text:
\section{Introduction}
The determination of the phase structure of strongly interacting matter
is one of the major challenges in theory and experiment.
In our contribution we study the phase transition from hadrons to a
quark-gluon plasma in asymmetric matter.
Based on a two-phase model we describe new qualitative features that arise as
a function of the isospin and that may be relevant for the phenomenological
description of highly energetic heavy-ion collisions.

The creation of the quark-gluon plasma and the elucidation of its
properties is the fundamental goal in relativistic heavy--ion physics.
Although experiments at the Brookhaven AGS and at the CERN SPS have provided
evidence that in highly energetic collisions an intermediate
state is formed which is characterized by very high energy densities
\cite{STACHEL92}, it is
not clear if this new phase of matter has actually been reached
(for a recent review, see \cite{HARRIS96}).

On the theoretical side the determination of the equation of state (EOS)
of strongly interacting matter at high temperatures and densities is a
major problem in QCD.
One of the most important issues here is revealing the phase
diagram of matter and the nature of the transition.
Most reliable results come from lattice calculations for systems at zero
baryon density (for an updated status report see \cite{KANAYA96}).
These calculations clearly indicate a first-order transition for pure
$SU(3)$ gauge theories \cite{BOYD95}. When dynamical quarks are added the
situation is less transparent. The nature of the transition
not only depends on the number of
flavors but also on their masses \cite{BROWN90,IKKY95}, particularly on the
mass of the strange quark.
For example, three light flavors show a first-order transition that is
absent for larger masses \cite{BROWN90}.
Despite the need of corresponding information
in applications to heavy--ion collisions, lattice calculations at finite
baryon density presently remain at an early stage without a definite
conclusion \cite{KANAYA96}.

To the best of our knowledge, there are no lattice
calculations available for asymmetric systems, {\em i.e.}, systems
at finite baryon density and with nonzero isospin.
However, it has been demonstrated in case of the liquid-gas phase transition
of nuclear matter that asymmetric systems have qualitatively different
properties than symmetric systems \cite{BB80,G92,HMUE95}. In particular, the
transition in an asymmetric system is {\sl continuous} and of second order
according to Ehrenfest's definition, in contrast to the discontinuous,
first-order transition in symmetric systems.
The goal of the present work is to extend these studies to the
deconfinement phase transition of asymmetric matter.
Since lattice calculations cannot provide the required information at present,
we resort to a separate description of the hadronic and the quark-gluon phase.
This approach is not new and was previously employed to investigate
the existence of quark cores in neutron stars \cite{COLLINS75,BAYM76}.
Although such a formulation oversimplifies the full complexity of the problem,
it is useful for providing a first orientation to the new features that
arise when a system with two conserved charges, {\em i.e.},
baryon number and isospin, undergoes a transition.

The EOS for the quark-gluon phase is based on a simple ``bag model'', where
the thermodynamic potential is modeled as a sum of a perturbative contribution
and a nonperturbative part which is represented by the bag constant.
Along these lines we adopt a model which is based on two massless flavors
and which includes the first-order correction in the strong coupling constant
$\alpha_s$ \cite{BAYM76,KUTI80}.

The hadronic EOS is generated in a relativistic mean-field approach
involving the interaction of Dirac nucleons with isoscalar scalar and vector
meson fields and with isovector $\rho$ meson and pion fields \cite{SW86,BDS92}.
The central object in this approach is an energy functional of the meson
mean fields, which, in principle, can be formulated without reference
to an explicit Lagrangian \cite{FST96}.
It has been shown in numerous applications that this type of model
provides an excellent description of nuclear matter and of bulk nuclear
properties throughout the periodic table
\cite{BDS92,FST96,BOGUTA77,REINHARD86,FPW87,FURNSTAHL89,BODMER89,GAMBHIR90,%
FURNSTAHL93}.
Thus we can calibrate our hadronic equation of state at zero temperature and
normal nuclear densities, and then extrapolate into the
regime of high density and temperature appropriate for the phase transition.
The model we study involves cubic and quartic isoscalar self-couplings.
Although nonlinear $\rho$ meson interactions are possible \cite{HMUE96},
the nuclear symmetry energy is achieved using the simplest
possible coupling of the $\rho$ meson field to the nucleon.
The pions are incorporated by adding their one-body contribution, {\em i.e.},
the contribution of an ideal Bose gas with an effective chemical potential,
to the thermodynamic potential. The effective chemical potential is chosen
such that the $\rho$ meson field couples to the total isospin density,
which receives a contribution from nucleons and pions.

At low temperatures, the qualitative features studied here depend strongly
on the nuclear symmetry energy.
At higher temperatures, the inclusion of the pions is crucial due to
the onset of a pion condensate in very asymmetric systems.
The pions are incorporated in a very simple manner. Generally
the isovector dependence of the hadronic EOS may be more complicated than
in our model;
however, these properties are not well known, particularly when one is far
from symmetric matter.
In this context it is important to realize that the hadronic model is
formulated in terms of effective degrees of freedom.
The two conserved charges, baryon number and total isospin, are the relevant
quantities in the thermodynamic analysis whereas
the particle numbers of the individual species may change when parameters,
{\em e.g.}, temperature and pressure, vary.
In the present case the pion condensed phase resembles closely matter
containing $\Delta$-resonances,
which we could include in our model as well as other unstable nucleon
resonances.
However, we expect that this will not change the qualitative features of the
EOS, since it depends only on the {\em total} baryon number and isospin.

Although our EOS can be calibrated very accurately at zero temperature and
normal nuclear densities, the extrapolation into the regime of high densities
is not unique.
In the context of neutron star calculations it has recently been demonstrated
\cite{HMUE96} that the high density EOS is sensitive to combinations of
parameters that
are difficult to calibrate at normal densities. As a consequence, large
uncertainties in the predictions arise.
The density regime where the transition of hadronic
matter to a quark--gluon plasma takes place corresponds to the interior region
of a neutron star. Therefore similar difficulties can be expected.
Although this limits the quantitative results of our analysis, the
qualitative features of the basic physics remain unchanged.

Studies of the deconfinement phase transition
in terms of a separate description of the two phases have a long history
in the literature. In particular, in the context of neutron star matter,
many calculations similar to ours have been performed earlier
\cite{G92,COLLINS75,BAYM76,KUTI80,SW86,PCL95,BDS87}.
The first analysis which considered the transition in a system with two
conserved charges was performed by Glendenning \cite{G92}, with the
restriction to zero temperature and to neutron star matter, {\em i.e.},
matter in beta-decay equilibrium.
Along these lines the effect of neutrino trapping on the composition of
cold protoneutron stars with quark cores has been investigated more recently
\cite{PCL95}.
We will extend the analysis to systems at arbitrary temperature, baryon
density and isospin.
By definition, the two-phase model cannot reveal the actual nature of the
transition.
In contrast, other phenomenological approaches which are directly inspired
by the symmetries of QCD, for example linear sigma models \cite{PISARSKI84},
have been applied to shed more light on the fundamental properties of the
transition.
However, whether it is of first or second order or a cross-over
phenomenon can only be established by full QCD studies, {\em i.e.},
by lattice calculations. We believe that, until this information is
available, our approach is useful for providing a first orientation
of the qualitative features which arise in the phase diagram of strongly
interacting matter at finite baryon density and isospin.
At zero baryon density the two-phase model implies a first-order transition.
Starting from there our results are qualitatively similar to what was found in
case of the liquid--gas phase transition of nuclear matter \cite{HMUE95}.
Primarily, the transition of hadrons to quarks and gluons in asymmetric systems
is of {\em second order}, in contrast to the first-order transition that occurs in symmetric matter (which behaves like a one-component system).
That means that some thermodynamic variables, {\em e.g.}, the entropy, are
continuous and smooth throughout the transition, whereas the first-order
transition is characterized by discontinuities in these quantities.
Furthermore, we find that the transition regime in terms of densities and
temperatures varies significantly with the isospin of the system.
In particular the density at the onset of the transition is always lower
in asymmetric matter. This result led us to the conclusion
that it is more likely that the transition region is reached in collisions
of very neutron-rich nuclei.

The outline of this paper is as follows:
In Sec.~II, we briefly summarize the general discussion
of phase transitions in multicomponent systems which can be found in
greater detail in Ref.~\cite{HMUE95}.
We focus on the new aspects which arise when a thermodynamic system is
described by two different equations of state.
In Sec.~III, we describe the models for the two phases
and summarize the relations that determine the equation of state.
In Sec.~IV, we apply our model to the deconfinement phase
transition.
We study the phase coexistence region and illustrate different thermodynamic
processes by the aid of various phase diagrams and Maxwell constructions.
We consider special situations which arise during ultra-relativistic
heavy-ion collisions.
We also discuss the parameter dependence of the thermodynamic features.
Sec.~V contains a short summary.
\section{Phase Transitions in Multicomponent Systems}
We consider a system characterized by a set of $n$ mutually commuting
charges $Q_i$.
The thermodynamic features of such a system have been discussed earlier
\cite{BB80,HMUE95} in connection with the liquid-gas phase transition
of asymmetric nuclear matter.
Here we will focus on the situation where the system can exist in two
phases each characterized by a {\sl different} equation of state.
The partition function might be generated by a Hamiltonian which is
formulated in terms of different degrees of freedom in each phase \cite{G92}.
For example, the elementary constituents (quarks and gluons) would be used
in the first phase and composite particles (hadrons) in the second.
As mentioned in the introduction, it is important to keep in mind that
the conserved {\em charges\/} are the relevant quantities in the thermodynamic
analysis.
A conserved charge does not necessarily imply an independent particle
species which may change during a process (by decay, for example);
it includes any conserved quantity resulting from the
underlying symmetries of the system, for example, isospin, baryon number,
electric charge, {\em etc.}

To describe the equilibrium state of the system in phase $\alpha$
($\alpha=1,2$) enclosed in a volume $V$ we choose the
Helmholtz free energy $F$
\begin{eqnarray}
F_{\alpha}(T,V,Q_i) \equiv V{\cal F}_{\alpha}(T,\rho_i)
\quad,\quad \alpha=1,2
\label{eq:f1}
\end{eqnarray}
with
\begin{eqnarray}
\rho_i= {Q_i\over V}
\quad,\quad i=1,\ldots , n \ .
\nonumber
\end{eqnarray}

Depending on the value of the free energy the system will be realized
in one phase or the other or in a mixture of both, indicating a phase
transition.
To be more precise, the system in phase $\alpha$ will be stable against
separation into two phases
if the free energy of the single phase $\alpha$ is lower than the free energy
in all two-phase configurations.
This requirement can be formulated as
\begin{eqnarray}
{\cal F}_{\alpha}(T,\rho_i)<(1-\lambda){\cal F}_{\alpha}(T,\rho_i^{\alpha})
        +\lambda{\cal F}_{\beta}(T,\rho_i^{\beta})
	\quad , \quad \alpha,\beta=1,2
        \label{eq:stab1}\ ,
\end{eqnarray}
with
\begin{eqnarray}
\rho_i=(1-\lambda)\rho_i^{\alpha} +\lambda \rho_i^{\beta}\ ,
\qquad 0 < \lambda < 1\ .\label{eq:c1}
\end{eqnarray}
Note that this also implies
\begin{eqnarray}
{\cal F}_{\alpha}(T,\rho_i) \leq {\cal F}_{\beta}(T,\rho_i)
        \label{eq:stab2}\ ,
\end{eqnarray}
so if Eq.~(\ref{eq:stab1}) is satisfied, phase $\alpha$ is not only stable
against phase separation, it is also the energetically favorable single-phase
configuration.
We assume that each single phase by itself describes a stable
configuration\footnote{ When it actually happens that the free energy of
one of the single phases describes an unstable configuration, {\em e.g.}, due
to the liquid-gas phase transition in nuclear matter, we take
${\cal F}_{\alpha}$ to be the free energy resulting from a Maxwell
construction in the unstable region, which is convex.},
so that Eq.~(\ref{eq:stab1}) is satisfied for $\alpha=\beta$, {\em i.e.},
the free energy in each phase is a convex function of the densities \cite{RV73}.
The last equation (\ref{eq:c1}) ensures that the
overall charges are conserved:
\begin{eqnarray}
V\rho_i= V^\alpha \rho_i^\alpha + V^\beta \rho_i^\beta \quad
\hbox{with} \qquad V&=& V^\alpha + V^\beta \ .\label{eq:c2}
\end{eqnarray}

