text:
\section{Introduction}

The nature of the interaction of the solar wind with the plasma environment
of comets as they approach the Sun, has been under investigation since the
early days of space physics as a discipline (Biermann 1951, Alfv\'en 1957,
see reviews by Cravens \& Gombosi 2004, and Ip 2004). The basic elements of the
interaction were developed in the 20 years following the work
of Biermann (1951), who proposed
that the interaction between the solar wind and the comet's plasma is
responsible for the observed aberration angle of plasma tails with respect
to the Sun-comet radius vector. Based on the inefficiency of Coulomb
collisional processes in the coupling of the solar wind and cometary plasmas,
Alfven (1957) proposed that the interplanetary magnetic field (IMF) is a
fundamental ingredient in the solar wind-comet interaction; being responsible
for channelling the cometary ions as it drapes into a magnetic tail.
Biermann et al. (1967) suggested that as cometary ions
are created and incorporated (picked-up) into the solar wind, the loading
of the flow with this additional mass results in a modification of the flow
properties as the solar wind approaches a comet; an idea further
developed by Wallis (1973) (for a review see Szego
et al. 2000). The IMF and mass loading are thus the main dynamical agents
generally considered when
developing models for the interaction of the solar wind with cometary
ionospheres, as well as with other solar system bodies having an ionosphere
and without a strong intrinsic magnetic field.

However, as has been pointed out by Perez-de-Tejada et al. (1980)  and
Perez-de-Tejada (1989), several features of the flow dynamics in the
cometosheath and plasma tail of comets can be attributed to the action of
viscous-like forces as the solar wind interacts with cometary plasma.
Such interaction processes are believed to be similar to those known
to be occurring in other solar system bodies that have an ionosphere
and no significant intrinsic magnetic field, particularly Venus and
Mars (for a review see Perez-de-Tejada 1995, Perez-de-Tejada
2009 and references therein). {\em In situ} measurements
indicate that, as in Venus and Mars, the solar wind flow in the ionosheath
of comet Halley exhibits an intermediate transition, also called
the ``mystery transition'', located approximately half-way between
the bow shock and the cometopause (Johnstone et al. 1986, Goldstein et al.
1986, Reme 1991, Perez-de-Tejada 1989 and references therein).
Below this transition,
as we approach the cometopause, the antisunward velocity of the shocked solar
wind decreases in a manner consistent with a viscous boundary layer
(Perez-de-Tejada 1989). Also
indicative of the presence of viscous-like processes is that the temperature of
the gas increases, and the density decreases, as we move from the intermediate
transition to the cometopause. Taking the distance between
the intermediate transition and the cometopause as the thickness
of a viscous boundary layer, which depends on the effective Reynolds number
of the flow ($R_{\rm eff}$), Perez-de-Tejada (1989) estimated that
$R_{\rm eff} \approx 300$ for the solar wind flow in the cometosheath
is necessary to reproduce the flow properties measured {\em in situ} by
the Giotto spacecraft on its flyby of comet Halley.

An additional argument  suggesting the importance of
viscous-like effects in the dynamics of the flow in the
cometosheath and tail regions, follows from the comparison of
the magnitude of the terms corresponding to momentum transport
due to viscous-like forces and ${\bf J} \times {\bf B}$ forces in
the momentum conservation equation. Perez-de-Tejada (1999, 2000)
has  argued
that downstream from the terminator in the ionosheath of Venus, a scenario
analogous to the one considered in this paper, the fact that the flow is
superalfvenic, as found from the {\em in situ} measurements of
the Mariner 5 and Venera 10 spacecraft,  suggests that viscous-like forces
may dominate over ${\bf J} \times {\bf B}$ forces in the flow dynamics
in the boundary layer formed in the interaction of solar wind and
ionospheric plasma. If the flow is characterized by a low effective Reynolds
number, $R_{\rm eff}$, this layer extends over a significant portion
of the ionosheath of the planet.

In comets, {\em in situ}
measurements obtained during the passage of the ICE spacecraft through the
tail of comet Giacobinni-Zinner (Bame et al. 1986, Slavin et al. 1986,
Meyer-Vernet 1986, Reme 1991) indicate that along the inbound trajectory
(which lies slightly tailward of
the comet nucleus) the magnetic field in the so-called transition and sheath
regions, is approximately 10 nT, the number density is approximately 10
cm$^{-3}$ and the tailward flow velocity varies from $\sim$
400 km/s (near the bow shock) down to 100 km/s. According
to Perez-de-Tejada (1999), the ratio of viscous-like to magnetic forces is
essentially the square of the alfvenic Mach number,
$M_A^2 = V^2 / (B^2/8\pi\rho)$.
From the data of the ICE spacecraft cited above, we find that $M_A^2$
ranges between 4 and 40 across the cometosheath and hence, viscous-like
stresses may dominate over ${\bf J} \times {\bf B}$ forces by a similar
amount, or more, throughout the cometosheath region tailward of the nucleus.
In the vicinity of the plasma tail, the measurements of the ICE spacecraft
(Bame et al. 1986, Slavin et al. 1986) indicate that the
midplane density, dominated by cometary ions, reaches values of 200 cm$^{-3}$
at the point where the magnetic field is a maximum 50 nT. With flow speeds
of approximately 20 km/s, the square of the alfvenic Mach number reaches a
minimum value of 2-3 so that, even in the plasma tail,
viscous-like forces are, at least, as important as ${\bf J} \times {\bf B}$ forces following
the arguments of Perez-de-Tejada (1999).

The fact that $M_A^2 >> 1$ in the cometosheath means that the magnetic
energy density is much smaller than the kinetic energy associated with the
inertia of the plasma. This implies that ${\bf J} \times {\bf B}$ forces
are not the dominant dynamical factor responsible for the large scale
properties of the flow in the region. In fact, one can argue that
the formation of a magnetic tail is an indication that
in the cometosheath, the large-scale magnetic field does not dominate the dynamics,
it is merely carried around by the superalfvenic flow. If the dynamics were controlled
by the magnetic forces, field lines would not bend onto a magnetic tail and the
direction of the ion tail would not be essentially in the direction of the local solar
wind velocity. We believe that the magnetic field does play a crucial role in
the momentum transfer between the solar wind and the cometary plasma,
but it is the small scale, ``turbulent'' magnetic field component, that mediates
the microscopic interaction between charged particles leading to the transfer of
momentum that we are modelling as an effectively viscous process.

\subsection{On the origin of ``viscosity''}

The precise origin of the viscous-like momentum transfer processes invoked
in the viscous flow interpretation of the intermediate transition, in
the ionosheath of comet Halley and in other ionospheric obstacles to the
solar wind, is not yet clear.  Typical properties of solar wind
and cometosheath plasma result in a ``normal'' viscosity, as it appears
in the Navier-Stokes equations when derived from Boltzmann's equation,
that can be considered negligible in the flow dynamics. Using for example
properties of the shocked solar wind in the vicinity of the tail measured
at comet Giacobini-Zinner, $n_i$ = 10 cm$^{-3}$,
$|B| = 10$ nT and $T$ = 3 $\times$ 10$^5$  K (Bame et al. 1986,
Slavin et al. 1986) one calculates the viscosity coefficient resulting
from particle interactions according to Spitzer (1962, eqn. 5-55) to
be $\mu \sim 10^{17}$ g cm$^{-1}$ s$^{-1}$ . This extremely low value most
likely represents a lower limit for the viscosity coefficient, since it
reflects the ability to transport momentum across field lines in a plasma
threaded by a strong, uniform magnetic field. A more appropriate expression
for the plasma viscosity coefficient in the conditions of a cometosheath is
probably given by the coefficient presented in Cravens et al. (1980), which
corresponds to a plasma in a strongly fluctuating magnetic field.
Perez-de-Tejada (2005) has calculated the viscosity coefficient for the
ionosheath of Venus based on these results. If we use the same procedure
to calculate the viscosity coefficient for the solar wind around the tail of
a comet (with the conditions measured at Giacobini-Zinner) we
find $\mu \sim 10^{-11}$ g cm$^{-1}$ s$^{-1}$.

With typical values for  the solar wind velocity and mass density in the
cometosheath around the tail of comet Giacobini-Zinner,
$V$ = 200 km/s and $\rho = 1.67 \times 10^{-23}$ gm cm$^{-3}$
respectively (Bame et al. 1986), and adopting a characteristic
lengthscale of 10$^5$ km for  the variation of the flow velocity
(roughly the thickness of the sheath region),
we find that the corresponding Reynolds number for the flow, based on
the ``normal'' viscosity coefficient estimated above, is $Re > 10^5$.
This indicates that viscous effects resulting from the collisions between
particles in this environment are negligible. Assuming that the Prandtl number
is not very different from unity, as argued by Perez-de-Tejada (2005), we can
also neglect heat conduction resulting from particle collisions.

However, as in Venus and Mars, strong turbulence
has been measured in the ionosheath of comets Halley and Giacobinni-Zinner
(Baker et al. 1986, Scarf et al. 1986, Klimov et al. 1986,
Tsurutani and Smith 1986) and, as it generally occurs in many fluid dynamics
applications, turbulence is characterized (sometimes even defined) by a
dramatic increase in the efficiency of transport processes, viscosity
included, in the flow (Lesieur 1990).  The likely importance of turbulent
viscosity in this scenario is also expected in view of the large value of
the Reynolds number estimated above. Also, as discussed by
Shapiro et al. (1995) and  Dobe et al. (1999 and references therein)
conditions in the ionosheath of Venus and Mars favour the development of
plasma instabilities leading to effective wave-particle interactions.
If this mechanism operates also in the cometosheath, it may lead, as in
these planets, to increased coupling between the solar wind and cometary plasma in
a viscous-like manner as suggested by Perez-de-Tejada (1989).
In our opinion this justifies a detailed
study of the hypothesis of viscous-like effects on the flow dynamics in
solar wind-comet interactions. It is the purpose of this paper to begin
these investigations.

In this paper we present results of 2D hydrodynamical, numerical simulations
of the flow of solar wind and cometary H$_2$O+ ions in the tail and tailward
cometosheath of a comet. This is our first attempt to model the interaction
of the solar wind with the plasma environment of a comet taking into account
viscous-like forces which. We
review the estimation of the effective Reynolds number of
Perez-de-Tejada (1989), based on the comparison of {\em in situ} measurements
at comet Halley with results from
numerical simulations of the viscous-like, compressible flow of the
solar wind over a dense, cold and slow velocity gas representing the
plasma tail of a comet. We also study the relative importance of
viscous-like forces and the coupling between the fast moving protons of
the solar wind and the slow H$_2$O+ ions in the tail. We do the latter by comparing
models with different values of the effective Reynolds number,
the parameter controlling viscous-like effects, and the effective
coupling timescale between both species.

