text:
#ifndef RHOTHREADIMPL_H
#define RHOTHREADIMPL_H

#include <QThread>
#include "common/IRhoThreadImpl.h"
#include "logging/RhoLog.h"

namespace rho{
namespace common{

class CRhoThreadImpl : public IRhoThreadImpl
{
    DEFINE_LOGCLASS

public:
    CRhoThreadImpl();
    virtual ~CRhoThreadImpl();
    virtual void start(IRhoRunnable* pRunnable, IRhoRunnable::EPriority ePriority);
    virtual void stop(unsigned int nTimeoutToKill);
    virtual int wait(unsigned int nTimeout);
    virtual void stopWait();
    virtual void sleep(unsigned int nTimeout);
private:
    void setThreadPriority(IRhoRunnable::EPriority ePriority);
private:
    class QRhoThread: public QThread
    {
    public:
        QRhoThread(IRhoRunnable* pRunnable): QThread(), m_Runnable(pRunnable) {}
        void run() { m_Runnable->runObject(); }
        static void sleep(unsigned long timeout) { QThread::sleep(timeout); }
    private:
        IRhoRunnable* m_Runnable;
    };
    QRhoThread* m_Thread;
    QThread* m_waitThread;
};

}
}

#endif // RHOTHREADIMPL_H

redpajama_set_name: RedPajamaGithub


The Concordia Stingers soccer teams have different objectives for the winter season. Head coach Greg Sutton wants to use the time as a way to prepare for next year and try new formations with his men's team, while maintaining consistency on the women's side.
The women's team finished the fall season sixth in the Réseau du sport étudiant du Québec (RSEQ), with a 4-9-1 record. For this winter season, due to injuries and players graduating, they don't have much depth.
The soccer teams each play seven games during the winter season. Photo by Gabe Chevalier.
Sutton was named head coach of the women's team last July, so this is his first full year of recruiting. He said there are players that will be joining the team in the fall, but aren't playing with them this winter.
On the men's side, a change of formation is a major priority for Sutton. They played with a four-man backline throughout the season, either in a 4-5-1 or 4-4-2 set-up, but this winter, he wants to try something different, with a 3-5-2 formation. It has become more popular in the soccer world after Antonio Conte used it when he was the manager with Juventus and Italy. By taking one defender away, it requires the centre backs to communicate well.
Sutton said he wanted to try the 3-5-2 because it allows his team to control possession and play with an extra attacker. In three games so far this winter season, the Stingers have two shutouts.