Equation (\ref{eq:stab1}) is a {\em global\/} criterion for
the stability of a one-phase configuration.
Whenever it is violated, a system with
two phases is energetically favorable.
The phase coexistence is governed by the Gibbs' conditions \cite{LL59}
demanding equal pressure $p$, temperature $T$ and chemical potentials $\mu_i$
in both phases
\begin{eqnarray}
\mu_i^\alpha (T,\rho_i^\alpha)&=&\mu_i^\beta(T,\rho_i^\beta) \ ,
\label{eq:g1}\\
p^\alpha(T,\rho_i^\alpha)&=&p^\beta(T,\rho_i^\beta) \ .\label{eq:g2}
\end{eqnarray}
It is important to realize, however, that under conditions of phase
separation, Eq.~(\ref{eq:stab1}) may still be valid {\em locally\/},
that means, in some small region $U=\{T,\rho_i\}$ of parameter space,
but it may nevertheless be possible
to find significantly different densities $\rho_i^{\alpha}$ and
$\rho_i^{\beta}$ in a larger domain $ U\subset G$ that violate this condition.
This leads to the existence of metastable states.

The two sets of densities $\{\rho_i^{\alpha},\rho_i^{\beta}\}$
that satisfy Eqs.~(\ref{eq:g1}) and (\ref{eq:g2}) form a surface
in the parameter space $\{T,\rho_i\}$; this is the phase separation boundary,
or binodal.
For $n$ conserved charges and two coexisting phases, Gibbs' phase rule implies
that the binodal is an $n$-dimensional surface \cite{LL59}.
It can also be shown that this surface encloses all points
that lead to a single (unstable) configuration with a higher value
for the free energy \cite{HMUE95}.

The binodal surface determines the stability boundaries of the system.
The mixed phase inside must be determined by a Maxwell construction.
This is achieved by solving Eq.~(\ref{eq:c1}) \cite{BB80,HMUE95}
for given values of $\rho_i$,
with $\rho_i^{\alpha}$ and $\rho_i^{\beta}$ lying on the binodal surface.
The free energy in the transition region is then given by
\begin{eqnarray}
{\cal F}(T,\rho_i)=(1-\lambda){\cal F}_{\alpha} (T,\rho_i^{\alpha})
+\lambda{\cal F}_{\beta}(T,\rho_i^{\beta})\ . \label{eq:femax}
\end{eqnarray}
Densities related to other extensive quantities
can be computed accordingly.

These ideas are illustrated in Fig.~(\ref{fig:max}).
We show the free energy density in both phases as a function of the density
coordinates $\{\rho_i\}$ at constant temperature. At the location of the points
$B_1$ and $B_2$, the system enters the binodal region. In between, a phase
mixture is energetically favorable. The free energy of the mixed phase as it
results from the Maxwell construction Eq.~(\ref{eq:femax}) is indicated by
the solid line which connects $B_1$ with $B_2$. The dotted lines
correspond to the free energy of the single-phase configurations. Between
the point of intersection $I$ and $B_1$ and between $I$ and $B_2$ lie
the metastable states of phase 1 and phase 2, respectively. The configurations
beyond $I$ are unstable. Here not only a phase mixture but also the single
(metastable) configuration of the opposite phase is energetically favorable.
Instability normally arises due to fluctuations, which no longer can be
restored by the system. This is signaled by the violation of a local
stability criterion, {\em e.g.}, a negative compressibility.
However, our description is based purely on the energetics and cannot
provide information about the physical mechanism which leads to instability.
This is certainly an indication that the separate description of the
two phases breaks down at this point.

We close this section by specializing the general formalism to asymmetric
matter.
In the hadronic phase it consists of strongly interacting nucleons and mesons,
and in the deconfined phase, weakly interacting quarks and gluons.
For two quark flavors
such a system is characterized by two conserved charges:
the total baryon number
\begin{eqnarray}
N_B \equiv V \rho_B
\end{eqnarray}
and the third component of isospin
\begin{eqnarray}
I_3 \equiv {1\over 2}\, V\rho_3 \ .
\end{eqnarray}
Thus we have for the thermodynamic potential, or equivalently the pressure,
\begin{eqnarray}
{\Omega_\alpha \over V}(T,\mu_B^\alpha,\mu_3^\alpha)= -p^\alpha =
{\cal F}_\alpha(T,\rho_B,\rho_3)
      -\mu_B^\alpha\rho_B-{1\over 2}\mu_3^\alpha\rho_3\ ,
\end{eqnarray}
where the baryon and isospin chemical potentials are given by
\begin{eqnarray}
\mu_B^\alpha =
   \left({\partial{\cal F}_\alpha
    \over \partial \rho_B}\right)_{T,\rho_3}
\quad , \quad
\mu_3^\alpha =
     2\left({\partial{\cal F}_\alpha
     \over \partial \rho_3}\right)_{T,\rho_B} \ .
\label{eq:chpot}
\end{eqnarray}
In the discussion of asymmetric systems it is also useful to introduce the
isospin ratio
\begin{eqnarray}
x \equiv {I_3 \over N_B}={\rho_3 \over 2\rho_B} \ ,
\label{eq:defx}
\end{eqnarray}
so that the free energy can be rewritten as
\begin{eqnarray}
{\cal F}_\alpha(T,\rho_B,\rho_3)=
       {\cal F}_\alpha(T,\rho_B,x) \ .
\label{eq:fx}
\end{eqnarray}
\section{The Equation of State}
To generate the nuclear equation of state in the hadronic phase, we adopt
the relativistic mean-field approach of Refs.~\cite{FST96,HMUE96}
involving valence Dirac nucleons and effective mesonic degrees of freedom,
which are taken to be neutral scalar $(\phi) $ and vector fields $(V^{\mu})$,
plus the isovector $\rho$ meson $({\bf b}^{\mu})$ and pion field
$(\bbox{\pi})$.
The basic quantity here is the thermodynamic potential as a functional of
the meson mean fields which, in principle, can be formulated without reference
to an explicit lagrangian.
For homogeneous nuclear matter, at finite temperature and chemical potentials
$(\mu_B,\mu_3)$, it is of the general form \cite{HMUE96}
\begin{eqnarray}
 {\Omega\over V}(T, \mu_B, \mu_3;\phi,V_{\nu},{\bf b}_{\nu},{{\pmb{$\pi$}}})&=&
               {\Omega_{N}\over V}+ {\Omega_{M}\over V}
 + {1\over 2}\,m_{\rm s}^2 \phi^2
      -{1\over 2}\,m_{\rm v}^2 V_{\mu} V^{\mu}
          -{1 \over 2}\, m_{\rho}^2{\bf b_{\mu}}
                             {\pmb{$\cdot$}}{\bf b}^{\mu}
 + {1\over 2}\,m_{\pi}^2 {{\pmb{$\pi$}}}^2 \nonumber\\
& &\null + \Delta{\cal V}(T, \mu_B, \mu_3; \phi,V_{\mu},
            {\bf b_{\nu}},{{\pmb{$\pi$}}})\ .
			   \label{eq:Omh}
                      \end{eqnarray}
The first two terms in Eq.~(\ref{eq:Omh}), $\Omega_{N}/V$ and $\Omega_{M}/V$,
are the one-body contributions due to valence nucleons and mesons.
The nonlinear potential $\Delta{\cal V}$ represents the unknown part of
the thermodynamic potential, which includes the effects of nucleon
exchange and correlations,
as well as contributions from the quantum vacuum \cite{FST96,FTS95}.

Following Ref.~\cite{HMUE95} the one-body fermionic contribution can be written
as
\begin{eqnarray}
{\Omega_{N}\over V} =
   -{1\over 3\pi^2}\Bigl[H_5(\nu_p,M^*)+H_5(\nu_n,M^*)\Bigr] \ ,
\label{eq:Omhn}
\end{eqnarray}
where the integral $H_5$ as well as others will be defined shortly.
The corresponding contributions of the heavy meson fields
$(\phi,V^{\mu},{\bf b}^{\mu})$ to $\Omega_{M}$ are negligible
in the relevant temperature range $(T\lesssim 200$ MeV).
Thus we keep only the pions and write
\begin{eqnarray}
{\Omega_{M}\over V} =
{\Omega_{\pi}\over V} = -{1\over 6\pi^2}\Bigl[B_5(\nu_{\pi},m_{\pi})
                              + {1\over 2} B_5(0,m_{\pi})\Bigr] \ ,
\label{eq:Omhm}
\end{eqnarray}
where the first term is the contribution of the charged pions
\cite{HABER82,KAPUSTA89}, and the latter arises from the $\pi^0$.
The nonlinear potential $\Delta{\cal V}$ can be expanded in a Taylor series
in terms of the meson mean fields \cite{FST96,HMUE96}.
In the normal phase of nuclear matter, {\em i.e.}, without a pion condensate,
the pion mean field vanishes and the pions contribute only to the coefficients
of this series via loops.
In practice, the series must be truncated, and the unknown coefficients
serve as model parameters, which are chosen to reproduce certain empirical
properties of equilibrium nuclear matter, as discussed below.
For our calculation we choose the explicit form
\begin{eqnarray}
\Delta {\cal V}= {\kappa\over 3!}\phi^3+{\lambda\over 4!}\phi^4
		-{\zeta\over 4!}g_{\rm v}^4(V_{\mu}V^{\mu})^2 \ ,
					  \label{eq:pot}
\end{eqnarray}
which includes a subset of the
meson self-interactions up to fourth order in the fields.
In principle, terms which couple different fields
and also nonlinear interactions involving the $\rho$ meson field
are allowed \cite{FST96}.
We also disregard contributions involving the
pion mean field which arise in the pion condensed phase.
Although disregarding these couplings  is ``unnatural'',  the present model
defined by Eq.~(\ref{eq:pot}) is already general enough for our purposes.
First of all, it can be accurately calibrated at normal densities, and
it can be related to the most common models discussed in the literature.
Unless one assumes scalar self-interactions only, the nonlinear couplings
cannot be uniquely constrained by the
calibration procedure, leading to uncertainties in the high-density EOS.
In particular, little information is available to
constrain contributions which explicitly depend on the pion field.
Moreover, among these nonlinear terms, the quartic vector coupling in
Eq.~(\ref{eq:pot}) is the most important one at high densities \cite{HMUE96}.
We will use this coupling to examine the uncertainties which arise in the
quantitative predictions for the transition from hadrons to a
quark-gluon plasma.