The paper is organized as follows. In section 2 we present the formulation
of the problem, the basic equations, approximations and parameters. Section 3 presents
results of a series of simulations with different model parameters. A
comparison of our results with {\em in situ} measurements at comet Halley
is discussed in section 4. Finally, in section 5 we
summarize our main results and present our conclusions.

\section{Formulation of the problem}
\label{sec:problem}

We model the interaction of the solar wind with the plasma tail of a comet
using a 2D hydrodynamic, two species ($a$ and $b$), finite difference code
that is an extension of the single species version presented in
Reyes-Ruiz et al. (2008).  Included in the dynamical equations is a coupling term
between both species: solar wind protons and cometary ions, which we assume
to be H$_2$O+ ions. This term allows the solar wind flow to get {\em mass loaded}
with cometary ions as they diffuse upwards from the tail,  and cometary ions to
be accelerated by the fast, streaming solar wind. The coupling
term is taken from the work of Szego et al (2000) who describe the treatment
of mass loaded plasmas. However, in order to isolate the effects of
the viscous-like forces, we do not consider the ongoing creation of new
ions in the flow, by photoionization or any other mechanism, as is usually
done in mass loading studies. Considering that we are modelling only the
flow in and around the tail of the comet, the only source of additional
ions in our problem is through the boundary condition at
the left hand edge of our simulation box (see \S 2.3).
It is clear that the 2D character of our simulations is an approximation
to the real problem and may not allow us to study
some processes that may be essential for the dynamical evolution of the flow.
We make this approximation considering that this is the first approach to
the problem in which viscous-like forces are taken into account. We also neglect
the effect of the IMF entrained in the solar wind flow, and leave for
future work the study of the dynamical effects of ${\bf J} \times {\bf B}$
forces, although we do not expect these to be dominant in the region
(see arguments in the Introduction section).

Since we are interested in the gas dynamics in the tail we focus on the
region behind the coma, starting from a few times 10$^4$ km behind the
comet's nucleus and extending downstream to a few times 10$^5$ km as
illustrated in Figure 1.

\begin{figure}
\resizebox{\hsize}{!}{\includegraphics{fig1.ps}}
\caption {Illustration of the computational domain we use for
our simulations. The box provides an approximate scale of the
simulated region. Image of
comet Halley taken the day of the encounter with Giotto by F.Miller,
University of Michigan/CTIO (Brandt et al. 1992).}
\label{fig1}
\end{figure}

\subsection{Basic equations}

The present code solves the  Euler equations for mass, momentum
and energy conservation, including terms representing the
viscous-like effects and interspecies coupling due to turbulence and/or
wave-particle interactions. In Cartesian
coordinates and in conservative form, for species $a$, these can be written as:

\begin{equation}
\frac{\partial \vec{U}^a}{\partial t} +
            \frac{\partial \vec{E}^a}{\partial x} +
            \frac{\partial \vec{F}^a}{\partial y} = \vec{S}^{ab}
      \label{eqnmot}
\end{equation}

\noindent where

\begin{equation}
\vec{U}^a = \left( \begin{array}{c}
  \rho^a \\
  \rho^a V_x^a \\
  \rho^a V_y^a \\
  E_t^a
       \end{array} \right),
\end{equation}

\begin{equation}
\vec{E}^a = \left( \begin{array}{c}
  \rho^a V_x^a \\
  \rho^a V_x^a V_x^a + k_1^a p^a - k_2^a T_{xx}^a \\
  \rho^a V_x^a V_y^a - k_2^a T_{xy}^a \\
  (E_t^a + k_3^a p^a) V_x^a -
     k_4^a (V_x^a T_{xx}^a + V_y^a T_{xy}^a) +
     k_5^a \dot{q}_x^a
       \end{array} \right) ,
       \label{Edef}
\end{equation}

\begin{equation}
\vec{F}^a = \left( \begin{array}{c}
  \rho^a V_y^a \\
  \rho^a V_x^a V_y^a - k_2^a T_{xy}^a \\
  \rho^a V_y^a V_y^a + k_1^a p^a - k_2^a T_{yy}^a \\
  (E_t^a + k_3^a p^a) V_y^a -
     k_4^a (V_x^a T_{xy}^a + V_y^a T_{yy}^a) +
     k_5^a \dot{q}_y^a
       \end{array} \right),
         \label{Fdef}
\end{equation}

\noindent and the inter-species coupling term

\begin{equation}
\vec{S}^{ab} = \left( \begin{array}{c}
  O \\
  \rho^a \nu_{ab} (V_x^a - V_x^b )  \\
  \rho^a \nu_{ab} (V_y^a - V_y^b ) \\
  \frac{3}{2} k_3^a \rho^a \nu_{ab} \left[ T^b - T^a \right] +
   \frac{k_3^a}{k_1^a} \rho^a \nu_{ab} \left[ {\bf V}^b - {\bf V}^a \right]^2
       \end{array} \right).
         \label{Sdef}
\end{equation}

In the preceding equations $\rho^a$ is the mass density of gas $a$, $V_x^a$ and
$V_y^a$ are its velocity components, $T^a$ is its temperature and $E_t^a$ is the total
energy density of species $a$ defined by;

 It is important to point out that this form of the interspecies coupling
term, although widely used in multispecies gas modelling in various astrophysical
scenarios (e.g. Schunk \& Nagy, 1980, Draine, 1986, Cravens, 1991,
Falle, 2003, Van Loo et al. 2009, Szego et al. 2000 and references therein),
can be derived strictly from the Boltzmann collision integral
only for the case corresponding to Maxwell molecules (see for example Gombosi, 1994).
We use it for lack of a similarly simple, alternative expression for charged
particles, and must be considered an approximation of uncertain validity in
our case. Schunk (1977) has discussed the modifications to these expressions
for interspecies coupling for electrically charged molecules and in future
contributions we shall explore the effect of such modifications. In the
present calculations we have chosen this approach to modelling multispecies
flow, which follows the dynamics of each species separately,
instead of an approach following a single fluid, composed of many
different species, in order to clearly disentangle the widely different
properties ($\rho, \ {\bf V}, \ T$, etc) of solar wind and cometary ions.

The coupling between species represented by the term $\vec{S}^{ab}$ in equation
(\ref{eqnmot}) is taken from the work of Szego et al (2000),
and has the form of the traditional coupling resulting from binary
collisions. The term $\nu_{ab}$ contained in $\vec{S}^{ab}$, reflects the
effective result of all processes able to transfer momentum and
energy from one species to another. Note that in the adimensional form
of the equations $\nu_{ab}$ is actually $t_o \nu_{ab}$, that can be viewed
as the ratio of the flow crossing time, $t_o = L/V_o$, to the inter-species
coupling timescale, $1/\nu_{ab}$. In order to preserve the symmetry between
the coupling terms for both species, guaranteed by the identity
$\rho^a \nu_{ab} = \rho^b \nu_{ba}$, we scale $\nu_{ab}$ as $\rho^b$ and
$\nu_{ba}$ as $\rho^a$ with a single proportionality constant, $\nu_o$,
which we take as uniform and constant. In our present code, $\nu_o$
enters as a parameter that can be varied to compare the importance of
inter-species coupling to viscous-like forces.

\begin{equation}
E_t^a = \rho^a e^a + \frac{1}{2} \rho^a (V^a)^2
\end{equation}

\noindent with $e^a$ being the internal energy per unit mass. In
equations (\ref{Edef}) and (\ref{Fdef}), the coefficients $k_i^a$ ($i=1,5$)
are the following
combinations of dimensionless numbers and the adiabatic index for
the gas, $\gamma^a$:

\begin{equation}
k_1^a = \frac{1}{\gamma^a M_o^2},
\end{equation}
\begin{equation}
k_2^a = \frac{1}{R_{\rm eff}^a},
\end{equation}
\begin{equation}
k_3^a = (\gamma^a - 1),
\end{equation}
\begin{equation}
k_4^a = \frac{\gamma^a (\gamma^a-1) M_o^2}{R_{\rm eff}^a},
\end{equation}
\begin{equation}
k_5^a = \frac{\gamma^a}{R_{\rm eff}^a Pr^a},
\end{equation}

\noindent where the Mach number ($M_o$), the Reynolds number ($R_{\rm eff}^a$) and Prandtl
number ($Pr^a$) for the flow of gas $a$, are defined respectively as:

\begin{equation}
M_o = \frac{V_o}{C_{so}},
\end{equation}
\begin{equation}
R_{\rm eff}^a = \frac{\rho_o V_o L}{\mu_o^a},
\end{equation}
\begin{equation}
Pr^a = \frac{\mu_o^a c_p^a}{\kappa_o^a}.
\end{equation}

Quantities with subindex $o$ are those used for the
normalization of the flow variables and parameters,  the reference
sound speed is defined as $C_{so} = \sqrt{\gamma^a P_o /\rho_o}$,
$c_p^a$ is the
specific heat at constant pressure for gas $a$, and $L$ is the normalization for
the spatial coordinates. For simplicity we have assumed that the flow parameters,
$\mu$ and $\kappa$, are uniform and that $\mu^a = \mu_o^a$, $\kappa^a = \kappa_o^a$,
$\mu^b = \mu_o^b$ and $\kappa^b = \kappa_o^b$.

The terms $T_{xx}^a$, $T_{xy}^a$ and $T_{yy}^a$ in equations (\ref{Edef}) and
(\ref{Fdef}) represent the components of the viscous-like stress tensor
given by:

\begin{equation}
T_{xx}^a = \frac{4}{3} \frac{\partial V_x^a}{\partial x} -
         \frac{2}{3} \frac{\partial V_y^a}{\partial y} ,
\end{equation}

\begin{equation}
T_{xy}^a =  \frac{\partial V_y^a}{\partial x} +
          \frac{\partial V_x^a}{\partial y} ,
\end{equation}

\noindent and

\begin{equation}
T_{yy}^a = - \frac{2}{3} \frac{\partial V_x^a}{\partial x} +
         \frac{4}{3} \frac{\partial V_y^a}{\partial y} .
\end{equation}

 As is done in multiple fluid dynamics applications (Lesieur, 1990), we
use the Boussinesq hypothesis in writing the Reynolds stress tensor, i.e.
we adopt a ``standard'' form for the relation between the viscous-like
stress tensor and the large scale flow velocity, using an effective viscosity
coefficient that encapsulates turbulent viscosity as well as the possible
effect of wave-particle interactions (Shapiro et al. 1995)
or any other plasma
instabilities leading to an increased coupling between ions in these
collisionless plasmas.