text:
October 19, 2021 October 22, 2021 Grab the Lapels
The Woman in Black by Susan Hill
Surely, it was popular when it first came out in 1983, but The Woman in Black by Susan Hill generated lots of attention when it was made into a movie starring Daniel Radcliffe.
The premise is simple: Arthur, a young lawyer, is assigned the task of handling the will of the recently deceased Mrs Drablow. The elderly woman lived in Eel Marsh House, unremarkable save for its location: a boggy island that is only accessible when the tide is out. A sturdy young man not taken in by the occult, Arthur kisses his fiance goodbye and heads first to the town a few miles from his destination in order to procure transportation. The townspeople are friendly until Arthur mentions why he's there; then, they ignore him.
Upon his arrival to Eel Marsh House, which is perfectly timed with when the tide goes out, Arthur sees a woman who looks as though she's suffering from a wasting disease. Also, he hears the sound of a carriage crash and child crying incessantly for help. Yet, a thick fog rolls in, and Arthur finds himself almost lost in his pursuit of the child, wondering if he'll be stuck on the small land connection between the house and the town when the tide rolls in, or if he'll drown in the wet, unstable ground that sucks at his feet and could swallow a man whole.
Susan Hill has crafted a novella that echoes Victorian novels, but reads a bit more smoothly, slightly more modern. She captures the atmosphere of each setting, no matter where Arthur is. For instance, before leaving for Eel Marsh House, he must brave the London weather:
Fog was outdoors, hanging over the river, creeping in and out of alleyways and passages, swirling thickly between the bare trees of all the parks and gardens of the city, and indoors, too, seething through cracks and crannies like sour breath, gaining a slight entrance at every opening of a door.
Arthur, though facing a serious job and the possibility of a ghost preventing him from doing his work, is a funny narrator. When he arrives at Eel Marsh House, he assumes the place to have gone to rack and ruin because Mrs Drablow lived alone. He admits he half expected the place to either be a shrine to a dead husband Mrs Drablow has mourned for years, or " . . . to be simply cobwebbed and filthy, with old newspapers, rags and rubbish piled in corners, all the debris of a recluse — together with some half-starved cat or dog." Now, perhaps my sense of humor has gotten too dark, but I found that description funny because it felt sadly spot on. There's another moment when Arthur describes a clerk as having "the complexion of a tallow candle, and a permanent cold, which caused him to sniff every twenty seconds . . ." Can't you just picture this fellow and feel simultaneously sad, grossed out, and like you've met him?
In a stroke of genius, Hill uses all the old Victorian tropes in haunted stories: the harbinger, the isolated setting, a dead woman with piles of paper that could contain secrets, creepy noises, even a dog that growls and barks when it seems like nothing is there. The Woman in Black is yet another novel that is not scary, but more spooky. If you enjoyed the plot of Shirley Jackson's The Haunting of Hill House or perhaps older novels like Northanger Abbey by Jane Austen, you'll enjoy Susan Hill's novella. I had great fun reading it and enjoyed such a stubbornly realistic narrator even when he was faced with the occult.
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I tried to start this one last week and couldn't get on with it at all. Must try again!
It starts with a story about the narrator with his family at Christmas, and they are telling ghost stories. Then, when he is unable to tell his own real story, he runs out of the room and realizes he must write his tale to get it out of his head. This is when we jump back to him as a man in his early 20s. Give it another go, Cathy!
I think I will, thanks!
And then all the U.K. folks on here are saying it's also a stage production. Maybe they have a cool version in Ireland!
I actually think I've seen the stage production years ago but all I remember is a very creepy rocking chair!
Lady Tessa says:
I love haunting tales, especially ones in the shorter novella format. Excellent review!
Novellas are actually my favorite format overall, though I think many people do them poorly. A writing professor once told me never let your short story become a long story, never let your long story become a novella, and never let your novella turn into a novel.
cupcakesandmachetes says:
I loved the movie with Daniel Radcliffe lmao. I have not read this though. Probably should change that one day. It does sound like something I would like.
You can read the whole thing in an afternoon. I wanted to watch the movie (I saw it when it came out in theater) right away, but didn't want to confuse myself if there were lots of differences in the plots.
RebeccaFrostWrites says:
I read it around the time they were hyping the movie and I thought it was going to be scary-scary, so I didn't like it, because it was just … eerie.
I think the dog adds the most tension with her barking at nothing and lovely loyalty. It was more so the setting that really made it for me. Hill does a great job of describing what the location feels like and how it influences people's emotions. This is more spooky than horror, so maybe if you reread it with the mindset that it is not so much stabby as haunted, you'd like it more?
This is one of the very few traditional ghost stories that works for me. I had to watch the original movie in school and the special effects were so bad we all found it hilarious 🙂 The Daniel Radcliffe version is better. It's also famous in Britain because of the West End stage show.
Ooooh, I did not realize Hill's story was taken to the stage, but I can see how it would work with a few simple set pieces and a good sound designer. I wanted to watch the Radcliffe version right away but did not want to confuse my review if the plots are different at all. I just looked up images from the original movie and am sad that the woman doesn't look nearly haggard/wasted away enough for what the author describes!
wadholloway says:
Novels like this rise out of the tradition of Gothic Fiction (which Austen was inclined to ridicule). One of the earliest was Ann Radcliffe's The Mysteries of Udolpho (1794) which I think you said you have read (I read another one of hers, The Italian). Probably the only other fiction in this vein I have read is Edgar Allan Poe.
I have not yet read The Mysteries of Udolpho, but I have mentioned it because Jane Austen mentions it in Northanger Abbey, in which the heroine reads Radcliffe's book and takes it to heart, which leads her to some pretty boring, mundane encounters. I know Austen was making fun of the Gothic novel, but Northanger Abbey fell flat for me. I do love Gothic fiction that has a good setting. I would even put Rebecca by Daphne du Maurier in there.
Now this one sounds right up my alley. 🙂 And it's a novella! I'm gonna have to look into this one.
Thanks to Hill's novella being somewhat of a classic and the Daniel Radcliffe movie tie in, it's likely that your library has a copy, too!
I have to confess that I got in trouble at school over The Woman in Black! I took GCSE Drama, and my teacher wanted to take us all to London to watch the West End show, but the plot sounded so terrifying that I never gave the permission slip to my parents. Everyone else went (and I did go to another play the next year) but my teacher was not very happy with me. Still, it does sound pretty spooky, and I think an atmospheric stage production might have been a bit much for me when I was 14. Though maybe I'm brave enough now to at least read the novella!
Oh, Lou, what a sweet story! Did your parents ever find out and say anything about your refusal to include them in the conversation? I hadn't realized there was a stage show until some of the U.K. and Canadian readers here pointed it out! I can just imagine how much or how little can be done with the set and atmosphere to make the show great. I think you can do the novella just fine. It's more Gothic/haunting, not really scary-scary.
annelogan17 says:
OH MY LORD this book came out in 1983? Jesus I thought it was like a century old! I thought it was written in the early 1900s LOL
Karissa says:
I absolutely thought the same thing! I've not read it or seen the movie but before reading this I would have guessed it was written in the early 20th century!
Susan Hill writes a convincing late 1800s novel! She uses all the Victorian tropes to great effect while keeping the novel FEELING modern, in a weird way. I can't quite describe why…perhaps the readability? Her refusal to include 50 extra characters who don't matter?
Hahaha! Why did those writers love to include so many unnecessary characters??!!
haha I'm glad I'm not the only one!
Right? I did, too. No, but she does write like it's an older book, though it's very readable. I quite enjoyed it and would recommend it to you if you liked the stage show.