The mean fields are determined by extremization of the thermodynamic
potential Eq.~(\ref{eq:Omh}).
The specific form of $\Delta{\cal V}$, introduced in Eq.~(\ref{eq:pot}),
together with Eqs.~(\ref{eq:Omhn}) and (\ref{eq:Omhm}), leads to the
self-consistency equations

\begin{eqnarray}
{m_{\rm s}^2 \over g_{\rm s}^2}\, \Phi
  +{\kappa \over 2 g_{\rm s}^3}\, \Phi^2
  +{\lambda \over 6 g_{\rm s}^4}\, \Phi^3 &=& \rho_s \ ,\label{eq:scalar}\\
W \left( 1 + {g_{\rm v}^2 \over m_{\rm v}^2}\,{\zeta\over 6}\, W^2\right)
        &=& {g_{\rm v}^2 \over m_{\rm v}^2}\, \rho\ , \label{eq:vector}\\
R &=& {g_{\rho}^2 \over 2 m_{\rho}^2}\, \rho_3 \ , \label{eq:Rrho}
\end{eqnarray}
where the scalar and baryon densities are given by
\begin{eqnarray}
\rho_s &=& {M^*\over \pi^2}\Bigl[H_3(\nu_p,M^*)+H_3(\nu_n,M^*)\Bigr] \ ,
           \label{eq:rhos}\\
\rho_B &=& {1\over \pi^2}\Bigl[G_3(\nu_p,M^*)+G_3(\nu_n,M^*)\Bigr] \ .
           \label{eq:rhob}
\end{eqnarray}
The isospin density receives contributions from nucleons and pions
\begin{eqnarray}
{1\over 2}\rho_3 &=& {1\over 2}\rho_3^N + {1\over 2}\rho_3^{\pi}
           \label{eq:rho3}\\
&\equiv& {1\over 2\pi^2}\Bigl[G_3(\nu_p,M^*)-G_3(\nu_n,M^*)]
            +{1\over 2\pi^2}A_3(\nu_{\pi},m_{\pi}) \ .
           \nonumber
\end{eqnarray}
The scaled meson fields are
$\Phi \equiv g_{\rm s} \phi$, $W \equiv g_{\rm v} V_0$, and
$R \equiv g_\rho b_0$, with $b_0$ the timelike, neutral part of the $\rho$
meson field.

The baryon effective mass and effective chemical potentials are defined in
terms of the meson mean fields and the baryon and isospin chemical potential
as
\begin{eqnarray}
M^* &\equiv& M- \Phi \ , \label{eq:mstar}\\
\nu_p &\equiv& \mu_B+{\mu_3\over 2} - W - {1\over 2}\, R \ , \label{eq:nup}\\
\nu_n &\equiv& \mu_B -{\mu_3\over 2} - W + {1\over 2}\, R \ . \label{eq:nun}
\end{eqnarray}
The effective chemical potential for the pions is given by
\begin{eqnarray}
\nu_{\pi} \equiv \nu_p-\nu_n = \mu_3- R \ , \label{eq:nupi}
\end{eqnarray}
so that the $\rho$ meson field in Eq.~(\ref{eq:Rrho}) couples to the total
isospin density in Eq.~(\ref{eq:rho3}).
We also introduce the required integrals over the thermal distribution
functions as
\begin{eqnarray}
G_{n}(\mu,M)&\equiv&\int_{0}^{\infty} k^{n-1} dk
\left( {1\over 1+{\rm e}^{\mkern2mu\beta [E(k,M) - \mu ]}}
      - {1\over 1+{\rm e}^{\mkern2mu\beta [E(k,M) + \mu ]}}\right) \ ,
           \label{eq:Gdef}\\[4pt]
H_{n}(\mu,M)&\equiv&\int_{0}^{\infty} {k^{n-1} dk \over E(k,M)}
  \left( {1\over 1 + {\rm e}^{\mkern2mu\beta [E(k,M) - \mu ]}}
      + {1\over 1 + {\rm e}^{\mkern2mu\beta [E(k,M) + \mu ]}}\right)\ ,
           \label{eq:Hdef}
\end{eqnarray}
for fermions and
\begin{eqnarray}
A_{n}(\mu,m)&\equiv&\int_{0}^{\infty} k^{n-1} dk
\left( {1\over {\rm e}^{\mkern2mu\beta [E(k,m) - \mu ]}-1}
      - {1\over {\rm e}^{\mkern2mu\beta [E(k,m) + \mu ]}-1}\right) \ ,
           \label{eq:Adef}\\[4pt]
B_{n}(\mu,m)&\equiv&\int_{0}^{\infty} {k^{n-1} dk \over E(k,m)}
  \left( {1\over {\rm e}^{\mkern2mu\beta [E(k,m) - \mu ]}-1}
      + {1\over  {\rm e}^{\mkern2mu\beta [E(k,m) + \mu ]}-1}\right)\ ,
           \label{eq:Bdef}
\end{eqnarray}
for bosons,
where $E(k,M) \equiv (k^2+M^2)^{1/2}$, and $n > 0$ to ensure convergence is
understood. Moreover, the boson integrals are subject to the constraint
$|\mu|\leq m$.

By inserting the solution of
Eqs.~(\ref{eq:scalar})--(\ref{eq:Rrho}) into Eq.~(\ref{eq:Omh}),
it is straightforward to compute the pressure
\begin{eqnarray} p = -{\Omega\over V}&=&
     -{\Omega_{N}\over V}(T,\nu_p,\nu_n, M^*)
     -{\Omega_{\pi}\over V}(T,\nu_{\pi})
      \nonumber\\
 & &\null + {m_{\rm v}^2\over 2g_{\rm v}^2}\, W^2 + {\zeta\over 24}\,W^4
          +{m_{\rho}^2\over 2g_{\rho}^2}\, R^2
          -{m_{\rm s}^2\over 2g_{\rm s}^2}\, \Phi^2
          -{\kappa\over 6 g_{\rm s}^3 }\Phi^3
	  -{\lambda\over 24 g_{\rm s}^4 }\Phi^4 \ .
           \label{eq:pressh}
\end{eqnarray}
Other quantities like the free energy, the entropy, {\sl etc.}, follow by using
standard thermodynamic relations.

For the quark-gluon phase we adopt a bag-model type EOS \cite{KUTI80}
involving massless $u$ and $d$ quarks $(N_f=2)$
\begin{eqnarray}
{\Omega\over V}(T,\mu_B,\mu_3) =
     {\Omega_{\rm{\scriptscriptstyle pert}}\over V}(T,\mu_B,\mu_3) + b \ ,
\label{eq:Omq}
\end{eqnarray}
where $\Omega_{\rm{\scriptscriptstyle pert}}/ V$ is the perturbative expansion
of the thermodynamic potential
\begin{eqnarray}
{\Omega_{\rm{\scriptscriptstyle pert}}\over V}(T,\mu_B,\mu_3)&=&
-{\pi^2\over 45} T^4 \Bigl(8+{21\over 4}N_f\Bigr)
-{1\over 2}\sum_{f=u,d}\Bigl( T^2 \mu_f^2 +{\mu_f^4\over 2\pi^2}\Bigr)
\nonumber\\
& &\null + {2 \pi\over 9}\alpha_s
\biggl(T^4 \Bigl[3+{5\over 4}N_f\Bigr]
+{9\over 2}\sum_{f=u,d}\Bigl[ {T^2 \mu_f^2\over \pi^2}
			     +{\mu_f^4\over 2 \pi^4}\Bigr] \biggr) \ ,
\label{eq:Omqp}
\end{eqnarray}
and $b$ is the difference between
the energy density of the perturbative and the nonperturbative QCD vacuum,
{\em i.e.}, the bag constant.
The chemical potentials of the two flavors are connected to the baryon and
isospin chemical potentials by
\begin{eqnarray}
\mu_u = {1\over 3}\mu_B+{1\over 2}\mu_3
\quad , \quad
\mu_d = {1\over 3}\mu_B-{1\over 2}\mu_3 \ ,
\label{eq:muq}
\end{eqnarray}
which allows the computation of
the corresponding densities according to
\begin{eqnarray}
\rho_B = -\left( {\partial\over\partial\mu_B}{\Omega\over V}\right)_{T,\mu_3}
\quad , \quad
{1\over 2} \rho_3 = -\left( {\partial\over\partial\mu_3}
{\Omega\over V}\right)_{T,\mu_B} \ .
\label{eq:rhoq}
\end{eqnarray}

We close this section with a short description of the calibration of the EOS.
The model for the hadronic phase has six free parameters.
Following Ref.~\cite{FST96} we choose the value of the coupling $\zeta$ and
determine the other parameters so that the five equilibrium properties
of nuclear matter,
as listed in Table~\ref{tab:one}, are reproduced.
The free parameter $\zeta$ is chosen within the natural range
$0\leq\zeta\leq0.06$ \cite{FST96,HMUE96}.
To fix the two parameters in the quark-gluon phase, namely the
bag constant $b$ and the strong coupling constant $\alpha_s$, we proceed
as follows. We specify the bag constant to $b = 160$ MeV/fm$^3$ and determine
$\alpha_s$ so that our model reproduces a transition temperature of 150 MeV
at zero baryon density, which is in the currently accepted temperature range
\cite{BLUM95}. As a consequence of this calibration $\alpha_s$ depends on
$\zeta$.
This dependence, however, is extremely weak. The value $\alpha_s= 0.349$
obtained for $\zeta=0$ changes only by $0.1\%$ when $\zeta$ is
varied within the natural range.
\section{Phase structure of asymmetric matter}
In this section we apply the formalism of Sec.~II to the
deconfinement phase transition.
Within our simple two-phase model
we consider highly excited asymmetric matter created in
an ultra-relativistic collision of two heavy-ions.
The dynamical evolution of the system during the collision is a very complex
process and it is convenient to divide the reaction into three stages:
the formation of a highly excited matter system, its expansion and the eventual
decay.
The question of whether the required energy densities can be achieved in an
experiment to form a
quark--gluon plasma during the first violent stage is a difficult one, which
we will not attempt to answer here.
We simply assume that such a state arises and
ultimately reaches equilibrium at some finite temperature, density and pressure.
We follow the subsequent expansion of the system during the second stage and
concentrate on the new features of the phase diagram that arise as a
function of the total isospin.
Although our general discussion will encompass the entire range of $x\leq 0$,
we will study systems with $-0.2\leq x\leq 0$ and $x=-0.5$ in more detail
to obtain estimates for the size of the new effects. The former range
covers the isospin ratios which are experimentally accessible in
heavy--ion collisions,
{\sl e.g.}, $x_{{\rm Au}+{\rm Au}},x_{{\rm U}+{\rm U}}\approx -0.1$,
whereas the latter value corresponds to neutron matter relevant in
astrophysical applications.