Also, in equations (\ref{Edef}) and (\ref{Fdef}),
$\dot{q}_x^a$ and $\dot{q}_y^a$
are the components of the effective heat flux vector for species $a$
 (under the Boussinesq hypothesis):

\begin{equation}
\dot{q}_x^a =  - \frac{\partial T^a}{\partial x} ,
\end{equation}

\noindent and

\begin{equation}
\dot{q}_y^a =  - \frac{\partial T^a}{\partial y} .
\end{equation}

Furthermore, we have assumed throughout this work that both gases are
ideal so that:

\begin{equation}
e^a = \frac{1}{\gamma^a -1} \frac{p^a}{\rho^a},
\end{equation}

\noindent with the equation of state, $p^a = \rho^a R T^a$. We have
assumed  that both the solar wind plasma and the cometary plasma,
in the tail region,
are characterized by an adiabatic index,
$\gamma^a = \gamma^b = 5/3$. In the section 4 of the paper we present
some results for $\gamma^b = 1.25$, and discuss the effects of changing
this property of the cometary plasma.

An analogous set of equations and definitions are written for species $b$, and
both set of equations, coupled by the source term $\vec{S}^{ab}$ in equation
(\ref{eqnmot}), are solved simultaneously.

\subsection{Numerical code}

The set of equations described above is discretized in space using 2nd order
finite differences,
and is advanced in time using an explicit, 2nd order MacCormack scheme
(Anderson 1995).  The implementation of the scheme is an extension of
that described in Reyes-Ruiz et al. (2008), but now with the additional source term
$\vec{S}$ in the equations of motion. In MacCormack's scheme the solution is
advanced over one timestep
by a sequence of intermediate steps, the predictor
and corrector steps. In the predictor step an intermediate solution ($U^{\ast}$)
is calculated from the values of the physical variables, $\vec{U}_{i,j}^t$,
at a given time, $t$, and position, ($x_i$, $y_j$), according to:

\begin{equation}
\vec{U}_{i,j}^{\ast} =  \vec{U}_{i,j}^{t}
     - c_1 \left[ \vec{E}_{i+1,j}^{t} - \vec{E}_{i,j}^{t} \right]
     - c_2 \left[ \vec{F}_{i,j+1}^{t} - \vec{F}_{i,j}^{t} \right]
     + \Delta t \ \vec{S}_{i,j}^t
\end{equation}

\noindent where $c_1 = \Delta t / \Delta x$, $c_2 = \Delta t / \Delta y$
and $\vec{E}^{t}$, $\vec{F}^{t}$  and $\vec{S}^t$are evaluated with $\vec{U}^{t}$
according to (\ref{Edef}), (\ref{Fdef}) and (\ref{Sdef}). This predicted
solution is then corrected to obtain
the solution at the next time, $t+\Delta t$, using:

\begin{eqnarray}
\vec{U}_{i,j}^{t + \Delta t} = \frac{1}{2} \left[
     \vec{U}_{i,j}^{t}  \right. &+&  \vec{U}_{i,j}^{\ast}
     - c_1 \left( \vec{E}_{i,j}^{\ast} - \vec{E}_{i-1,j}^{\ast} \right)
      \nonumber \\
     & - &  c_2 \left( \vec{F}_{i,j}^{\ast} -
     \vec{F}_{i,j-1}^{\ast} \right)
     + \left. \Delta t \ \vec{S}_{i,j}^{\ast}
     \right]
\end{eqnarray}

\noindent where $\vec{E}^{\ast}$, $\vec{F}^{\ast}$ and $\vec{S}^{\ast}$
are computed from $\vec{U}^{\ast}$ using (\ref{Edef}), (\ref{Fdef})
and (\ref{Sdef}). Further details of the implementation of MacCormack's
scheme are given in Reyes-Ruiz et al. (2008).

A final upgrade to our previous code
is the ability to handle some types of non-uniform, cartesian grids. For
the simulations done in this work, the
grid is defined by a series of ($x_i$, $y_j$) coordinates for which the
spacing is arbitrary. In our simulations the $x_i$ points are geometrically
distributed from $x_{min}$ to $x_{max}$ with $nx$ elements. The $y_j$
points are equispaced at the initial location of the tail (from $y = 0$
to $y = 1$ having 30 gridpoints) and geometrically distributed
from $y = 1$ to $y = y_{max}$.
In both series the common ratio is 1.02. The 2nd order approximation for the
$x$-derivative of a function $f$ at $x_i$ can be easily obtained from the
Taylor series expansion of the function at $x_{i-1}$  and $x_{i+1}$, and
is given by:

$$
\left(\frac{df}{dx}\right)_i =
\frac{\Delta x_{i-1}^2 f_{i+1} +
       [\Delta x_{i}^2 - \Delta x_{i-1}^2] f_i - \Delta x_{i}^2 f_{i-1}}
      {[\Delta x_{i-1} \Delta x_{i}^2 - \Delta x_{i} \Delta x_{i-1}^2]}
$$

\noindent where $\Delta x_{i} = x_{i+1} - x_{i}$. An analogous expression
exists for the $y$-derivative. This grid allows a higher
resolution in the vicinity of the region of strong interaction,
while putting the $y=y_{max}$ boundary sufficiently far to avoid numerical
artifacts in our results.

\subsection{Initial and boundary conditions}

The solution for the flow is evolved from the following initial conditions.
A dense, cold, slow moving plasma representing the tail is located between
$y=0$ and $y=1$. Both H$_2$O+ and H+ ions are present in the tail, but with
protons much less abundant than H$_2$O+. Between $y=1.5$ and $y=y_{\rm max}$,
the gas has the properties of a shocked, hot, fast moving solar wind
that contains both H$_2$O+ and H+ ions, with the number density of protons
50 times greater than H$_2$O+. In all the calculations presented
here, we have adopted a value $M_o = 2$ for the Mach number of the shocked
solar wind incident on our computational domain. This assumption is made
based on the results of Spreiter \& Stahara (1980) who computed the
the gas dynamics of the flow of the shocked solar wind in the ionosheath of
Venus. Spreiter \& Stahara (1980) found that the flow is characterized
by $M = 2$, as the solar wind crosses the terminator of the planet (the
line separating the day and night sides) and
heads tailwards.  In comets, we take the terminator to coincide approximately
with the location of the nucleus.
Between $y=1.0$ and $y=1.5$ there is
transition region where the flow properties change smoothly in an exponential
manner from those in the tail to those in the solar wind. The initial density
of each species is taken to be:

\begin{equation}
\rho^{a}(t=0) = \left\{ \begin{array}{rl}
  0.025 \rho_{\rm tail} &\mbox{ if $y<1$} \\
  \rho_{\rm sw} &\mbox{ if $y>1.5$}
       \end{array} \right. \label{BCda} ,
\end{equation}
\begin{equation}
\rho^{b}(t=0) = \left\{ \begin{array}{rl}
  \rho_{\rm tail} &\mbox{ if $y<1$} \\
  0.32 \rho_{\rm sw} &\mbox{ if $y>1.5$}
       \end{array} \right. \label{BCdb} .
\end{equation}

We assume both species are moving initially with the same velocity:

\begin{equation}
V_x^{a,b}(t=0) = \left\{ \begin{array}{rl}
  V_{\rm tail} &\mbox{ if $y<1$} \\
  V_{\rm sw} &\mbox{ if $y>1.5$}
       \end{array} \right. \label{BCvx}  ,
\end{equation}

\begin{equation}
V_y^{a,b}(t=0) = 0.\label{BCvy}
\end{equation}

In normalized quantities $V_{\rm sw} = 1$ and $V_{\rm tail}= 0.01$.
For the results shown here we use, in normalized variables,
$\rho_{\rm sw} = 1$ and $\rho_{\rm tail}= 400$. The local temperature
of both species is assumed the same inside the tail, with
$T_{\rm tail}^a = T_{\rm tail}^b = T_{\rm tail}$ and
$T_{\rm sw} = 100 T_{\rm tail}$, with $T_{\rm sw} = 1$ in normalized
units. Outside the tail, for $y > 1.5$, cometary ions are injected with
a temperature an order of magnitude lower than the streaming solar
wind protons, $T_{\rm sw}^a = 10 T_{\rm sw}^b = T_{\rm sw}$.
This choice of temperatures and densities is made to yield an initial
pressure balance between the H$_2$O+ plasma (species $b$) inside the
tail, and the proton plasma (solar wind, species $a$) outside.
With $p^a = \rho^a T^a$ and $p^b = ( m_p^a / m_p^b) \rho^b T^b$,
$m_p^a$ and $m_p^b$ being the particle mass for species $a$ and $b$
respectively, we find that our choice of initial conditions
is characterized by a pressure in-balance among each species.
Whether the rapid movement of cometary ions resulting from
this initial condition is prevented by the wrapped-around IMF over
the comet's tail will be the subject of future studies.
Although significantly different from the flow properties
at later times in the simulations, for all the cases we have
studied these
initial conditions do not give rise to any long lasting instability
in the flow so that the final state does not depend on their
precise form or value.

\begin{figure}
\resizebox{\hsize}{!}{\includegraphics{fig2.ps}}
\caption {Density contours (shades of gray) and flow geometry (velocity vectors)
for Case 1 ($Re^{a,b} = 30$, $\nu_o = 0.1$) after 1234 simulation time units.
The top panel shows the configuration for the proton plasma (species $a$) and
the right side panel shows the ``equilibrium'' configuration for cometary
H$_2$O+ ions. Density and velocity are in normalized units.}
\label{fig2}
\end{figure}

The boundary conditions are chosen to be consistent with the
initial conditions. At the left boundary, $x=x_{min}$, the flow
density and velocity follow exactly that given by the initial condition
in equations (\ref{BCda})-(\ref{BCvy}). Considering that the
inflow to the comet's tail ($y<1$) is subsonic, we allow the
inflow pressure to float freely as a linear extrapolation of the
active mesh values (e.g. Anderson 1995). The right side boundary,
$x=x_{max}$, corresponds to the commonly used outflow conditions for
supersonic flows, namely the derivatives being zero for all flow variables.
We have also run simulations with an outer boundary condition
obtained from linearly extrapolating the flow variables, resulting
only in minor differences
in the last gridpoints before the $x=x_{max}$ boundary.