redpajama_set_name: RedPajamaCommonCrawl


" European Music Day is celebrated to coincide with the summer solstice on 21 June with the aim of promoting cultural exchange through music. ..."
European Music Day is celebrated to coincide with the summer solstice on 21 June with the aim of promoting cultural exchange through music. To mark this day, Spain's main cities arrange a programme of concerts and special musical activities in numerous different styles and genres.
It was first held in France in 1982 under the name of 'Fête de la Musique', with the motto 'bringing musicians out into the streets'. Three years later in 1985 the initiative was extended to the European level, and 21 June was named European Music Day. This cultural event encourages diversity and is open to all kinds of music and musicians, both professional and amateur.
In Spain, public and private institutions take part in the event by organising activities for all types of audiences in various places and urban venues. On this day, the main cities in Spain stage –for example– open air symphony concerts, music festivals and marathons, free opera performances, DJ sessions in the street, model-making competitions, recitals by students, etc… Whatever your musical tastes, this is the perfect occasion to enjoy them.


Set on 11.7 Ha of land this established smallholding is just 20 minutes from Pietermaritzburg. Dwellings consist of a spacious three bedroomed home with two bathrooms and a large covered verandah with magnificent views, as well as a fully self contained three bedroomed thatch cottage with separate entrance. The property comes with two fully automated chicken houses (38m x 4m x 5m) including chainfeeders, nest boxes, drinking lines and two automated storage silos. Outbuildings consist of an office, large storage sheds, five domestic rooms and an unfinished one bedroomed cottage. The entire property runs on a 1000l/hr Borehole. Call today more information and a personalised viewing.
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Words containing PREQUALIFY. With this 10 letter combination (P R E Q U A L I F Y) you can create 1 anagrams that contain all the same letters. We found partially matching words lists! We searched for words in our database of more than 182 000 anagrams.


The Flour Shop Bakery is excited to celebrate Valentine's Day with you! Take your littles over for some fun themed Cookie Decorating from 2-5pm! Purchase each child a Cookie Kit for $10 and they will get to decorate them with icing and sprinkles.
All ages are welcome however some ages may need more parent help than others.