As discussed in the context of the liquid-gas phase transition of asymmetric
nuclear matter \cite{BB80,HMUE95}, the phase structure of binary systems
is more complex than in one-component systems.
The basic quantity in the analysis is the phase separation boundary or binodal,
which forms a two-dimensional surface in parameter space
as discussed in Sec.~II.
Before we discuss the binodal structure of the deconfinement
phase transition as it arises in our model, let us briefly point out
the role of the pions.
To this end, assume our system is prepared in the hadron phase at some fixed
isospin ratio $x$, as defined in Eq.~(\ref{eq:defx}), and let us follow an
isothermal compression. At some critical baryon density $\rho_B^c$ the chemical
potential of the pions will approach the (negative) value of the pion mass,
{\em i.e.},
\begin{eqnarray}
\nu_{\pi} \to -m_{\pi}
\quad \hbox{for} \quad
\rho_B \to \rho_B^c \ , \label{eq:cond}
\end{eqnarray}
indicating the onset of a pion condensate \cite{LL59}. The critical density
depends on $x$ and on $T$, and will be smaller in more asymmetric systems.
At this point a macroscopically occupied $\pi^-$ mode arises which
is characterized by a nonvanishing pion mean field. In principle, the
corresponding contributions to the thermodynamic potential in Eq.~(\ref{eq:Omh})
must now be kept explicitly, and the value of the mean field is determined
by minimization \cite{HABER82,BAYM73}.
As discussed in the last section we will disregard the explicit
mean-field contributions of the pions in the following.
That means we neglect the pion-nucleon as well as the pion self-interactions.
To incorporate the condensed phase consistently we will be satisfied
to add the contribution of the zero-momentum states of the pions to the
isospin density in Eq.~(\ref{eq:rho3})
\begin{eqnarray}
{1\over 2}\rho_3^{\pi}=-2 m_{\pi}\kappa^2
		   + {1\over 2\pi^2}A_3(-m_{\pi},m_{\pi}) \ ,
		                   \label{eq:rho3PiC}
\end{eqnarray}
where the effective chemical potential
\begin{eqnarray}
\nu_{\pi}=\nu_p-\nu_n= -m_{\pi}
\label{eq:nuPiC}
\end{eqnarray}
is held fixed in the condensed phase. The parameter $\kappa^2$
is the continuous order parameter of this transition, which
specifies the amount of isospin charge carried by the zero-momentum states
\cite{HABER82,KAPUSTA89}.
In contrast, the condensate does not contribute to the pressure
of the system; thus, one simply substitutes the value of $\nu_{\pi}$, as given
by Eq.~(\ref{eq:nuPiC}), in the expression for the hadronic
pressure Eq.(\ref{eq:pressh}). We will leave the study of the contributions
arising from pionic interactions as an important topic for future work.

We now return to the general discussion of the phase diagram in
our system.
We begin the analysis with $\zeta=0$ for the value of the quartic vector meson
coupling in the hadronic EOS. We will study the influence of this parameter
at the end of this section.

The binodal is determined by Gibbs' conditions
(\ref{eq:g1}) and (\ref{eq:g2}) which enforce
equal pressure and chemical potentials for the hadronic phase and for the
quark--gluon phase in equilibrium.
In general these two phases have a different isospin ratio $x$.
The binodal surface in $\{x,p,T\}$ space is indicated in Fig.~\ref{fig:slices}.
A sequence of several slices at fixed $T$ is shown.
For a given temperature,
the binodal section is divided into two branches.
One branch, at the lower pressure, describes the system in the hadron phase,
while the other branch, at the higher pressure, describes the quark--gluon
phase.
These two branches contain the beginning and ending configurations of the
phase transition.
The shape of the binodal slices changes drastically
between $T=0$ and $T=150$ MeV.
One observes that the enclosed area becomes smaller with increasing
temperature until, at $T_c = 150$ MeV,
the two branches coalesce to a single line at constant pressure $p = 19.08$
MeV$/$fm$^3$ with isospin ratios ranging from $x\approx-4.5$ to $x=0$.
This line of critical points marks the transition point of systems at
zero baryon density.

Another important observation is that the pressure steadily decreases
when the temperature increases.
At the same time, the transition regime, {\em i.e.}, the difference in pressure
between the two phases at the beginning and at the end of a transition, becomes
smaller.
Also indicated in Fig.~(\ref{fig:slices}) are the special
configurations that separate into two phases with the same isospin ratio.
The coordinates of these configurations form the two lines of equal
concentration (LEC), one of which coincides with the projection $x= 0 $ in our
system.
The isospin ratio of the second LEC increases with temperature and
eventually the two LEC intersect at $T\approx 137.2$ MeV.
For a fixed temperature the pressure necessarily attains an extremum
at the points of equal concentration \cite{LL59}.

Generally, the hadronic configurations are divided into normal states and
states exhibiting
a pion condensate. The coordinates of the configurations at the onset
of the condensation also form a two--dimensional surface. This critical
surface can be parametrized in terms of two coordinates in $\{x,p,T\}$ space,
{\sl e.g.}, as $p_c(x,T)$.
The intersection of the critical surface with the binodal forms the
line of three phases (LTP),
which marks the onset of the pion condensate on the hadronic
branch\footnote{Since there is no two-phase coexistence
in a Bose condensation,
the LTP is not a line of triple points which could arise
in a binary system \cite{LL59}.  The LTP is merely a boundary between areas
in parameter space which describe two different two-phase configurations.}.
In Fig.~(\ref{fig:slices}) these states are emphasized by the bold dashed
lines. The isospin ratio of the LTP decreases with increasing temperature. Above
$T\approx 136.2$ MeV the critical pressure curve and the binodal no longer
intersect.

The binodal in $\{\rho_B,x,T\}$ space is indicated in
Fig.~(\ref{fig:bintvsrho}),
where several branches at different $x$ are projected onto the
$\{\rho_B,T\}$ plane. The onset of the condensate,
{\em i.e.}, the critical temperature as a function of the baryon density and
isospin ratio, is marked by an open circle. Note the change of density
in the two--phase region. The most extreme situations are encountered at $T=0$.
For example, in symmetric matter the density increases between the onset and
the completion of the transition by more than 3.5$\rho_B^0$.
This density regime becomes even larger in asymmetric systems.
Another important observation is that the density at the onset decreases
with increasing asymmetry. If we compare these points for $x=0$ and $x=-0.2$
at $T=0$ we find an decrease of $\Delta\rho_B\approx 0.5\rho_B^0$.

The role of the pions becomes more apparent in Fig.~(\ref{fig:slice}).
Part (a) indicates one slice of Fig.~(\ref{fig:slices}) at $T = 50$ MeV.
Also included is the projection of the critical surface in the form of the
critical pressure curve $p_c (x)$.
Nuclear matter in the normal phase resides on the right-hand side,
and the states with a pion condensate on the left-hand side.
The critical curve intersects the binodal at TP.
In contrast, the pion contributions are not included in part (b). With nucleons
only, the isospin ratio in the hadronic branch is limited by
$-0.5 \leq x \leq 0$ which leads to a widely open binodal surface.
Furthermore, only one point of equal concentration arises (at $x = 0$).

To illustrate the phase-separation scenarios,
we study the behavior of matter under an isothermal compression.
Assume that the system is initially prepared in
the hadronic phase with isospin ratio $x = -0.4$ and $p\lesssim 50$ MeV/fm$^3$.
The situation is also indicated in part (a) of Fig.~\ref{fig:slice}.
During the compression, the system first crosses the critical pressure
curve at the point $A$, where pion condensation begins.
Starting with $\kappa^2=0$ at $A$ the contribution of the condensate to
the (fixed) isospin ratio increases during the compression.
At the point $B$ the two-phase region is encountered and now a quark--gluon
phase is about to emerge.
The solution of Gibbs' conditions
(\ref{eq:g1}) and (\ref{eq:g2})
determine the density and the isospin ratio $x_{\scriptscriptstyle C}$ of this
new phase, which occurs at the point labeled $C$.
As the system is compressed, the {\em total\/} isospin ratio $x$ remains
fixed, as dictated by the conservation laws, but the hadronic phase evolves
from $B$ to $E$, while the quark--gluon phase evolves from $C$ to $D$.
At the point $D$, the system leaves the region of instability.
The original hadronic phase (which now has no pion condensate) is about to
disappear, and it exists in an
infinitesimal volume with a density and isospin ratio
$x_{\scriptscriptstyle E}$ corresponding to the point $E$.

An important observation is that if the system encounters the binodal
between the two points of equal concentration then the quark--gluon phase is
always more asymmetric and has a higher baryon density than the hadronic
phase.
This behavior is due to the {\sl symmetry energy}, which is higher in the
hadronic phase. Therefore it is energetically
favorable for asymmetric matter to separate into a denser and
more asymmetric quark--gluon phase and a hadronic phase that is more
dilute and symmetric.

The energetics also implies a significant simplification if the
system is initially prepared with an isospin ratio corresponding
to one of the points EC.
It is now energetically favorable for the system to separate into two phases
with the same composition. In this so-called ``indifferent
equilibrium'' \cite{HS69}, matter behaves like a
one--component system (see also the discussion in \cite{HMUE95}). In contrast
to the previous case the system becomes unstable at one of the points EC in
Fig.~\ref{fig:slice}
and stays at this point until the transition is completed.
Note that the location of the point EC at $x=0$ is model independent
since symmetric matter is always the configuration with lowest energy.
The location of the second point depends on specific model features,
particularly on the predicted values for the symmetry energy and on the
pionic contributions.

The results of the corresponding Maxwell constructions are indicated
in Fig.~\ref{fig:pvsrho}.
We consider different isospin ratios at $T=0$ in part (a) and at $T= 50$ MeV
in part (b), respectively.
For symmetric matter $(x = 0)$, we obtain the familiar result
with a constant vapor pressure, represented by a horizontal line.
At $x<0$ the equal demand of Gibbs' conditions and the conservation of the
overall isospin forces the pressure to change during the transition.
Also shown in Fig.~\ref{fig:pvsrho} are isotherms for ``neutron matter''
$(x=-0.5)$. The name is somewhat misleading since the system contains
a finite number of protons even without the pions.
It is common in the literature \cite{HMUE96,COLLINS75,BAYM76,BDS87} to treat
neutron matter as a single-component system.
The qualitatively different features which
arise in a proper treatment as a system with {\sl two} conserved charges
have been pointed out earlier by Glendenning \cite{G92} in the context
of neutron star calculations (see also Ref.~\cite{PCL95}).
In addition, part (b) of Fig.~\ref{fig:pvsrho} also includes a system with an
isospin ratio which corresponds to the second point of equal concentration.
As discussed above, this system also stays at a constant vapor
pressure throughout the transition.

The change of the pressure throughout the phase separation
in asymmetric systems is an indication of
a {\sl smoother} transition than in symmetric or one--component systems.
A more precise characterization of the transition can be obtained from
the isobaric process indicated in Fig.~(\ref{fig:svst}).
The entropy as a function
of temperature for three different isospin ratios
is shown.
In symmetric matter we find a discontinuity at the transition temperature,
which gives rise to a latent heat $Q_L$, {\em i.e.}, all the heat is used to
convert hadrons into quarks.
In asymmetric matter the entropy remains
smooth but the temperature now changes throughout the transition so that no
strict latent heat can be assigned to this process.
For example, the isospin ratio $x= -0.2$ shown in Fig.~(\ref{fig:svst}) gives
rise to a temperature change of $\Delta T\approx 30$ MeV.
As discussed in more detail in Ref.~\cite{HMUE95}, these are the features
which lead to a first-order transition in symmetric matter and to a
second-order transition in the asymmetric system,
according to Ehrenfest's definition.