\section{Results}

We have performed a series of simulations with different set of parameters
$R_{\rm eff}^{a,b}$ and $\nu_o$ to determine the effect of viscous forces and
inter-species coupling in the flow dynamics.
For all cases considered, the flow evolves
from the prescribed initial condition [eqns. (\ref{BCda})-(\ref{BCvy})],
passing through a fast transient phase, during which a considerable portion
of the mass originally in the tail is eroded by the solar wind exiting
our simulation domain. The relevance of this transient phase, lasting a few
tens of solar wind crossing times ($t_o = L/V_o$), in relation to
observed features in the evolution of the ion tail, will be
analysed in a future publication. In this work we concentrate on the
following, quiescent stage of evolution since, given its longer timescale
for existence, is more likely to be encountered.
In all cases, we present results for the flow velocity, density and
temperature after a time long enough that a quasi-steady state
has been reached.   All results are presented in terms of normalized
quantities as defined in the previous section. For a particular application,
appropriate values of $L$, $V_o$, $\rho_o$ and $T_o$ can be chosen as
exemplified in Section 4 for comet Halley.

\begin{figure*}
\centering
\includegraphics{fig3.ps}
\caption {Vertical profiles of the flow properties for Case 1 at three different
positions; $x = 2$ (left column of panels), $x=5$ (middle column) and
$x=8$ (right column). In all cases, gray lines indicate the properties
of the proton plasma (species $a$) and black lines denote the properties of
the H$_2$O+ plasma (species $b$). The top row shows the $x$ component of
velocity, $V_x^{a,b}$,
the middle row shows the temperature, $T^{a,b}$, and the bottom row shows the
mass density, $\rho^{a,b}$. All quantities are in normalized units.}
\label{fig3}
\end{figure*}

To determine the appropriate value of the effective Reynolds number for each species
we consider the following. According to Perez-de-Tejada (1989)
the geometry of the flow, measured
{\em in situ} by the Giotto spacecraft
in its fly-by comet Halley in march 1986, implies an effective
Reynolds number around 350 for the shocked solar wind flow above the
cometopause along the spacecraft trajectory. In contrast, in a
similar region in the ionosheath of Venus, Perez-de-Tejada (1999)
and Reyes-Ruiz et al (2008) estimate a value of the Reynolds
number an order of magnitude smaller ($R_{\rm eff}$ = 20), based on
a comparison of {\em in situ} measurements (by the Venera 10
and Mariner 5 spacecraft) at Venus with the flow properties
derived from a numerical simulation of the viscous-like solar wind-ionosphere
interaction. To assess the estimation of Perez-de-Tejada (1989) we
have conducted simulations with 3 different values of the Reynolds
number. A high value, $R_{\rm eff}$ = 100, similar to that estimated
by Perez-de-Tejada (1989) for comet Halley; an intermediate value,
$R_{\rm eff}$ = 30, comparable to the value estimated by Reyes-Ruiz et al. (2008)
for the solar wind flow in the ionosheath of Venus; and a low value,
$R_{\rm eff}$ = 10, used to verify the tendency in the results
as $R_{\rm eff}$ is decreased.

In most cases, the value of the effective Reynolds number for both species is
assumed to be the same, In our view, the lack of knowledge of the precise mechanisms
giving rise to the effective viscosity in these plasmas justifies
this assumption. However, we have analysed a case with different
values of the effective Reynolds number for each species in the Discussion section.

The value of $\nu_o$ is also varied to explore the relative importance of
inter-species coupling, $versus$ viscous forces, which are
proportional to $R_{\rm eff}^{a,b}$. We will show results for 3 different cases:
a strong coupling case characterized by $\nu_o$ = 1, which can be interpreted as
having the timescale for inter-species coupling equal to the solar wind crossing
timescale, $t_o = L/V_o$; a medium coupling case, in which the coupling timescale
is an order of magnitude greater than the crossing timescale, $\nu_o$ = 0.1; and
a weak coupling case, for which $\nu_o$ = 0.01, so that inter-species coupling
effects are much smaller than other dynamical effects.

To compare the state
of the flow at the same time in its evolution for all cases,
starting from the same initial condition, we have chosen,
arbitrarily, to show results at $t$ = 1234,
with time units in multiples of the solar wind crossing time. The number of
timesteps required to reach this time depends on the model parameters,
for most cases less than 200 000 timesteps are required.

\begin{figure}
\centering
\includegraphics{fig4.ps}
\caption {Same as in Figure 3 but for simulation Case 2
($R_{\rm eff}^{a,b} = 30$, $\nu_o = 1.0$).}
\label{fig4}
\end{figure}

\subsection{Effect of inter-species coupling}

Our fiducial model, Case 1, is characterized by model parameters
$R_{\rm eff}^{a,b}$ = 30 and $\nu_o$ = 0.1.
In Figure \ref{fig2} we show density contours and the flow velocity for each species.
Initially the tail contained a uniform density, $\rho^a$ = 10 (protons)
and $\rho^b$ = 400 (H$_2$O+ ions) for $y < 1$, and after $t = 1234$ $t_o$,
a significant portion of
the tail has been eroded by the effect of viscous forces and inter-species coupling.
A shock wave is evident in the deflection of the flow velocity from the initial
uniform distribution imposed by the boundary condition at $x = x_{\rm min}$. Also
noticeable is the strong velocity gradient around $y = 2$ which corresponds to
the viscous boundary layer. Both effects are
also shown in Figure \ref{fig3}, where vertical profiles of the $x$ component of
velocity, $V_x$, temperature, $T$, and mass density, $\rho$, are shown for three
different $x$-positions, $x = 2, \ 5$ and $8$; in the left, middle and right
columns of each figure, respectively.

In Figure \ref{fig3} the shock front and the boundary layer can be identified
at all 3
positions, but they are well separated only for $x = 5$ and $x = 8$, shown
in the middle and right hand columns, respectively. For a given $V_x$ profile,
the shock front corresponds to the uppermost
decrease from the uniform velocity ($V_x = 1$) in the free flowing solar wind. In the
middle panel, corresponding to $x = 5$, this transition is located approximately
at $y = 5$. A second transition, located approximately at $y = 2.5$ for $x = 5$,
marks the top of the viscous boundary layer, below which the velocity drops sharply
to the very low flow velocities in the middle of the tail. The shock front can
also be seen as an increase in both temperature and density in the corresponding
panels for each position. The temperature increase and density
decrease characteristic of viscous boundary layers and found in previous studies
of viscous flow over a flat plate (e.g. Reyes-Ruiz et al. 2008),
is also observed in other cases modeled here. This clearly indicates
that the region around $y = 2$ (at $x = 5$) is indeed a viscous boundary
layer.

\begin{figure}
\centering
\includegraphics{fig5.ps}
\caption {Same as in Figure 3 but for simulation Case 3
($R_{\rm eff}^{a,b} = 30$, $\nu_o = 0.01$).}
\label{fig5}
\end{figure}

For Case 2 we use the same Reynolds number, $R_{\rm eff}^{a,b}$ = 30, as in Case 1, but
increase the importance of inter-species coupling by using $\nu_o$ = 1.0. A Figure
showing the general flow geometry is not shown since no
appreciable differences are found with Case 1 (shown in Figure \ref{fig2}).
However, the vertical profiles of flow
properties, shown in Figure \ref{fig4}, clearly illustrate
the effect of a much stronger inter-species coupling used in this model. Namely,
as both species are more tightly coupled, their velocity and temperature
distribution tend to be almost identical. The density distribution
conforms to the different boundary conditions for each species, since these
are different, there is no reason why both densities should tend to
equalize and they do not. Figure \ref{fig4} shows that the
shock front and the boundary layer
are not well separated at the rightmost position shown, $x = 2$. From the shock
front height and boundary layer thickness shown in the middle and right columns
of Figure \ref{fig4}, we see that both are proportional to the
inter-species coupling (see \S4). The shock front height at $x = 5$, for example,
changes from $y = 4.7$ for Case 1, to $y = 5.5$
in this case, while the thickness of the boundary layer goes from $y = 2.8$ to $y = 3.2$
as we increase the inter-species coupling parameter from 0.1 to 1.

In Figure \ref{fig5} we show the results for Case 3 characterized by a very weak
inter-species coupling, $\nu_o = 0.01$. The general
flow geometry (not shown) is very similar to that in Figure \ref{fig2}. A comparison
of Figure \ref{fig5} (weak coupling) with Figures \ref{fig3} and \ref{fig4}
(medium and strong coupling respectively), clearly shows that in Case 3 the dynamics of
both species is essentially uncoupled. The location of the shock front and the
top of the boundary layer are different for each species. For example,
at $x = 5$, only for the cometary H$_2$O+ ions the shock front and boundary layer
are clearly separated. For the H$_2$O+ ions the shock front is located
approximately at $y = 5$ and the top of the boundary layer is at $y = 2.5$,
while for protons the shock front and the top of the boundary layer are
both located around $y = 2$.

\begin{figure}
\resizebox{\hsize}{!}{\includegraphics{fig6.ps}}
\caption {Same as in Figure 2 but for simulation Case 4
($R_{\rm eff}^{a,b} = 10$, $\nu_o = 0.1$).}
\label{fig6}
\end{figure}

\subsection{Effect of viscous-like forces}

To analyse the effect of the viscous-like momentum transport between the solar
wind and material in the comet's plasma tail, we compare 3 simulations with
the same inter-species coupling parameter, $\nu_o = 0.1$, but different values
of the effective Reynolds number. Figures \ref{fig6} and \ref{fig7} shown the resulting
flow geometry and vertical profiles, respectively, for our Case 4, characterized
by a higher viscosity corresponding to a lower effective Reynolds number, $R_{\rm eff}  = 10$,
than Case 1. Comparing the global geometry of the flow in this case (Figure \ref{fig6})
with that in a case with greater Reynolds number, $R_{\rm eff}^{a,b} = 30$
(Figure \ref{fig2}) we see that after 1234 crossing
times, the erosion of the tail is much greater in this high viscosity case
for both species. This result is expected as well as the increase in the
thickness of the boundary layer as we decrease the effective Reynolds number. This is
clearly seen when comparing the vertical profiles of the flow properties shown in
Figure \ref{fig3} (medium viscosity) and Figure \ref{fig7} (high viscosity). For example,
as shown in Figure \ref{fig7} for $x = 5$, the top of the boundary layer
increases from $y = 2.8$ for $Re^{a,b} = 30$ to approximately
$y = 3.7$ for $R_{\rm eff}^{a,b} = 10$.
The increased thickness of the boundary layer as we decrease $R_{\rm eff}^{a,b}$, effectively
represents a more blunt obstacle to the solar wind flow. Hence, the height of the
boundary layer also increases as we decrease $Re^{a,b}$. This is also shown in Figure
\ref{fig7} where, for example at $x = 5$, the height of the shock front is
located approximately at $y = 7$; about 2 scale units higher than the shock
front location for
the model with lower effective viscosity (Figure \ref{fig3}).

\begin{figure}
\centering
\includegraphics{fig7.ps}
\caption {Same as in Figure 3 but for simulation Case 4
($R_{\rm eff}^{a,b} = 10$, $\nu_o = 0.1$).}
\label{fig7}
\end{figure}

The tendency seen in going from high ($R_{\rm eff}^{a,b} = 10$) to medium
effective viscosity ($R_{\rm eff}^{a,b} = 30$) is confirmed by
comparing with results with an even smaller viscosity, such as Case 5 which
corresponds to a model with $Re^{a,b} = 100$, shown in Figures \ref{fig8} and
\ref{fig9}. As expected, a decreased viscosity leads to significantly less
erosion of the tail than in Cases 1 and 4 (medium and high viscosity respectively)
as shown in Figure \ref{fig8}.
Also, as discussed above and as shown in Figure \ref{fig9}, the top of the
boundary layer decreases as we increase the Reynolds number, and consequently
the location of the shock front also decreases.
For example, in the profiles corresponding
to $x = 5$ in Figure \ref{fig9}, we find that the top of the boundary layer
decreases from $y = 2.8$ for $R_{\rm eff}^{a,b} = 30$ to $y = 2.2$ for
$R_{\rm eff}^{a,b} = 100$.
In regards to the location of the shock front, this
goes from $y = 4.8$ for $R_{\rm eff}^{a,b} = 30$ to
approximately $y = 3.7$ for $R_{\rm eff}^{a,b} = 100$.