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Home/Science/Dog Domestication May Have Begun because Paleo Humans Couldn't Stomach the Original Paleo Diet
Dog Domestication May Have Begun because Paleo Humans Couldn't Stomach the Original Paleo Diet
News Opener Publishers1 week ago
It's easy to understand why early humans domesticated dogs as their new best friends. Tame canines can guard against predators and interlopers, carry supplies, pull sleds and provide warmth during cold nights. But those benefits only come following domestication. Despite more than a century of study, scientists have struggled to understand what triggered the domestication process in the first place. A new theory described today in Scientific Reports posits that hunter-gatherers whose omnivorous digestive system prevented too much protein consumption likely shared surplus meat with wolves. Those scraps may have initiated a step toward domestication.
"This is the first time that we have an ecological explanation for dog domestication," says lead author Maria Lahtinen, a senior researcher at the Finnish Food Authority and a visiting scholar at the Finnish Museum of Natural History. "I personally don't think that there is a simple, easy answer behind dog domestication, but we need to see the full picture and complexity of the process."
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Lahtinen did not originally set out to solve a long-standing dog mystery. Instead she was studying the diet of late Pleistocene hunter-gatherers in Arctic and sub-Arctic Eurasia. At that time, around 20,000 to 15,000 years ago, the world was engulfed in the coldest period of the last ice age. In frigid environments then, as today, humans tended to derive the majority of their food from animals. Nutritional deficiencies came from the absence of fat and carbohydrates, not necessarily protein. Indeed, if humans eat too much meat, diarrhea usually ensues. And within weeks, they can develop protein poisoning and even die. "Because we humans are not fully adapted to a carnivorous diet, we simply cannot digest protein very well," Lahtinen says. "It can be very fatal in a very short period of time."
During the coldest years of the last ice age—and especially in harsh Arctic and sub-Arctic winters—reindeer, wild horses and other human prey animals would have been eking out an existence, nearly devoid of fat and composed mostly of lean muscle. Using previously published early fossil records, Lahtinen and her colleagues calculated that the game captured by people in the Arctic and sub-Arctic during this time would have provided much more protein than they could have safely consumed.
In more ecologically favorable conditions, wolves and humans would have been competing for the same prey animals. But under the harsh circumstances of the Arctic and sub-Arctic ice age winter, sharing excess meat with canines would have cost people nothing. The descendants of wolves that took advantage of such handouts would have become more docile toward their bipedal benefactors over time, and they likely went on to become the first domesticated dogs. As the authors point out, the theory makes sense not just ecologically but also geographically: the earliest Paleolithic dog discoveries primarily come from areas that were very cold at the time.
The new study presents a "fascinating idea about lean protein being a food that humans would have discarded but wolves may have relied on during winter months in the Arctic," says Brian Hare, an evolutionary anthropologist at Duke University, who was not involved in the work. "I think it offers another vital clue for how the human-dog partnership might have been initially fueled."
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Will Smith and Martin Lawrence Return to Form
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I'm on my way back from back surgery. Just wanted to say "hi" and let you know that I'm now also posting to the Shivas Irons Society blog at http://www.shivas.org, at the Sierra Golfer magazine website at http://www.sierragolfer.com as well as here.
Please stay tuned for an upcoming post about PGA & LPGA Tour golfers and Twitter. There's a cool surprise "Twitter interview" with one of the most vivacious golfers on the LPGA that I think you'll like.
I'm also posting this code 94442FFMPXB9 so that Technorati knows this is my blog.
2 users commented in " On the Mend "
"Twitter interview" with one of the most vivacious golfers on the LPGA ".
it would be very interesting.Pay attention to your everything!


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Bluewater's Upcoming Events
Upcoming Event List
POSTPONED: Baltimore Boat Show on January 20, 2022
POSTPONED: The Princess Experience on January 21, 2022
Mid-Atlantic Sports & Boat Show on January 28, 2022
Viking VIP Winter Preview on February 4, 2022
Miami Yacht Show on February 16, 2022
Miami International Boat Show on February 16, 2022
Ocean City Seaside Boat Show on February 18, 2022
Palm Beach International Boat Show on March 24, 2022
Viking Key West Challenge on April 6, 2022
Oriental Boat Show on April 8, 2022
Bay Bridge Boat Show on April 21, 2022
Hatteras Village Offshore Open on May 10, 2022
Big Rock Keli Wagner Lady Angler Tournament on June 10, 2022
Big Rock Blue Marlin Tournament on June 13, 2022
Virginia Beach Tuna Tournament on June 22, 2022
Hatteras Marlin Club Blue Marlin Release Tournament on June 26, 2022
Ocean City Tuna Tournament on July 8, 2022
Big Rock Kids Billfish Tournament on July 13, 2022
Ducks Unlimited Billfish Tournament on July 20, 2022
White Marlin Open on August 8, 2022
Alice Kelly Tournament on August 14, 2022
Pirate's Cove Billfish Tournament on August 16, 2022
Virginia Beach Billfish Tournament on August 24, 2022
Wilmington Boat Show on September 30, 2022
United States Powerboat Show on October 6, 2022
Fort Lauderdale International Boat Show on October 26, 2022
Mid-Atlantic Rockfish Shootout on December 8, 2022


Alldo \a-ll-do\ as a boy's name is a variant of Aldo (Italian, Old German) and Aldous (Old German), and the meaning of Alldo is "old one, elder".
The baby name Alldo sounds like Aled, Alto, Elado and Waldo. Other similar baby names are Ado, Allyn, Allon, Allin, Allie, Alley, Allen, Allan, Alano, Allcot, Aldon, Alejo, Aleko, Aleco, Alfio, Alfeo, Alfo, Allton, Amado, Alcado, Clodo, Aroldo, Araldo and Naldo.