The processes we have considered so far correspond to very specific idealized
situations and served mainly to study the basic thermodynamic features of
our system.
Generally, it is not clear if the expansion of the highly excited matter
created in a heavy--ion collision can be described by a distinct thermodynamic
process.
However, the situation simplifies at extremely high collision energies.
In this so-called scaling regime, the colliding nuclei become transparent and
the excited plasma is created between the two nuclei when they recede from
the collision point. The basic assumption here is that the total entropy
is created in the initial stage of the collision and remains nearly constant
during the later evolution. Under this assumption, the expansion of the plasma
is nearly adiabatic and can be described by relativistic hydrodynamics
\cite{CHIU75,BJORK83}.

To make contact with this discussion, we also studied adiabatic processes.
The properties of the system in the $(\rho_B,T)$ plane can be studied in
Fig.~(\ref{fig:tvsrhos}).
Adiabats for various values of the entropy per baryon are indicated for
symmetric matter in part (a) and for asymmetric matter in part (b),
respectively. The dashed lines are the coexistence curves, {\em i.e.}, the
projection of the hadronic and the quark--gluon branch of the binodal,
which intersect at the critical point CP.
The curves in the coexistence region are the
result of a Maxwell construction.
Note the behavior of the system in the mixed phase.
Throughout the transition the temperature {\em decreases}
with increasing density,
in contrast to the pure phases where the temperature increases monotonically.
This peculiar behavior arises because for a given baryon density and
temperature, the entropy in the quark--gluon phase is always higher.
If we think in terms of a ``boiling'' or ``condensation'' process and compare
to a liquid-gas transition one would expect the opposite
behavior \footnote{A system which exhibits a similar behavior is the
liquid-solid phase transition of $^3$He, for which the entropy in the
high-density solid phase is higher than in the low-density liquid phase due to
the spin disorder present in the solid phase \cite{GOLD92}.}.
In an ordinary liquid the high-density phase has the lower entropy and the
temperature would rise steadily during the transition.

If we compare the extension of the transition regime in the symmetric and
asymmetric systems, we find a similar quantitative difference as observed in
the previous discussion. Generally, for a given value of the entropy per
baryon, the onset of the transition occurs at a lower density and temperature
in asymmetric matter. For example, if we compare the adiabat $S/N_B = 2$ in
Fig.~(\ref{fig:tvsrhos}a) and (\ref{fig:tvsrhos}b), the density
decreases by $\Delta\rho_B\approx \rho_B^0/3$ and the temperature
by $\Delta T \approx 4$ MeV.
Compared to the overall scale set by the critical temperature of $150$ MeV
this temperature difference is certainly less significant.
However, the qualitative difference between
the two systems could be an indication that the transition region is
experimentally better accessible in a collision of extremely neutron-rich
systems, which might be obtainable with radioactive beams.

Finally, we briefly discuss how the properties of the phase transition
change when the parameter $\zeta$ in the hadronic EOS is varied.
This point has been discussed in Ref.~\cite{HMUE96} for pure neutron matter
and here we will extend the analysis to arbitrary isospin ratios.
Up to now the hadronic EOS in Eq.~(\ref{eq:pressh}) was generated
without the quartic vector meson interaction.
In the following we allow a nonzero coupling within the natural range
$0\leq \zeta \leq 0.06$.

Figure~(\ref{fig:rhovszeta}) shows the baryon density at the onset and at the
end of the transition for the isospin ratios $x=0, -0.2, -0.5$ at $T=0$.
Note that all values of $\zeta$ reproduce identical properties of nuclear
matter and a transition temperature of $T=150$ MeV at zero baryon density.
Generally, one observes that for arbitrary isospin ratios, increasing
$\zeta$ softens the EOS, which leads to substantially higher transition
densities.
The increase in the symmetric system is remarkable (note the logarithmic scale);
at sufficiently large values of $\zeta$ the transition vanishes altogether.
The transition is driven by the energetics in both phases and therefore
this behavior is most easily understood by examining the high-density limit of
the energy per baryon \cite{HMUE96}.
Using Eq.~(\ref{eq:Omqp}) and the relation ${\cal E}=3p+4b/3$,
one obtains for the quark phase
\begin{eqnarray}
{\lim_{{\rho_B}\to \infty}}
 {\cal E}_Q/ \rho_B = c_Q\rho_B^{1/3} \ .
 \label{eq:epsq}
\end{eqnarray}
The asymptotic behavior of the hadronic EOS depends on $\zeta$ and $x$.
For $x<0$, $\zeta\geq 0$ or $x=0$, $\zeta =0$ the quadratic terms
in Eq.~(\ref{eq:pressh}) dominate, which leads to
\begin{eqnarray}
{\lim_{{\rho_B}\to \infty}}
 {\cal E}_H/ \rho_B \propto \rho_B \ .
 \label{eq:epsh1}
\end{eqnarray}
Thus, at sufficiently high densities, the hadronic matter always has higher
energy compared to the quark phase and a transition is possible.

A special situation arises for $x=0$ and $\zeta>0$. In this case the
leading behavior is, up to the prefactor, identical to Eq.~(\ref{eq:epsq}),
{\em i.e.},
\begin{eqnarray}
{\lim_{{\rho_B}\to \infty}}
 {\cal E}_H/ \rho_B = c_H\rho_B^{1/3} \ .
 \label{eq:epsh2}
\end{eqnarray}
By comparing the factors $c_Q$ and $c_H$ in
Eq.~(\ref{eq:epsq}) and in Eq.~(\ref{eq:epsh2}), respectively, one arrives at
the remarable result that a transition is possible only if
(see also the discussion in \cite{HMUE96})
\begin{eqnarray}
{1\over 3}\left[1+\Bigl({4\over \pi^2\zeta}\Bigr)^{1/3}\right]
		  > 1+{2\alpha_s\over 3\pi}
       \label{eq:condition} \ .
\end{eqnarray}
This implies that for sufficiently large values of the nonlinear
coupling, {\em symmetric matter remains in the hadron phase}.
Note that we would arrive at this result for {\em arbitrary} isospin
ratios if we included an additional quartic $\rho$ meson coupling.
In accordance with Ref.~\cite{HMUE96}, we conclude that the parameter
dependence of the hadronic EOS at high densities leads to large uncertainties
in the predictions for the transition region of the
deconfinement phase transition (if it exists).
In principle, reproducing the quantitative features of the transition
could be a tool for calibrating the hadronic EOS better in the high-density
region. However, more information is required than available
at present, and quantitative predictions are limited.
\section{Summary}
In this paper we studied the deconfinement phase transition from hadronic
matter to a quark-gluon plasma as a function of the isospin.
The analysis was based on a separate description of the hadronic
and the quark-gluon phase.
We have demonstrated that in a consistent treatment of the two conserved
charges, baryon number and isospin, qualitatively new features arise.
Most importantly, the phase transition in asymmetric matter is generally
continuous and of second-order. This is in contrast to the
discontinuous first-order behavior of symmetric systems, which arise
as singular points in the phase diagram of asymmetric matter.

The analysis was based on the determination of the phase separation
boundary, the binodal, which indicates the
region where a separation into two phases is energetically favorable.
The binodal is determined by Gibbs' criteria for phase
equilibrium. In a system with two conserved charges, it forms a two-dimensional
surface in parameter space, in contrast to the one-dimensional surface
in one-component systems.
The greater dimensionality leads to the qualitatively new behavior.
Primarily, the transition in asymmetric matter is continuous and of second
order. We saw that the pressure, temperature and isospin ratios in the
participating phases change throughout the transition. That means that in
general, asymmetric systems pass through a transition region rather than
staying at a transition point which leads to discontinuities in one-component
and symmetric systems.

To apply these results to the deconfinement phase transition in nuclear matter,
we employed a simple two-phase model.
The hadronic EOS was generated in a relativistic mean-field
model involving the interaction of baryons with isoscalar scalar and vector
fields and with the isovector $\rho$ meson and pion field.
This model involves cubic and quartic isoscalar self-couplings and
allows for an accurate calibration at normal nuclear densities to reproduce
bulk properties of finite nuclei and nuclear matter.
For the description of the quark-gluon phase, we adopted a bag-model type
EOS involving massless $u$ and $d$ quarks.
In this framework thermodynamic quantities consists of two parts. A
perturbative contribution, where we included the first order correction
in the strong coupling constant, and a nonperturbative contribution, represented
by the bag constant, which accounts for the QCD trace anomaly.
Guided by recent results from lattice
calculations, we chose the bag constant and the strong coupling constant to
reproduce a transition temperature of 150 MeV for matter at zero baryon
density.
However, the calibration of the hadronic EOS at normal densities is not
unique and predictions at high densities are sensitive to the model
parameters.
By studying variations of the quartic vector meson coupling within the natural
range, we found significant uncertainties in the predictions for the onset of
the deconfinement phase transitions in systems at finite baryon density.
For sufficiently large values of this coupling the hadronic EOS becomes so
soft that the transition vanishes altogether.

This two-phase model was then used to study the deconfinement phase transition
in highly excited matter that is
produced in ultra-relativistic heavy-ion collisions.
By construction, an approach based on a separate description of the two phases
cannot reveal the actual nature of the transition.
However, until more concrete and reliable lattice calculations are available,
we believe that despite this limitation our analysis is useful for providing
a first orientation and concrete description of the qualitative features which
arise in the phase diagram of strongly interacting {\em asymmetric} matter.
There are several significant differences between the phase diagram
for an asymmetric system and that for symmetric matter.
In the first place, the location of the transition region in parameter space
depends on the isospin ratio of the system. Generally, the onset of phase
separation occurs at lower baryon densities and temperatures in more
asymmetric systems.
More importantly, the dimensionality of the phase-separation region
is larger in asymmetric matter leading to a {\em continuous} transition.
This implies that the thermodynamic properties of the participating
phases change throughout the transition.
Although these effects are small for realistic isospin ratios
$x\approx -0.1$, the trend in the isospin dependence to lower densities
and temperatures could be an indication that the transition region
is easier to reach in collisions of very neutron rich nuclei, which might
be created in radioactive beam facilities.

The analysis also revealed interesting physics in the isovector
channel. Most importantly, the incorporation of the pions into the model for
the hadronic phase was crucial for the shape of the binodal
surface and therefore also for the path of the system through the mixed-phase
region. The salient feature is the onset of a pion condensate at large baryon
densities and in very asymmetric systems.
This phenomenon is certainly of minor practical importance since the relevant
isospin ratios lie beyond the experimentally accessible region.
However, interest in Bose condensation has recently been revived in the
literature, particularly since the possibility of kaon condensation in neutron
star matter has been proposed \cite{POLITZER91}.
Analyzing these effects in connection with the deconfinement phase transition
provides an important topic for future work on this problem.