\begin{figure}
\resizebox{\hsize}{!}{\includegraphics{fig8.ps}}
\caption {Same as in Figure 2 but for simulation Case 5
($R_{\rm eff}^{a,b} = 100$, $\nu_o = 0.1$).}
\label{fig8}
\end{figure}

\section{Discussion}
\label{sec:discussion}

In view of the uncertainty about the precise physical mechanisms
giving rise to the effective viscosity, we have assumed
that the effective Reynolds
number for both species is the same in the calculations presented above.
However, we have also carried out simulations having distinct effective
Reynolds number for each species and find that for a medium value of
the inter-species coupling, $\nu_o = 0.1$, the results are almost identical
to those with a single value for the effective Reynolds number for both species
(equal to the effective Reynolds number of species $b$). For example, for a
case with $R_{\rm eff}^a = 100$, $R_{\rm eff}^b = 10$ and $\nu_o = 0.1$,
the vertical profile
of flow properties for the H$_2$O+ ions at all $x$ locations is almost identical
to that shown in Figure \ref{fig7} for Case 4, characterized
by $R_{\rm eff}^a = R_{\rm eff}^b = 10$
and $\nu_o = 0.1$.
The vertical profile of flow properties for the protons, while not identical, is
still very similar to Case 4.  This suggests that viscous stresses, particularly
in the species that dominates the mass of the problem, are the
dominant factor in the flow dynamics.

\begin{figure}
\centering
\includegraphics{fig9.ps}
\caption {Same as in Figure 3 but for simulation Case 5
($R_{\rm eff}^{a,b} = 100$, $\nu_o = 0.1$).}
\label{fig9}
\end{figure}

 As mentioned in section 2, in the results presented above we have assumed
that the adiabatic index for both species is the same, $\gamma^a = \gamma^b = 1.67$.
While this value of $\gamma$ can be safely assumed for the solar wind plasma
(assuming thermal equilibrium for the species), it is not so clearly valid for
the H$_2$O$^+$ plasma in which the excitation of rotational and vibrational
degrees of freedom may lead to a lower value of $\gamma$ (again assuming
thermal equilibrium for the species). In order to illustrate the effect of
a different, lower value of the adiabatic index for cometary plasma, we
have also conducted simulations with a value $\gamma^b = 1.25$ for the
adiabatic index of the H$_2$O$^+$ plasma. This value corresponds to a
gas composed of triatomic molecules in thermal equilibrium at a high enough
temperature for all molecular degrees of freedom to be excited.
Results for this case, $\gamma^a = 1.67$ and $\gamma^b = 1.25$, with
the same effective viscosity and interspecies coupling parameters as Case 1
($R_{\rm eff}^{ab} = 30$ and $\nu_o = 0.1$) are shown in Figure \ref{fig10}
which shows the vertical profiles of $V_x$, $T$ and $\rho$ for both
species in both cases.

\begin{figure}
\centering
\includegraphics{fig10.ps}
\caption {Comparison of the vertical profiles of flow properties
for a case characterized by the same value of $R_{\rm eff}$ and
$\nu_o$ as Case 1, but with $\gamma^b = 1.25$.
Profiles at $x = 2$ (left column of panels),
$x=5$ (middle column) and $x=8$ (right column) are shown.
Gray lines indicate the properties
of the proton plasma and black lines denote the properties of
the H$_2$O+ plasma. All quantities are in normalized units.}
\label{fig10}
\end{figure}

 Clearly evident when comparing Figure \ref{fig10} ($\gamma^b = 1.25$)
and Figure \ref{fig3} ($\gamma^b = 1.67$) is the fact that if the cometary
plasma is characterized by a lower value of the adiabatic index,
the heating of the H$_2$O$^+$ plasma is significantly
reduced in the boundary layer, since part of the dissipated energy goes
to the excitation of the additional degrees of freedom corresponding
to the lower value of $\gamma$. This leads to less plasma expansion in
the region and a thinner velocity boundary layer. The height of the shock front
is consequently reduced. In future contributions we shall address the
issue of the appropriate value of $\gamma$ for the cometary plasma.

\subsection{Comparison with {\em in situ} measurements}

A comparison of our results with the {\em in situ} measurements
made by the Giotto spacecraft, as it flew by comet Halley in March of 1986, is
not straightforward. The simplified geometry we are using in our
simulations to study the interaction
in the tail region exclusively, precludes a direct
comparison. Nevertheless, some insight into the implications
of our results can be obtained from a simplified comparison.

 Once a particular application scenario has been chosen, values for the
characteristic length, velocity, density and temperature used in
the adimensionalization of the equations of motion (section \ref{sec:problem})
can be established. For comet Halley, using the {\em in situ} measurements
reported in Goldstein et al. (1986), Johnstone et al. (1986) and Perez-de-Tejada (1989),
we adopt $L$ = 150,000 km, $V_o$ = 250 km/s, $\rho_o$ = 1.67 $\times 10^{-23}$
gm/cm$^3$ and $T_o$ = 2.5 $\times 10^5$ K.

According to Johnstone et al. (1986), the Giotto spacecraft observed 3 distinct
transitions in the plasma properties on its inbound trajectory towards comet
Halley's nuclear region: (1) The outermost transition occurs about 900000 km from
the point of closest approach and can be identified as the
bow shock crossing. (2) The cometopause, where the density of cometary ions sharply
increases, can be located at around 150000 km from closest approach
(Perez-de-Tejada, 1989). (3) Approximately midway between the shock location and
the cometopause, at about 400000 km from closest approach, the so called intermediate
transition signals the top of the viscous boundary layer according to
the viscous flow interpretation of the solar-wind-comet interaction
given by Perez-de-Tejada (1989). Pending a more
detailed comparison of the Giotto measurements with the results of our simulations,
which should take into account the full geometry of the problem, let us
identify the cometopause detected in the measurements with the region of
very strong H$_2$O+ density increase in our simulations, located
at $y = 1.0$ (approximately) in our normalized units.
Under this assumption, in Figure \ref{fig11}
we compare the thickness of the boundary layer and the height of the shock
front evaluated from our simulation results at $x = 5$, for models with
different effective Reynolds number ($R_{\rm eff}^{a,b}$)
and inter-species coupling parameter ($\nu_o$). As
already seen, both the thickness of the boundary layer and the height of the
shock front decrease with increasing Reynolds number so that, almost irrespective
of the value of $\nu_o$, a low value of $R_{\rm eff}^{a,b}$ is required to explain the
measured transition locations.

\begin{figure}
\resizebox{\hsize}{!}{\includegraphics{fig11.ps}}
\caption {Height of the shock front, $H_{sh}$ (gray lines with
squares) and thickness of the boundary layer, $\delta$
(black lines with triangles), as a function of effective
Reynolds number, for a set of models with
different value for the inter-species coupling parameter, $\nu_o$. Values
for these scale-heights correspond to $x = 5$ in our model. The dotted
lines indicate the height of the shock front (gray) and the location of the
intermediate transition (black) during the inbound portion of Giotto's flyby
through the tail of comet Halley.}
\label{fig11}
\end{figure}

Also evident in Figure \ref{fig11} is the
dependence of the transition locations on the value of the inter-species
coupling parameter. In simulations
with a strong inter-species coupling, the solar wind ions
are able to transfer momentum to cometary ions more
efficiently giving rise to a thicker boundary layer and
higher shock front. The opposite is true when
both species are weakly coupled ($\nu_o = 0.01$).
In such case solar wind ions flow by cometary
plasma interacting very weakly. Less momentum is
transferred between the solar wind and cometary plasma
in a situation reminiscent of a high Reynolds number case.
Our analysis of scale-heights
is based not only on the properties of the velocity profiles in our simulations.
As pointed out by Perez-de-Tejada (1989), there are corresponding
changes in the density and temperature of the gas as one enters a boundary
layer. The heating and expansion characteristic of
viscous boundary layers are also found in our results, particularly
for cases with low Reynolds number and high inter-species
coupling parameter..

It is worth mentioning that somewhat similar properties of the flow were also
measured by the ICE spacecraft in its flyby through comet Giacobinni-Zinner
as discussed in Ip (2004). A comparison of the location of the transition from
the sheath region to the so-called transition region and the bow shock location
as estimated by Reme (1991), corrected for the different height of the
cometopause, yields very similar relative positions to those shown by the
dotted lines in Figure \ref{fig11} for the transitions in comet Halley.
In future work we will address the differences in the flow properties measured
in comet Halley and in comet Giacobinni-Zinner.

\subsection{Implications for 3D geometry}

It is important to emphasize that the geometry presented in this paper is
derived from a 2D model. In Venus, as discussed by Perez-de-Tejada
(1995), the viscous-like interaction between solar wind and ionospheric plasmas
takes place preferentially over the magnetic poles of the planet (defined in terms
of the incident IMF), where the pile-up of magnetic field lines is
less than around equatorial latitudes. According to Perez-de-Tejada (1995),
up to about 80$^{\rm o}$ SZA, the piled-up magnetic field over the
dayside ionosphere and along the flanks, inhibits in some degree a direct,
viscous-like interaction
between solar wind and ionospheric plasmas.

If we apply these ideas to the solar wind-comet interaction, this implies
that the flow properties we have computed here, correspond more closely
to locations
over and downstream from the magnetic poles of the comet. For different
locations along the tail, the piled-up magnetic field may prevent an
efficient viscous-like dragging of ionospheric material, ${\bf J} \times {\bf B}$
forces may be more important and the flow dynamics may be
better modeled in terms of an MHD model as those of Wegmann (2002) and
Jia et al. (2007). As the IMF is constantly changing direction on a wide
range of amplitudes and timescales, the region of viscous-like interaction
between the solar wind and cometary plasma, changes with time. Given
the typical IMF orientation is approximately in the ecliptic plane, one
should expect that the flow within +/- 20$^{\rm o}$, measured in the
$y$-direction (as typically defined) from the magnetic poles of the comet,
is best described by our model.

\section{Conclusions}

We have presented results for the numerical simulation of the interaction between
the solar wind and the plasma in the tail of a comet, taking into account the effect
of viscous-like stresses previously argued to be important by Perez-de-Tejada et al
(1980). To our knowledge, this is the first time that viscous-like effects have been
incorporated into such studies.
Our results indicate the existence of 3 distinct transitions in the flow properties:
outermost we find a shock front, innermost we have the cometopause and an
intermediate transition which we can identify with the height of the boundary layer
characterized by a fast decline in the anti-sunward flow velocity, and the onset of
plasma heating and expansion due to viscous-like dissipation. The location of these
transitions depends on the flow parameters, namely the effective Reynolds number of
the flow for each species, $R_{\rm eff}^{a,b}$,
and the inter-species coupling parameter, $\nu_o$.

By comparing the flow properties from our numerical
simulations to the location of the shock front and intermediate transition,
as measured by the Giotto spacecraft as it approached the nucleus of
comet Halley, we find that, almost irrespective of the
strength of the inter-species coupling, $\nu_o$; a low value of the
effective Reynolds number,
approximately $R_{\rm eff}^{a,b} \lesssim 20$ for both species, is required to reproduce the
measured transition locations. This implies, in the context of our model,
that the measured flow
properties cannot be explained if one does not take into account the
viscous-like forces in the interaction of the solar wind and the plasma tail of a
comet. Although the conclusions drawn from this study are
strictly applicable only to comet Halley and solar wind conditions
at the time the {\em in situ} measurements were taken, one may
speculate that viscous-like processes may be important in the
solar wind-comet interaction in general.

 It is important to emphasize that, this being the first
attempt to include viscous-like
forces in the numerical simulation of the interaction of the solar wind
with a comet's plasma environment, there are many pending issues
still to be addressed that could have potentially important
consequences on the details of the solutions obtained under our
simplified treatment. First and foremost, the precise forms we
are using for the viscous like stress and effective interspecies coupling,
may be questioned. As we have argued in the Introduction,
plasma properties imply that ``normal'' viscosity is
negligible in the region under consideration. Hence, we are invoking an
effective viscosity presumably resulting from plasma turbulence and/or
wave-particle interactions. However, the precise form of the
terms corresponding to viscous-like momentum transfer in the
equations of motion (Bousinessq hypothesis) is not formally
demonstrated. Also, as we have discussed in the Formulation section
of the paper, the interspecies coupling terms we are
using can not be strictly derived for a plasma as the one we are modelling.
In view of these arguments, one may consider that the work reported in this
paper is only an academic exercise of
questionable applicability to the problem of solar wind-cometary plasma
interaction. In such case, a similar conclusion must be reached in
regards to many other studies of fluid dynamics that use
similar approaches to modelling effective viscosity and interspecies
coupling.

Additional important effects still to be considered are the
following: geometrical
effects due to the curvature of the ionosphere are required
for a more direct, quantitative comparison between {\em in situ}
measurements by the Giotto spacecraft and the results of simulations;
the interaction of the charged species with neutral gas ejected
from the comet which, especially in the vicinity of the nucleus,
is the most abundant species;
the effect of the magnetic field on the
flow (particularly in the dayside and around the midplane of the near-tail
region), 3D effects, incoming flow time dependence, etc. We
believe that the further assessment of the relevance of these factors
is beyond the present study. They are the subject of work
currently in progress and will be reported in future contributions.

\begin{acknowledgements}
      MRR acknowledges the support of research grant IN109409 of DGAPA-UNAM.
HA acknowledges the support of research grant IN121406 of DGAPA-UNAM
and CONACYT-M\'exico grant No. 508807.

\end{acknowledgements}

redpajama_set_name: RedPajamaArXiv


text:
Open Call: Documenting St Andrews: Spring and Summer 2020
Documenting St Andrews: Spring and Summer 2020
What is the town of St Andrews like during the pandemic? What are the townspeople doing? How are the workers and the students, the elderly and the young? And the seagulls, the ducks, the crabs, the oak trees, the bell towers and the relentless waves of the North Sea. What is happening in St Andrews and what is not?
Documenting St Andrews: Spring and Summer 2020 is a participatory project that produces and reproduces memory about St Andrews through photographs. The call for submissions is open to anyone using photography to document St Andrews between early March and late August 2020. Documenting is understood in its broadest sense here, derived from photography's capacity to capture and preserve fleeting moments, and encompassing all kinds of ordinary shots. At the end of this summer, the photographs submitted to the project will cumulatively make up a unique image archive.
Deadline : 28th August
This project is initiated by Weitian Liu, a research student at the University of St Andrews pursing an Mphil in History of Photography.

redpajama_set_name: RedPajamaCommonCrawl


text:
Le calendrier aztèque
Les Aztèques utilisaient trois calendriers :

 Le tonalpohualli, calendrier divinatoire sacré d'une durée de 260 jours, comprenant 20 signes. Chaque signe gouvernait 13 jours du calendrier.
 Le calendrier solaire, constitué de 18 mois de 20 jours (18 x 20 = 360) + un  de cinq jours.
 Le calendrier séculaire, le "siècle" aztèque se fondant sur un cycle de 52 ans, comprenant quatre signes et 13 nombres. Les quatre signes : Maison, Lapin, Roseau, Silex sont associés à un nombre compris entre 1 et 13. Le cycle complet ayant une durée de 52 ans, deux personnes nées le même jour à 52 ans d'écart auront donc le même signe de jour et le même signe annuel.

En pratique

Donc, d'après le calendrier, chaque personne a trois signes :

 le signe de jour
 le signe de treizaine
 le signe annuel

Le signe de jour décrit la personne au quotidien ; comportement, humeur générale, nature intime. On lui accorde la priorité.
Le signe de treizaine agit comme une protection à l'égard de la personne. Son importance est moins grande, mais le signe peut agir de manière à équilibrer la personnalité.
Le signe annuel renseigne davantage sur les influences qu'exerce la société sur un individu. Il faut voir le signe annuel comme un apport supplémentaire, comme le facteur chance de la vie d'un être.

Les signes

Les signes sont chacun associés à une direction.

 1. Crocodile (Cipactli) - Est
 2. Vent (Eecatl) - Nord
 3. Maison (Calli) - Ouest
 4. Lézard (Cuetzpallin) - Sud
 5. Serpent (Coatl) - Est
 6. Mort (Miquiztli) - Nord
 7. Cerf (Mazatl) - Ouest
 8. Lapin (Tochtli) - Sud
 9. Eau (Atl) - Est
 10. Chien (Itzcuintli) - Nord
 11. Singe (Ozomatli) - Ouest
 12. Herbe (Malinalli) - Sud
 13. Roseau (Acatl) - Est
 14. Jaguar (Ocelot) - Nord
 15. Aigle (Quauhtli) - Ouest
 16. Vautour (Cozcaquauhtli) - Sud
 17. Mouvement (Ollin) - Est
 18. Silex (Tecpatl) - Nord
 19. Pluie (Quiauitl) - Ouest
 20. Fleur (Xochitl) - Sud

Source
Luis Huerta, Astrologie aztèque simplifiée, édition Quebecor.

Astrologies par tradition
Aztèques

redpajama_set_name: RedPajamaWikipedia


Precious for hand knitters, this booklet provides four hundred knitting styles in either written and chart shape. It covers quite a few styles comparable to knit-and-purl sew styles, cable and aran styles, lacy styles, ribs and two-colour styles. It additionally includes a thoughts part which provides directions within the fundamentals of this renowned craft.
Knitting anything by means of hand after which using the centuries-old means of rainy felting ends up in attractive items which are sturdy, green, and undying. In middle Felt Knits, actress-turned-crafter Tamara Mello deals twenty-five knitted and felted initiatives, from darling nesting bowls to stylish hats, comfortable wraps, and elegant hair add-ons.
This e-book collects 25 marvelous styles for socks encouraged through knitting traditions from worldwide. styles from most sensible designers together with celebrity Athena, Beth Brown-Reinsel, Candace Eisner Strick, Chrissy Gardiner, Janel Laidman and Anna Zilboorg are featured, besides an advent from Nancy Bush, writer of people Socks.
Review: easily Knitting is the UK's best-selling knitting journal. even if you're a newbie or you've been knitting for years you'll locate plenty of interesting styles, knitting information and nice buys in each factor. And don't put out of your mind, each factor comes with a gift!
No matter if creamy and hot or wintry cool, white conjures up a feeling of vintage purity. have a good time its spectacular type with a suite of 25 attractive all-white tasks for intermediate to complicated knitters, all made of the main sumptuous yarns ever. From sensuous sweaters for ladies to lovely child and children's clothes to rugged masculine clothes, those clothing take white to new degrees of pleasure and opulence.
Rep Rnd 1 for patt. BODY With MC, longer needle and longtail method, CO 200 (224, 252, 280, 312, 340) sts. Place marker (pm) and join in the rnd. Join CC and work in 2-color rib (see Stitch Guide) for 5¾". With MC, knit 1 rnd. Purl 1 rnd. Next rnd With MC, purl inc 2 sts evenly around—202 (226, 254, 282, 314, 342) sts. Set-up rnd [With MC, k1, beg and ending as indicated for your size, work Tracery chart over 99 (111, 125, 139, 155, 169) sts, with MC, k1, pm] 2 times (using rnd m as last pm). Inc rnd [With MC, k1, LLI, work in patt to 1 st before m, RLI, with MC, k1, sl m] 2 times—4 sts inc'd.
YARN: Imperial Yarn Columbia. com 6/27/13 3:20 PM Tracery Vest Designed by by Kathleen Sperling. PAGE 45. YARN: Plymouth Yarn Company Happy Feet. indd 31 • The Unofficial Harry Potter Knits 31 6/27/13 3:21 PM History of Magic Modern Stripes House Scarves Kim Haesemeyer F rom the Quidditch pitch to a late night walk to Hagrid's hut, these scarves will ward off the chill. The faux seam is created by a simple yarnover that is passed over the next two stitches, hiding the color change. indd 32 • F I N I S H E D S I Z E 8¼" wide and 71" long.
Dec rnd [Knit to 2 sts before m, ktog, sl m] 11 (12, 13) times—11 (12, 13) sts dec'd. Knit 2 rnds even. Rep last 3 rnds 7 more times—22 (24, 26) sts rem. Next rnd [K2tog] 11 (12, 13) times—11 (12, 13) sts rem. Break yarn and thread through rem sts. Pull tight to close. FINISHING Graft 6 st I-cord edges tog. Weave in ends. TASSELS Cut 6 lengths of 32" yarn choosing any combination from the 4 yarn colors. With a tapestry needle, sl the lengths of yarn through the top knot of the hat so that 6 strands of 16" are on either side of the top knot.