\acknowledgments

I am pleased to thank B. D. Serot for many useful comments and stimulating
discussions.
This work was supported by the U.S. Department of Energy under
contract No.~DE-FG02-87ER40365.
\newpage
\begin{table}[tbhp]
\caption{Equilibrium Properties of Nuclear Matter}
\medskip
\begin{tabular}[b]{cccccc}
$k_{\scriptscriptstyle\rm F}^0$ &
		 $\rho_B^0$
                & $M_0^* /M$ &
                $e_{\scriptscriptstyle 0}$ & $K_0$ & $a_4$ \\
\hline
1.30\,fm$^{-1}$ & 0.1484\,fm$^{-3}$ & 0.60 & $-15.75$\,MeV & 250\,MeV &
					 35\,MeV\\
\end{tabular}
\label{tab:one}
\end{table}
\newpage

redpajama_set_name: RedPajamaArXiv


Food: slow cooked ribs....Costco has great deals on big packs of ribs.
"You can't ever work too much because there's no such thing as being in too good condition. You can't ever lift too many weights because you can't ever get too strong. You can't ever wrestle too much because you can always do better. "


Mick McCarthy's passionate defence of wronged midfielder Nenad Milijas is in the best interests of the beautiful game.
The Wolves player was sent off in the 1-1 draw against Arsenal despite winning the ball as McCarthy has clearly demonstrated.
But there is a lot more at stake here than a bad refereeing decision. We are talking about whether or not we want to kill the art of tackling.
While I am not advocating a return to the brutal days – when hardmen like Chopper Harris, Norman Hunter and Nobby Stiles ruled the roost – we must beware not to turn the game into a non contact sport.


text:
What Is a Spiral Galaxy?
By Nola Taylor Redd 2018-11-19T18:05:00Z
This Hubble Space Telescope photo of Messier 74 reminds us that spiral galaxies are some of the most beautiful and photogenic residents of the universe. Nearly 70 percent of the galaxies closest to the Milky Way are spirals. New research finds that spiral arms are self-perpetuating, persistent, and surprisingly long lived. Image released April 2, 2013.
(Image: © NASA/ESA/Hubble Heritage Team)
Spiral galaxies are twisted collections of stars and gas that often have beautiful shapes and are made up of hot young stars. Most of the galaxies that scientists have discovered so far are spiral galaxies, as opposed to the other two main categories of galaxy shapes — elliptical and irregular.
The Milky Way – the galaxy that includes Earth and our solar system – is an example of a spiral galaxy.
Spiral galaxies make up roughly 72 percent of the galaxies that scientists have observed, according to a 2010 Hubble Space Telescope survey.
Most spiral galaxies contain a central bulge surrounded by a flat, rotating disk of stars. The bulge in the center is made up of older, dimmer stars, and is thought to contain a supermassive black hole. Approximately two-thirds of spiral galaxies also contain a bar structure through their center, as does the Milky Way.
The disk of stars orbiting the bulge separates into arms that circle the galaxy. These spiral arms contain a wealth of gas and dust and younger stars that shine brightly before their quick demise.
How the spiral arms form continues to puzzle scientists. One theory suggests the galaxy arms could be the result of density waves traveling through the outer disk. Encounters between galaxies could cause such waves as the mass of the smaller galaxy could affect the structure of the larger galaxy as the two combine.
Spiral galaxies are thought to evolve into elliptical galaxies as the spirals get older. But it's unclear how common elliptical galaxies are as they're made up of older, dimmer stars, and are more challenging to spot.
One of the largest known spiral galaxies is NGC 6872, which is 522,000 light-years across from the tips of its outstretched spiral arms — that's about 5 times the size of the Milky Way.
In 2017, astronomers discovered an 11-billion-year-old ancient spiral galaxy called A1689B11. Its discovery will help scientists understand how galaxies transition from "highly chaotic, turbulent discs" to more organized and thinner discs, like that of the Milky Way.
This article was updated on Nov. 19, 2018 by Space.com Contributor, Elizabeth Howell.

redpajama_set_name: RedPajamaCommonCrawl


This you do not get. When you support BSL you support ALL OF IT. Its YOUR fault that innocent dogs are being put to death. How do you NOT get that?
Glad to see the person who resorted to an infantile practice of impersonating another member has been removed. But I did save one of that person's quotes, solely because any lurkers that might be following this thread need to know the truth.
The quote saved is the second time that particular troll has accused me of "spreading lies" about BSL and where such policies lead. It's important that people know the truth about the consequences of BSL ... so hope other members and mods don't mind me saving the quote ... the exact words are intact but the impersonation is removed.
They're too busy spreading lies and telling everyone that BSL means that they're going to take your dog and kill it.
"Lies", eh? Get your own facts straight before blindly accusing others of lying. Apparently you are incapable of independent research, so here's some direct links. Read the stories below regarding dogs taken away from their families and killed, not for any problems at all ... but just because they were pit bulls.
Guess who was targeted first? If your guess is "gang-bangers, ganstas, and other irresponsible owners" ... then you are dead wrong. The first to be targeted were responsible dog owners who had followed the law and had previously licensed their pit bulls through the city of Denver. Additionally, all pit bulls already in Denver shelters were automatically put down ... including those with excellent temperment that had been declared adoptable and including pit bull puppies.
Best Friends Network: Denver kills dozens of friendly pit bulls, including puppies, despite offer to move them to a rescue out of state.
This link is broken, is there an updated one?
Have only just spotted this thread and what a read it was too!
Just wanted to chip in to air my own personal opinion that BSL is a disgraceful, prejudicial, ignorant and uninformed knee jerk reaction to NEWSPAPER sensationalism and public ignorance.
Its so easy to jump on a bandwagon when one major news story hits the headlines, but it takes a lot more EFFORT and WORK to trawl through the LOGIC in your own mind, and make an intelligent rational decision. This is precisely WHY sensationlism SELLS, people react to it, they BUY on it, they TALK about it, it spreads the marketing word virally and its generally just a fantastically successful technique, but that doesn't mean it doesn't stink.
In my (very humble) opinion, but an opinion which should COUNT nonetheless, if we follow the same 'logic', all the news stories of black men committing crimes could easily cause us to think black people are the source of all crime and social depravity, and if there were not laws preventing (thank GOD) then maybe we would be banning their very existence under similar 'BSL' for humans. Maybe its down to the fact that WHITE men generally write the news? Maybe not, as i said its just my opinion. Its also my opinion that most dog owners involved in writing the news own a Labrador or a Retriever or something similarly beautiful in the public eye's image of dogs.
2. The general public's complete IGNORANCE and FLOCK mentality about anything which some editor shoves under their nose every day. Since these people are in far greater numbers than bad owners will ever be, i blame these people even more than the disgraceful owners. Why can't people just be more rational, look at the bigger picture, and make some logical conclusions based on numbers and facts rather than headlines and shocking videos or pictures.
More importantly, in the ten years since the Dangerous Dogs Act banned the last 4 dogs in the UK (Fila, PB 'type', Dogo Argentino and Japanese Tosa) dog bites have INCREASED BY FIFTY PERCENT.
If anybody still wants to argue that banning breeds is a solution, then i have nothing to respond with, you clearly don't work on the same definition of logic and common sense as i do!
I am all for the public's safety and boy have i seen some dangerous dogs in my time, but have they all been of similar breed type? NO WAY! Most of them were totally 'normal' dogs which we see in every play park in the UK on a daily basis. I know how to make the public safer, and that is to make laws which prevent bad OWNERS, not certain BREEDS.
Thats my opinion, take it or leave it, but please at the very least accept it as coming from someone who walks and talks dogs daily and i have done for years. Also i am someone with two beautiful children in my home (as well as 2 Rottweilers, 2 GSDs, Spaniel and a Dobermann and two Border Collies which often stay with us too) and i would NEVER allow my chlidren to be anywhere near a dog which i can see carries a risky temperament or unpredictable tendencies. My dogs don't, and neither does any other breed of dog, only individuals which i have assessed can be judged by me and advice given based on their behaviour not their colour or gene pool.
It seems mankind looks at Hitler's beliefs and actions as a shameful slur on our species, but then we throw all those learned lessons out the window when we come to dogs? It seems we haven't learned much at all but the difference is dogs can't rise up and shame us very easily, so i fear it will be many decades before people use their heads instead of their headlines to decide the fate of thousands of innocent and beautiful dogs.
I often see the phrase: DEED NOT BREED and i like it, but i prefer... OWNER, NOT BREED, NOR DEED, OWNER OWNER OWNER.
Thanks for your time and a great topic. May dogs one day live and serve in the knowledge and safety of a world where intelligence reigns, and idiots do not.
How the hell do you ban a Great Dane, one of the sweetest dogs around?
Because they have caused fatalities.
While as a rule they are supposed to be gentle, in the wrong hands or from crappy breeders, not so much.
It's stupid, and I don't agree with it, but hey...people are ban-happy and big dogs often take the fall for their size alone.
Very true, as it is with any breed.
It just struck me by surprise, in 20 years of being around Great Dane's, I can count maybe one overly aggressive Dane I've been around and the dog had a history of abuse and neglect from its previous owners.
The breed is still quite uncommon so I can only hope new backyard breeders stay far away, last thing the breed needs is for thousands of people breeding them with temperamental and physical/health related issues.
I'm glad where you are they're not overly common and byb's haven't taken over...but I don't consider that the norm, unfortunately.
I volunteer with a multi-state dane organization and we're inundated with great danes year-round. The BYB's are everywhere in our region. It's heartbreaking.
I correspond regularly with quite a few breeders in Ohio and California quite regularly and the topic of Dane backyard breeders comes up quite regularly. From what I've been told and gathered from our conversations though it seems that while backyard breeders are on the rise, Great Dane's are still by and large generally a pretty, for lack of a better term, uncommon breed for them (BYB's) in relation to other breeds. APBT's, Shepherds, Huskies, Rotties, Dobe's, ect.
What organization are you a part of? We used to have our own Western rescue up here but it went under. Tons of Dane's were placed through it; we found tons of Dane BYB's but it seemed they paled in comparison to even the Irish Wolfhound rescue we have up here.
It's great to hear that you're doing your part however to give these fabulous dogs a great home and a loving family.
Well, I'm glad to hear that somewhere they're not being exploited to the hilt. I live in the south, so every breed is exploited if they are eyecatching enough. BYB's here LOVE the big breeds, the "thug" breeds, anything that makes them feel macho.
I know what you mean, except up here it's mainly Rottie's and Dobe's.
That seems like an absolutely fantastic rescue! I checked the site out and wound up very impressed. It still saddens me that our rescue up here is gone.
Check out BHRR in Ontario. While the name doesn't specify Great Dane rescue, Gwen primarily focuses on the giants - especially danes.
I know it's probably a little out of your way (or a lot, lol), but you may want to contact her anyways. I'm sure she'd be able to point you in the right direction if you're wanting to volunteer. She may know of something a little closer to you. I can PM you her email address if you're interested.
Sure, I would appreciate that.
The government has much better things to do now than to think about restricting different breeds. The way they created that list, the only breed you can safely keep is a Chihuahua. I think that some Chihuahuas are more aggressive than some of the breeds listed there lol. It makes sense why they would ban or restrict pit bull type breeds in some areas because too many people were breeding them for fighting and the dogs were not socialized at all. They bred them as disposable objects that were only good while they could fight, and that is just cruel. Saying that a Golden Retriever is a dangerous breed is ridiculous. Golden Retrievers make some of the best guide dogs if trained properly. Whoever made that list must have been bitten by a Golden Retriever when they were little, and now they just seek revenge!
You really have no idea about much of anything, do you.
Thanks to BYBers and millers, the number of aggressive Goldens has been on the rise over the last decade or so. Subjecting them to BSL however, is purely ridiculous, as is the idea of subjecting anything else to BSL. It's a knee-jerk reaction to a wider problem. Nothing about BSL makes sense and you're a bleeding moron to think so.
And obviously, with the amount of new legislation that comes across daily, the government has nothign better to do with their time than to screw with our dogs.
So there is NO agressive golden retrivers or labs (I know you didnt add them in, but they fall under the same family pet as a golden). tell that to my dog who has been attacked by 2 goldens, and a handful of labs.
any dog, of any breed can be agressive. EVERY SINGLE breed has bad apples who ARE agressive. maybe due to health, bad breeding, bad owners, or a combination of a few of those.
To say its ridiculous that goldens are added is ridiculous in itself. to say that breed wont and cant turn is ridiculous.
That's what I said! Pug?!!?! WTF? This is stupid.... it's not breeds, it's irresponsible breeders and RETARDED owners. It's not the dogs' fault.
This is dumb.... gotta figure out who to write to complain to.