text:
Home / Bikman's Best Bets
By Margaret Bikman January 12, 2020 January 12, 2020 Categories: Best Bet
I know Gigi Berardi primarily as a nationally renowned dance critic, but her primary career is as a professor of environmental studies at Western Washington University's Huxley College. She's been talking about her new book, "FoodWISE:A Whole Systems Guide to…
...continue reading
By Margaret Bikman January 4, 2020 January 4, 2020 Categories: Best Bet
Bellingham Symphony Orchestra harpist Jill Whitman hosts award-winning musician and composer Maria Newman and friends at 3 p.m. Sunday, Jan. 5, at Whitman's home, 2400 E. Hemmi Road, featuring harp, flute, piano and strings. Enjoy the Pied Piper story with…
By Margaret Bikman December 26, 2019 Categories: Best Bet
Celebrate the publication of Jim Bertolino's latest book of poetry, "Galaxy in Thrall," at 4 p.m. Sunday, Dec. 29, at Village Books, 1200 11th St. Bertolino has been a faculty member at Cornell University, University of Cincinnati, Western Washington University…
By Margaret Bikman December 8, 2019 Categories: Best Bet
Join the Shellebration— the third year of open shellfish harvesting in Drayton Harbor — from 4 to 6 p.m. Friday, Dec. 13, at the H Street Plaza in downtown Blaine. This free event will include refreshments, oyster samples courtesy of…
Humanities Washington Speakers Bureau host author Clyde Ford, leads a discussion on race in modern-day United States, with audience participation, from 7 to 8:30 p.m. Tuesday, Dec. 3, at Whatcom Museum's Old City Hall, 121 Prospect St. $5 suggested donation,…
Post-Thanksgiving Events
By Margaret Bikman November 27, 2019 November 27, 2019 Categories: Best Bet
A Native American Indian Heritage Day event will recognize the pride in the unique heritage and ways of the people, featuring Cindy Minkler and J.P. Falcon Grady, who'll perform a variety of heartfelt music and stories celebrating their roots from…
Bellingham Tonight!, A Book Project at WWU, "Dracula's Daughters" at WCC, and An Arts Fest at the Firehouse
Veritas Media presents: Bellingham Tonight! with Kevin Coleman and Kristina Michele at 7 p.m. Tuesday, Nov. 19, at Mount Baker Theatre, 104 N. Commercial St. Be a part of the live studio audience of Bellingham Tonight! As an audience member,…
Giving Thanks in Whatcom County Through Literature and Music
Mark Ashworth and Mark Kelly perform jazz standards and Latin tunes from 7 to 9 p.m. Thursday, Nov. 14, at Greene's Corner, 2208 James St., and at 7 p.m. Thursday, Nov. 21 at the Firehouse Arts and Events Center, 1314…
By Margaret Bikman November 9, 2019 November 9, 2019 Categories: Best Bet
If you want an evening of hilarity, go see all three plays of "The Norman Conquests," Alan Ayckbourn's trilogy of 1970s English farces, which continues to be performed in Sylvia Center's Lucas Hicks Theater through Nov. 30 by iDiOM THEATER….
The Power in Dance
By Margaret Bikman November 8, 2019 Categories: Best Bet
Bellingham Repertory Dance's Blush Punch, six works by regional and nationally-known choreographers, packs an emotional wallop with its show of strength by (mostly) female dancers. The performance opens at 8 p.m. tonight, Nov. 8, and continues at 8 p.m. Saturday,…
Click ad to visit their website


Solid, flush stone or concrete paved surfaces to suit every style and situation from patios, courtyards, terraces, paths, steps, driveways and cast concrete work. We like to use reclaimed materials where suitable to promote sustainability. We are also experienced in installing contemporary products such as artificial grass and resin bonded aggregates.


Meteroids, asteroids, comets and dwarf planets are some of the smallest bodies in our solar system and are the focus of several recent space missions: Rosetta, Dawn, and New Horizons. Learn about how Pluto, Ceres and these other tiny wonders continue to amaze and surprise us.
Rachel Ward-Maxwell received her PhD in astrophysics from McMaster University in 2015, where she used computer simulations to model the structure of interstellar clouds and formation of Sun-like stars. As the Researcher-Programmer in Astronomy and Space Sciences at the Ontario Science Centre, Dr. Ward-Maxwell develops astronomy program offerings, including planetarium shows, and supports the Research Live! program, an initiative where visitors participate in current active research studies conducted by visiting scientists. She is passionate about communicating science with the general public and is a strong advocate for women in STEM (science, technology, engineering, mathematics) disciplines.
During her academic career, Dr. Ward-Maxwell developed content and organized free science programming for children and youth across Hamilton and surrounding communities. Her experience in education and public outreach also includes time spent over the past ten years as a science communicator and program developer for a variety of organizations.
Enter off of Mississauga Road. Park in lot 4 or the parkade, across from the fitness centre south of theDavis Building. Enter through the Fitness centre, walk up the stairs until you reach the main corridor then turn right. (If you need an elevator,follow the corridor to the right of the stairs, then go up to the mainfloor.) Look for the Mississauga Centre sign in front of the lecture room.
Apr 1: Engineering Tiny Space Telescopes!
Cordell Grant is the Manager of Satellite Systems at the University of Toronto Space Flight Laboratory (UTIAS-SFL) and was project manager, systems engineer, opto-mechanical engineer and assembly/integration lead for the BRIght Target Explorer (BRITE) Constellation of six nanosatellites operated by a consortium of universities from Canada, Austria and Poland.
Mr. Grant will discuss the unique challenges associated with designing, building and testing not just space telescopes but tiny space telescopes. He will also provide a unique glimpse into the world of "rocket science" by providing insight into the design of the spacecraft that support, power and point those telescopes through launch and in orbit.
All stars are born from hydrogen and during their lives they produce elements through nuclear fusion. High-mass stars end their lives as supernovae, perhaps the most cataclysmic events in the universe, producing the heavy elements.
This talk merges James Edgar's love of woodworking, astronomy, genealogy, chemistry, physics, and poetry from Northern Ireland, although the main thrust of the presentation is about how elements form within stars.


MONTREAL -- The Nashville Predators were not only able to make it through overtime without losing, they came close to a rare 3-on-3 win before Craig Smith redeemed himself in the shootout.
Smith scored on Nashville's third attempt after missing a great scoring opportunity in overtime to give the Predators a 2-1 win against the Montreal Canadiens at Bell Centre on Monday.
Smith hesitated and shot past Montreal goalie Mike Condon into the right side of the net after three Canadiens shooters failed to score on Pekka Rinne.


text:
Q: strange behavior of Chrome Developer Tools Console If you type in the console
> new Object()

Empty js object will appear in the console and it is expected, but if you type
> {}

You get undefined
It is strange. Doesn't it ?

A: Calling a function with new always results in a value. Now, your second line,
{}

is an empty code block, not an object literal.
Try:
({})

or:
0,{}

The console parses lines you type as statements, not expressions.  An open curly brace at the start of a statement is a block delimiter, therefore, and not the start of an object literal. By including other tokens to force the parser into parsing an expression, you can then begin an object literal.

redpajama_set_name: RedPajamaStackExchange


text:
February 7, 2019	John Nguyen
Disney plans to have future Deadpool films be rated R
With the Disney and Fox deal almost closing, many fans have expressed concern about the future of Deadpool. Fans are adamant about Deadpool being rated R, but with Fox being under Disney, they were afraid that the character would receive the PG-13 treatment. During an investors call, Disney CEO Bob Iger said that Deadpool could still be rated R, but the films will be made in a way that won't confuse audiences.
"We do believe there is enough room for the Fox properties to exist without significant Disney influence over the nature of the content," Iger said. "Meaning that we see there is certainly popularity amongst Marvel fans for the R-rated Deadpool films. For instance, we're going to continue in that business and there might be room for more of that. There's nothing that we've really seen in the Fox library or activities that Fox is engaging in today that would be of concern to us as long as we're very carefully branding them and making sure that we're not in any way confusing the consumer with product that would be Disney product or the more traditional Marvel product."
With Disney not looking to put Deadpool under the Marvel or Disney banners, it sounds like we won't be seeing him mingle with characters from the Marvel Cinematic Universe. As for X-Men and Fantastic Four, Feige is excited about having access to them under Marvel Studios.
"The notion of the characters coming back is great, Feige said. "It's nice when a company that created all these characters can have access to all those characters. It's unusual not to. But in terms of actually thinking about it and actually planning things, we haven't started that yet."
There's a rumor of the Black Widow movie possibly being rated R, but with Iger being careful about not confusing audiences, it doesn't look like that's going to happen.
Source: Disney


Former Oklahoma City Mayor James Norick has died.
Norick's son, former Oklahoma City Mayor Ron Norick, said Thursday that his father died Wednesday of natural causes. Ron Norick said funeral services are set for Monday, but details are not yet complete.
James Norick was elected Oklahoma City mayor twice, serving from 1959-63 and again from 1967-71.
His terms included the construction of a 100-mile pipeline from Lake Atoka in southeastern Oklahoma to Lake Stanley Draper in Oklahoma City to provide a reliable water supply in Oklahoma City. He also oversaw an annexation program in which Oklahoma City grew from about 90 square miles to about 600 square miles.
Norick also served on the City Council from 1951-55.
He's survived by his son, daughter Vickie Norick, four grandchildren and six great-grandchildren.
In the more rural parts of Oklahoma City there are thousands of residents who don't pay for trash pickup, and they never have.


text:
Poet and playwright Sabrina Mahfouz to join judging panel for Wicked Young Writer Awards 2016
The award-winning poet and playwright Sabrina Mahfouz is joining the judging panel in the sixth year of the prestigious WICKED YOUNG WRITER AWARDS. The WICKED YOUNG WRITER AWARDS were set up by the team behind the award-winning musical to recognise excellence in writing and encourage creativity. The closing date for entries is 11 March 2016.
Since launching, over 20,000 young people, aged between 5 and 25, have entered original and thought-provoking pieces of writing that consistently reflect the interests, concerns and deepest thoughts of young people, providing a first-look at the emerging voices of a new generation.
As in previous years, entrants can enter one of five different age categories; 5-7, 8-10, 11-14, 15-17, 18-25. In addition, the 2016 awards scheme marks the launch of the FOR GOOD Award for Non-Fiction, encouraging 15-25 year olds to write essays or articles that recognise the positive impact that people can have on each other, their communities and the world we live in. The new category celebrates the WICKED: FOR GOOD programme, which supports the charitable causes at the heart of the stage musical.
Sabrina Mahfouz writes plays, poems and librettos for theatre and television including: Paines Plough; BBC3; Kate Whitley; Futures Theatre; Theatre Centre and Aakash Odedra. She has been a Sky Arts Academy Scholar for Poetry, a poet in residence for Cape Farewell and an Associate Playwright at the Bush Theatre. Her creative work has been recognized with a number of awards including a 2014 Fringe First Award; a 2013 Sky Arts Futures Fund Award; an Old Vic New Voices Award and a Westminster Prize for New Playwrights.
Sabrina Mahfouz comments on the Award, "Young people's writing is what makes me optimistic and excited about the future, so being involved in anything that encourages more of it is a huge honour, especially alongside such legendary judges. I can't wait to spend cosy nights in reading the stories from the stars of tomorrow!"
A shortlist of 120 entrants from across the UK will see their work published in the WICKED YOUNG WRITER AWARDS Anthology. They are also invited to an exclusive ceremony at London's Apollo Victoria, home to the hit musical since 2006, where judges and members of the Wicked cast will announce who has won in each category.
Pieces of original writing can be submitted, either individually or as part of a school group, until 11 March 2016. The overall winners from each category will receive tickets to the West End production of Wicked, £50 book/eBook tokens plus £100 worth of books for their school library donated by Hachette Children's Books. The individual school with the highest number of entries will receive a bespoke writing workshop at their respective school.