This photograph shows a London Midland & Scottish Railway corridor composite coach in 1949. It carries the number 4994.
It had originally been part of the Highland Railway's rolling stock.
This photograph shows a London Midland & Scottish Railway corridor composite coach in 1949. It carries the number 4994.

 It had originally been part of the Highland Railway's rolling stock.


My father pinned the wings on my uniform that he wore as an Army Air Corps pilot in WWII. We stood at the same airfield near Valdosta, Georgia where he trained to become an 8th AF bomber pilot. Thirty years later, I would follow his footsteps as a pilot with the 2nd AF during the War in Southeast Asia. We were native Atlantans sent to the far reaches of the planet as young men during striff and global conflict. We weren't the first, my forefathers has served with the military in every conflict America faced since they sailed up the James River in Viginia in the mid 17th century.
My wife and I have lived on the East coast of Florida for the past 20 years. It is from my balcony overlooking the Atlantic Ocean that I found the inspiration to take my love of storytelling and put it to words. My work is fiction, and my current work is inspired from nights of telling fantasies to my grandchildren. For the adults, the Thomas MacLaine series is rooted in the life story of my father, and is told for my three daughters that he so loved during his lifetime.


Not too long ago, Anthill Films announced their upcoming film, Return to Earth. With a release date sometime later this year, we're stuck patiently waiting for the main event, but Anthill hasn't left us hanging in the meantime. In a six-part web series to be released over the coming months, Blink dives into the scenes of Return to Earth, giving us a peek through the keyhole at what the final film will hold.
Episode 1, "Fall Colors," follows Anthill to Bromont, Quebec in search of Eastern Canada's most vibrant fall forest landscape.
For more insight on Fall Colours and an interview with Thomas Vanderham, head to Anthill's website.
The 100% Accuri Enduro goggles are one of the few pieces of eye protection that won't turn into "foggles" when conditions turn sour.


UNITED NATIONS, New York (April 29, 2000 – Radio Australia)---Tonga and other Pacific countries have called again for safeguards from countries that ship radioactive fuel through their waters.
Tonga's United Nations ambassador, S. Tu'a Taumoepeau Tupou, has told a conference on the Nuclear Nonproliferation Treaty that current safeguards are inadequate.
Pacific and Caribbean nations say they maintain the right to deny any shipment of radioactive and toxic waste through their territories.
But Japan and France are calling for freer reign in shipping. Spent Japanese nuclear power plant fuel is sent to France and the United Kingdom for reprocessing and then shipped back to Japan.
The Tongan ambassador said those nations shipping nuclear waste should compensate any industries -- such as tourism -- whose markets are affected by having nuclear material transported through their regions.
PAPEETE, Tahiti (April 27, 2000 – Oceania Flash/SPC)---French Polynesia officials have announced a 7% price increase for car fuel and 9% for other oil-derived products, effective May 1st, the daily newspaper La Dépêche de Tahiti reports.
This makes the price of a liter of super grade fuel a maximum of 127 French Pacific Francs (just above the US$ 1.00 mark), 121 CFP for a liter of unleaded fuel and 68 CFP for a liter of kerosene, French Polynesia economy minister Georges Puchon announced.
Puchon said although prices had remained stable in French Polynesia since July 1997, the rise, which was due to the increase in the world price of oil, had also taken place in most countries worldwide, for the same reasons.
French Polynesia's cabinet reviews the price of fuel every four months, based on world oil prices, importation costs and other taxes.
HONIARA, Solomon Islands (April 28, 2000 – Radio Australia)---Solomon Islands Foreign Minister Patteson Oti says the country's 18 month ethnic conflict has inflicted serious damage on the economy, although it may not be particularly noticeable until later this year.
Authorities are predicting a budgetary crisis at year end, and are calling on donors for an increase in foreign aid, especially in areas such as health and education.
Mr. Oti said the closure of Solomon Islands Plantation Limited (SIPL), producer of palm oil, has been particularly hard, because it earned 20 percent of national export receipts.
"It was one of the basic demands by militants on Guadalcanal," he said. "About 80 percent of the employees of SIPL were from Malaita and because Malaitans had to go, the company had to go. It was employing more than 2,000 workers."
SAIPAN, Northern Mariana Islands (April 28, 2000 – Saipan Tribune)---The chair of the Senate Federal and Foreign Relations Committee is eyeing more U.S. funding for the Commonwealth government for various infrastructure projects and local economic programs.
In preparation for this step, Sen. David M. Cing has asked the Department of Commerce to produce a detailed report on the financial aid granted by the U.S. Economic Development Administration (EDA) to the CNMI to see how these funds have been spent.
Sen. David M. Cing made the request to Commerce Sec. Frankie B. Villanueva as part of his efforts to seek funding for critical projects needed by the Commonwealth government.
He said a federal grant such as the EDA is what is needed by Tinian for its own economic growth as he noted that a proposed harbor breakwater in the island municipality is seeking funding for its construction.
NOUMEA, New Caledonia (April 27, 2000 – Oceania Flash/SPC)---The University of New Caledonia, one year after its official establishment, is to elect its first Chancellor on May 10, the daily newspaper Les Nouvelles Calédoniennes reports.
Last June, what was then known as the Université Française du Pacifique with one branch in New Caledonia and another one in French Polynesia became the Université de Nouvelle-Calédonie in New Caledonia and the Université de Polynésie in French Polynesia.
Paul de Dekker was then appointed interim administrator.
De Dekker, a former anthropology professor, who is now one of the two candidates, had at the time to draft a constitution and form a board of directors for the newly-established institution.
The other candidate, Claudet Chauvet, is also a scholar, a biology professor in charge of the university's marine biology lab.
SUVA, Fiji Islands (April 30, 2000 - PINA Nius Online)---Pacific Islands News Association (PINA) members in the Solomon Islands and Papua New Guinea will mark World Media Freedom Day by focusing on UNESCO's Culture of Peace.
They will hold special programs on the role of the news media in reporting recent deadly conflicts in their countries and in the peace and reconciliation process.
PINA's World Media Freedom Day priority this year is the Solomon Islands and Papua New Guinea because of the conflicts there, the peace processes now under way and the key role the news media can play.
In Honiara, PINA national affiliate the Media Association of Solomon Islands (MASI) is focusing on the Guadalcanal ethnic conflict and this coming week's peace talks.
PAGO PAGO, American Samoa (April 27, 2000 - Samoa News/PINA Nius Online)---Daewoosa Samoa, Ltd. may now face a class action suit instead of the several individual civil suits brought against the beleaguered Tafuna-based garment manufacturer by its Chinese and Vietnamese workers.
The Chinese workers filed the first suit in early 1999, followed by the Vietnamese workers in late 1999. The suits sought primarily payroll payments, among other issues.
The High Court recently okayed the consolidation of these two cases as the basis of a class action suit. The court found that "there are questions of law or fact common" to plaintiffs and their cases, a major prerequisite to a class action.
The structure of a regional network of public health laboratories was established by health professionals at the Inaugural meeting of the Public Health Laboratory Network, which aims to improve the recognition and control of epidemics in the Pacific region.
The technical meeting, jointly sponsored by SPC and WHO, was held on 19 and 20 April at SPC Headquarters in Noumea, New Caledonia. Participants were laboratory specialists and health department representatives from Fiji, Guam, New Caledonia (Pasteur Institute) and French Polynesia (Malardé Institute).
Representatives of New Zealand, Australian and the United States laboratories also took part, together with observers from regional organizations.
PORT VILA, Vanuatu (April 27, 2000 - Vanuatu Trading Post/PINA Nius Online)---Sir Dennis Buchanan, the retired entrepreneur who now lives in Vanuatu, is interested in putting together a consortium of local shareholders to make a bid for Vanair, the government owned airline.
Sir Dennis, in the 1980s, had the biggest third level group of airlines in the world, owning Talair in PNG with a fleet of 100 aircraft, Solair in the Solomons and Air Melanesie in Vanuatu.
After confrontations with the Lini government in 1989 over a decision to nationalize Air Melanesie and after problems with obtaining a work permit for a family member who was chief pilot and married to Sir Dennis' daughter who was the General Manager of Air Melanesie, he left Vanuatu abruptly towards the end of 1989.
AUCKLAND, New Zealand (April 30, 2000 Agence France-Presse)---Guadalcanal militants who sparked a near civil war in the Solomon Islands have agreed to attend peace talks later this week but their rivals, and a mysterious hit squad called the "Seagull Group," are staying out, diplomatic sources said Sunday.
The agreement by members of the Isatambu Freedom Fighters (IFF) to attend may save the Australian backed talks ahead of plans later in the year for talks in New Zealand.
Commonwealth Special Envoy Sitiveni Rabuka, the former prime minister of Fiji, arrived in the Solomons Sunday while his deputy, Ade Adefuye of Nigeria, was en route from London after persuading the IFF to attend.
The talks will take place beginning May 4 in Buala, the capital of Isabel Island, considered a neutral venue.


text:
School for Life Romania
The next step towards independence | Romanian Orphans
Our Student Charter
Previously living and working in Siret during 1991 – 1994 this team returned to the UK, to set up support systems to empower the growing Scoala Pentru Viata Romanian team to manage and develop the work both at the centre and within the childrens neuro-psychiatric hospital, also known by the media as Siret orphanage.
The UK Team
Ruth Brown BA PGCE PGCE , Trustee – a teacher specialising in reading and writing, lived and worked in Siret for nearly 2 years, now living in Glasgow she gives much support with fund raising and publicity.
Dave Emptage NVQ, Trustee – dedicated to working with people with profound and moderate learning disabilities and sensory impairment in long stay residential homes and educational settings since 1989. Volunteering in Romania for 2 years from 1992, bringing his experience and music to the great appreciation of the residents, staff teams and the local community. Now living in Lancaster and working in Special Needs Education, he uses his experience and music to continue to raise finance, awareness and skill sharing on his return trips to Siret.
Katie Goodier MA PGCE , Trustee – now a special needs teacher working in Glasgow, teaching children with special needs having volunteered for over 2 years in Siret from 1992 and been actively involved since.
Professor William Gould PhD, Trustee – a professor of history at Leeds University volunteered in his gap year from 1991 – 1992, in later years returning to Siret to help develop the project where he met and later married his wife Olivia. They now live in Todmorden and ensure good communication and translation between the UK and Romanian teams.
Sylvia Gurr MA UKCP (reg.), Trustee – experienced in working with people with profound learning difficulties and sensory impairments. She volunteered in Romania for approx. 3 years from the beginning of 1992, helping to run and develop the project and has returned regularly since to support the Romanian team developed our work. She has also worked in mental health and homelessness in London during which gained her Masters in Integrative Child Psychotherapy. Now a Child Psychotherapist and Clinical Supervisor, she also blogs on Romania and the story behind the orphans, www.sylviagurr.com
Lizzy Hartley MA (hons) DipSW, Trustee – a Social Worker in child protection and experience in mental health is able to bring her knowledge and expertise of independent living to the team having volunteer in the hospital in 1993 for over a year
Col Phil Keetley (retd.) MBE, Trustee – previously a Colonel in the British Army, Phil volunteered in Siret from late 1992 to 1994.
Roger Mason Bsc (hons), Trustee and Treasurer – volunteered in 1994 at the children's hospital


There is no adequate measure for the love I bear this book. Lucilla Andrews was a brilliant writer, with the rare gift of writing believable people, and while many of her books are on my keeper shelf, this one remains my favourite.
It's the story of Rose Standing, a young probationary nurse at a busy London hospital, who finds the challenges of completing her training made yet more complicated by her growing feelings for the Senior Surgical Officer, Jake Waring.
Rose is just the best character. She's funny and fearless, imperfect, and easy to like. If you've never read Lucilla Andrews, The First Year is where to start.
This is not only one of my favourites, it's one of my treasures, dating from the time in the early 1970s when my mother owned and ran a bookshop in the little town where I grew up.
The penciled price inside the cover, written in my mother's lovely and familiar hand, tells me she would have sold this for $2.49, and gained a profit. But instead she let me take it from the shelf, and bring it home.
I love pretty much everything L.M. Montogmery ever wrote. Like many a Canadian girl of my generation I was brought up with Anne Shirley and Green Gables and the handsome Gilbert Blythe, and count those books among my favourites (also loving, maybe just a little more, the story of their daughter, Rilla).
In my Hall of Fame of heroes, Barney Snaith still sits right up there with the Pickle Man from the film Crossing Delancey (and those who know me know how high that puts him).
Oh, I love this novel. I found it in 1978 on the shelves of my then local library, and must have taken it out half a dozen times to read it again and again.
It's got nearly everything I love: intriguing history, romance, a road trip, politics, swords, and a man in Very Cool Boots.
Set in the Napoleonic War, it tells the story of Major Lev Orlov who, wounded in battle himself and knowing that the wounded left behind in Smolensk will be made captives or killed, takes it upon himself "to lead a company of wounded Russian soldiers away from the battle-scarred city" and across perilous terrain to safety in Kaluga. Along the way, he also takes on responsibility for the young Countess Irina Barova, and what happens afterwards makes for one of my favourite reads.
This is, by the way, the exact copy I read all those years ago. I'd searched for years for a copy without success (this was pre-Internet), so when my own book Mariana was first published in 1994, I went back to that library and talked the librarian into letting me trade a signed hardcover copy of Mariana for this copy of The Road to Kaluga, which was languishing down in the storeroom, unloved and on its way to the annual book sale. It has been very well loved ever since.
(It's also been published under the title Flight From the Eagle, and has sequels, though I admit I love this book so much I was afraid to spoil that by reading those sequels. I wanted to leave Lev and Irina the way they were, with the life I imagined for them).
My mother still remembers vividly the day when, as a teenager, she was ill in bed and, seeking a diversion, opened the newspaper to find a condensed version of Bride of the MacHugh. She loved it so much she sought out the book in her local library, and loved the full version even more. Years later, she found a second-hand copy on sale and added it to our family bookshelves.
I still remember vividly the day when, as a not-quite-teenager, I came home from school on an already-darkening winter afternoon and, seeking a diversion, scanned the titles of the books on the second shelf down in our kitchen and settled on Bride of the MacHugh. I took it up to my room, snuggled under my covers, and found myself so magically transported I'm not even sure I made it down for dinner.
This is my own paperback copy (my mother's is a hardback), and you can see how many times it's been read, and how much it's been loved. There's good reason for that.
It's been 42 years since the first time I read This Rough Magic, and Max is still setting the bar pretty high!


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Oakland Teachers Are Getting Ready to Strike as Contract Fight Escalates
January 9, 2019 | Last Updated September 20, 2021 | Ken A. Epstein | Charter schools and privatization, Education/Schools/Youth, labor, School closures
Educators across the state are demanding more funding for California's underfunded public schools
Rally for Oakland teachers
Starting this week with solidarity events before school Friday and a huge rally Saturday of educators from many East Bay districts in Oakland, the Oakland Education Association (OEA) is escalating its contract fight and is strongly considering a strike authorization vote by the end of this month.
Living wages to end teacher turnover, smaller class sizes and more resources for the district's 37,000 students remain the OEA union's urgent priorities. OEA is demanding a 12 percent raise over three years, while the district is only offering 5 percent.
In addition, educators and parents will also spoke out, Wednesday, Jan. 9, at the Oakland Unified School District school board meeting about the district's disrespectful ongoing plans to close up to 24 neighborhood school sites in the next few years, many in low-income areas. Parents and teachers have launched a petition to save Roots International Academy and all of the targeted schools. Roots middle school could close in June.
The Oakland educators' showdown comes as more than 30,000 Los Angeles Unified School District educators represented by the United Teachers Los Angeles union are mobilizing for a potential strike on Monday, Jan. 14, in the nation's second-largest school district.
After seven Oakland mediation sessions and working a year and a half without a contract, Oakland educators are considering all options to protect public schools, said OEA President Keith Brown.
"Educators in Oakland are ready to fight for the public schools our students and our community deserve," Brown said. "We are tired of being undervalued and disrespected at the bargaining table. We are being loud and clear about our priorities. We demand a living wage, lower class sizes and the resources our students want and need."
The union expects to take the final steps this month in the bargaining process before it can legally strike – a fact-finding hearing by a state-appointed neutral and a strike authorization vote that would allow OEA leaders to call a strike.
Local teachers' unions statewide are organizing a #RedForEd Day of Action on Friday, Jan. 11in solidarity potential looming strikes by the Oakland Education Association and United Teachers Los Angeles.
Many teachers will wear red, joining parents or students and starting the school day by walking in together.
Also in support of Oakland and Los Angeles Unified teachers – and calling for more funding for California's underfunded public-school system – hundreds of East Bay educators from many school districts will converge for a rally at noon Saturday, Jan. 12, at the Oakland City Hall Frank Ogawa Plaza.
The rally is organized by the East Bay Coalition of Public Educators, a group of at least 13 CTA union chapters that will be joined by parents and students. The Oakland contingent will meet at 11 a.m. at the Lake Merritt Amphitheater, and then march at 11:30 a.m. to the nearby rally.
In a special community solidarity event, the OEA is hosting three days of a public "art build for public education" to show support for Oakland educators during their potential strike. The art could be used in rallies, marches and picketing.
The family events are all at the OEA offices, 272 East 12th St., Oakland, 94606. Local food vendors will offer meals. These events will be held from 4-10 p.m. Friday, Jan. 18, and then from 10 a.m. to 10 p.m. Saturday and Sunday, Jan. 19-20.
For more details, call OEA at (510) 763-4020 or go to www.OaklandEA.org
← 2019 Oakland Women's March, Saturday, Jan. 19
New Year, New Leadership, New Oakland? →


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The Floor Scrapers and the Making of Caillebotte's Masterpiece
by Julie Schauer | Aug 24, 2015 | 19th Century Art, Degas, Gustave Caillebotte, Impressionism and Post-Impressionism, Monet, National Gallery of Art Washington, Paul Durand-Ruel, Philadelphia Museum of Art, Seurat
Gustave Caillebotte, The Floor Scrapers, 1875 Musée d'Orsay, now on view
at the National Gallery of Art, Washington,
Right now the National Gallery is having an exhibition of an Impressionist whose reputation has grown over the last 25 years, Gustave Caillebotte. Gustave Caillebotte: The Painter's Eye will be on view until October 4.
It's interesting how his first masterpiece, The Floor Scrapers was rejected by the Salon in 1875, but part of the Impressionists' exhibition the next year. The masterful painting granted Caillebotte entry into the Impressionist group. He repaid his dear friends by buying up many of their works and then donating them to the French state after he died. Many of the paintings he owned are part of Paris' great early modern museum, Musée d'Orsay. It's appropriate that the museum that houses so many Impressionist works is a former train station, since modern trains inspired viewers to observe the transient views of the world that the Impressionists transience painted so well.
There are so many reasons The Floor Scrapers is my favorite work by Caillebotte. The composition is extraordinarily well balanced with an artful asymmetry. There's the tilted floor plane, a view that artists would only start to use after they discovered photography and how it frames pictures differently. There's also the dignity given to labor and the beautiful anatomy.
Finally it's incredible to see how Caillebotte painted tactile contrasts on wood in the various stages of sanding, what looks like with or without varnish, and in the light and shadow. Compared to the other Impressionists, Caillebotte painted with definition and a moderate amount of precision. Yet when he illuminates the floor with natural light from the window, we see a wonderful scintillating values, colors and textures. Yellow shines through with touches of blue, but in the distance it becomes an earthy brown.
To understand how good this painting actually is, it's useful to compare it with another version of floor scrapers that he did. It's a simpler composition from a different angle, with fantastic lighting effects. Enlarging the photo here will really show off the reflections on the floor. (It isn't in the National Gallery's show, but was also part of the 2nd Impressionist exhibition in 1876.)
Caillebotte, The Floor Scrapers
Many of Caillebotte's other paintings in the exhibition give us a view into his amazing sense of perspective: Le Pont de l"Europe, 1876, for example. He lived at the time that Paris had just experienced a major rebuilding campaign. Paris, A Rainy Day gives an impressive viewpoint of how the new city must have looked to the public, in the eyes of a new bourgeoisie class. Since streets corners were set up in star patterns, the linear perspective has multiple vanishing points and appears to go very deep. The even greater and more famous artist, Georges Seurat, borrowed from the composition of Paris: A Rainy Day when he did his iconic narrative painting of Paris on a sunny day, Sunday Afternoon on the Island of the Grande Jatte.
Monet and Van Gogh are two more prominent artists who shared Caillebotte's deep perspective space. Degas went even further than Caillebotte to exploit the unusual viewpoint. Right now there is an important Impressionist exhibition is in Philadelphia, Discovering the Impressionists, until September 13. The exhibit showcases Paul Durand-Ruel, the art dealer who took a gamble and went into great financial risk by buying up Impressionist painters because he believed in them. The exhibit includes Monet's beautiful Poplars series. However, one of the really important works in the group is by Degas, The Dance Foyer at the Opera on the rue Le Peletier.
Edgar Degas, The Dance Foyer at the the Opera on the rue Le Peletier, 1872,
Musée d'Orsay, Paris, now on view at the Philadelphia Museum of Art
This panoramic ballet scene of dancers offers a wonderful comparison with the Caillebotte, The Floor Scrapers. This painting is also asymmetric and appears to look spontaneous, while it is actually exceptionally well-planned. Degas offers many more layers of observation: into another room and out the window, through a mirror (?) or another room in the back center. We imagine that the major source of light is a an unseen window to the right. Whites and golds predominate the scene, with touches of blue and orange. Degas's dancers, though quite strong may seem delicate next to Caillebotte's muscular workers. In truth, Degas' dancing girls and Caillebotte's hard-working men are much the same. Their work is a labor of love, as the Impressionists saw it. The same can be said about Caillebotte, Degas, Durand-Ruel and those who left us with a wonderful record of life in Paris in the 1870s. The ballet painting was done in an opera house that destroyed by fire the very next year, probably caused by gaslights.
Copyright Julie Schauer 2010-2016
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