Held once a semester, the Fulton Schools Career Fair is your opportunity to recruit for internships and full-time positions. Our students are ready to enter the workforce with technical training and soft skills.
Have you ever thought "I wish I had known that!"? Career Exploration Night is your chance to share your experiences and life lessons with students just getting started on a STEM career path.
Students in the competitive FURI program present their research at a semi-annual poster symposium.
Students in the Engineering Projects in Community Service solve engineering problems for community partners.
Collaborating with industry partners, students work on meeting tangible industry and societal needs by producing, refining and developing inventions, new methodologies and fresh ideas.
Corporate affiliates build long-term relationships with students and develop targeted recruitment strategies. Raise awareness through on campus opportunities in research collaboration, capstone projects, student organizations, and events like hackathons and competitions. Members receive priority invitations to special events.
Join us for this three-day event to meet engineering, technology and construction candidates for full-time and internship positions. Our students and alumni are well prepared for technical careers. Tailor your visit to target the candidates you're looking for — bachelor's, master's or doctoral students on ASU's Tempe campus or Polytechnic campus.
Open to anyone with formal education in aviation, engineering, technology, computer science, construction management or any related technical discipline. You represent YOU and your path from freshman to professional! Share your college experiences, career history and advice with future innovators — and help students complete a class assignment at the same time!
Join the Ira A. Fulton Schools of Engineering at free events throughout the year. Catch the cutting-edge of engineering and technological research conducted by our students or bring the family at ASU for fun and demos.
Visit this an open house-style poster display and learn about student-conducted research. Students from the competitive FURI program, Grand Challenges Scholars Program, KEEN and master's students present their posters and share what the knowledge they've created and the experiences working in labs.
Got a problem? Our students can solve it! Innovation Showcase is a massive exhibit of student-produced projects, demonstrating how we solve real-world problems with innovative and imaginative solutions. Take a look at how our students work together with faculty and industry mentors.
Join us at family-friendly events and have fun with hands-on activities, games and demos. We can't wait to reconnect with alumni and friends at the Homecoming Block Party in the fall. And bring the family back to campus in the spring and explore what happens at a world-class research university at ASU Open Door.
Our students aren't waiting until graduation to get involved in their communities or start businesses. You shouldn't wait either! Get involved by becoming a mentor, guest speaker or sponsor.
Using a service-learning model, the Engineering Projects in Community Service give students the skills they need to be successful in bringing ideas to life. The projects are performed without charge for not-for-profit host organizations such as a community organization, school or government entity.
There are dozens of Fulton student organizations and teams ranging from honors and professional associations to groups creating underwater robots, concrete canoes, and launching rockets. Many of the student groups operate in conjunction with industry professional societies. Develop the next generation of the workforce through sponsorship and mentorship.
Throughout the year, the Fulton Schools hosts a multitude of events designed to engage Pre-K- Community College students through sparking and fostering an interest in engineering and STEM. Community support is one of the driving forces behind the success of these events. If you're interested in giving your time and energy to FSE, please see how you can make a difference.
When it comes to providing rich experiential education for current students or building a pipeline of future innovators and problem solvers, we can't do it without you. Your experiences, time and energy and support are invaluable. You can change the lives of students and their families.
Our student experience is much more than learning in a classroom. We encourage students to work on real-world challenges and in professional situations. Bring your project to a program chair or contact our Development office to find out more.
The Fulton Schools Engineering Education Outreach team is fostering awareness and engagement of STEM fields and engineering practices. The Fulton Schools are passionate about investing in Arizona's youth, and invite you to join this world-changing endeavor.
We believe that engineering is more than a discipline — it's a mind-set, a way of looking at the world to determine how challenges can be met. Your gift can directly change lives and inspire our students and faculty to shape the future for all of us.
By their nature as builders and innovators, Fulton Schools students have enormous potential to become game-changing entrepreneurs. Entrepreneurship + innovation invites all 20,000+ Fulton innovators to explore their startup ideas, tackle grand challenges, and change the world through entrepreneurship and innovation.
Be a part of signature degree and certificate programs, courses, workshops, expert mentoring, new venture competitions, and other curricular and co-curricular opportunities.
If Fulton Schools was its own university, we would be ranked no. 36 in the world with 61 utility patents. Find out which faculty are turning their ideas and inventions into impactful startups.
This event advances university student innovators who aim to develop hard-tech ventures. The ASUio provides critical venture mentorship and funding for student competitors who are launching a hardware enterprise within a wide variety of cutting-edge marketplaces.
ASU and the Ira A. Fulton Schools of Engineering have a proven track record for leading complex research centers and initiatives in geotechnical infrastructure, PV systems, clean water technologies and the modern electric grid to name a few. Partner with us and find out how far your next idea will go.


In January, I found myself with an unexpectedly healthy post-xmas bank balance, so treated myself to yet another new gadget - an ereader. I chose a Kobo Mini, in white.
Three months later I've read 33 books in about 135 hours. It's great! e-ink is very natural to read from, and the reader itself is small and hand sized. Definitely better for taking on holiday than a stack of paperbacks.
I bought another computer. An Asus TF300T - android tablet with keyboard dock. I've got the white one, which was a 'web exclusive' from Comet.. bought 2 weeks before they went down the pan. phew!
There's no way I could justify spending money on a tablet, but the added keyboard fixed that - it has a full size USB slot, and an SD card reader. Incredibly useful for transferring photos off my cameras, viewing on a bigger screen, and copying to an external hard drive - something I do fairly often on paddling trips away.
The Raspberry Pi. a small cheap computer - very exciting, all over the news, massive waiting lists, etc etc.
And I've finally got my hands on one. Ok, so it actually arrived several weeks ago, but I've only just found enough spare time to do anything with it.
I don't need another 'plain' linux machine, and haven't yet had any genius ideas for other cool projects, so it's currently sat next to my tv/stereo, running raspbmc and acting as a media centre.
First signs of impending badness: odd segfaults, mostly with apt. Then my filesystem started randomly going read only, with system logs showing a lot of I/O errors and problems with the journalling. hmm. To start with, nothing a reboot and quick forced fsck wouldn't fix.
So, my lovely gadget phone is about 18 months old now. For the last month, the market's been oddly broken on it - refusing to work with my google account (I'm 'difficult' and use my domain account, rather than a 'normal' gmail one). I don't know why it suddenly stopped.. it always used to work, albeit without the ability to purchase apps. I could cope with that.
I have a new computer! A replacement for my laptop, which has been doing odd overheaty things and making bad noises for the last month or so. Poor thing. Still, not bad for being 3 years old and heavily (ab)used on a daily basis.
The new box is a desktop - a little teeny quiet one. It's a Dell Inspiron Zino HD. In purple. And even though obviously I know what spec it is, I can't be arsed to list it because I'm not a hardware geek, hah.
I've had my gadget phone for over six months now. The novelty value of millions of pointless applications has worn off, meaning I'm down to a sensible number of actually quite useful ones.
I'm not a morning person, so I tend to have several alarms going off at different times, so I can ignore or snooze them for a while whilst I gradually wake up.
March can easily be summed up in one word: expensive.
As if buying a kayak wasn't bad enough, I've also been spending not insignficant amounts on things like deposits for holidays (French Alps in June, woo!), a shorty cag, car MOT, etc etc.
And when I popped into Halfords to get a bulb for the car, I managed to come out with a bike. Oops.
The bike does not have a name, and is a greeny colour, which this photo does not show very well.
Actually I'm not 100% sure what did happen to it... it was certainly squashed against the tarmac of my parents drive by something, either a foot or a tyre. I reckon car, because if you trod on it I think you'd slip. Also I found it underneath where a car had been.
I have a new toy. It's one of these, and it's rather cool. Been eyeing up some of the more 'basic' (also cheaper) models for a while now, because it's a nice geeky gadget (woo, gyroscopes!), but this one is extra cool because it lights up and has a counter.


text:
Un archivo falso, referido habitualmente con el anglicismo fake y a veces como archivo malicioso o maligno, es un archivo informático cuyo contenido realmente no se corresponde con el nombre o la función que tiene. El término fake también se utiliza para designar un archivo dañado, corrupto, con virus o fraudulento; por extensión, fake igualmente se usa para describir un servidor o un sitio web cuando estos no son lo que aparentan y sirven de guía hacia delitos a modo de malware.

Problemática
La obtención de un archivo falso es uno de los principales problemas que pueden surgir entre los usuarios de programas de intercambio y en redes P2P, como por ejemplo el eMule. Una manera de evitar inconvenientes durante la carga y descarga es observar los comentarios que pueden indicar que se trata de un archivo sospechoso; y en caso de advertir un fake, agregar otro comentario denunciando este hecho para mejorar la experiencia de usuario. También es posible realizar un escaneo del archivo y generar un número que intente identificar cada uno de los archivos en la red, usando un checksum.

Fraude asociado
La piratería en línea ha generado varios sistemas de fraude que se sirven de archivos falsos, en detrimento de los usuarios. Existe la posibilidad de sustraer información confidencial mediante un mensaje de correo electrónico con remitente falso o inexistente, asociado a una solicitud de datos personales que el usuario, creyendo que el mensaje es original, suele conceder. Un uso común se puede encontrar en los e-mails publicitarios (spam) para engañar a usuarios sin experiencia y que hagan clic en enlaces que se conectan a inicios de sesión falsos de bancos, sitios comerciales, etc. (este fenómeno se conoce como phishing). A menudo, los correos electrónicos ingresados en el inicio de sesión falso se pasan a otras bases de datos, y eso aumenta el spam. En internet hay muchos programas para enviar correos falsos, incluso gratuitos, que permiten enmascarar al remitente o falsificarlo, así como disfrazar las direcciones IP presentes en el encabezado de un mensaje.

Véase también
 Bulo
 Historia de las aplicaciones P2P
 Plug-in
 Proxy
 SSL
 Trol
 URL
 Web spoofing

Referencias

Cultura de Internet


A friend of Green Day who passed away. JAR is also a song (International Superhits, track 8).
Track 9 on Warning album.
Billie Joe's youngest son born on September 12 1998.
Billie Joe and Mike's childhood friend who lived in Rodeo, California.
Green Day fill in guitarist. He is also in The Influents.
Green Day have trashed his green room.
The hair product Billie Joe uses to get his hair nice and crunchy.
Jesse Micheals, ex-lead singer of Operation Ivy did the disc and cover art for 1,039 Smoothed Out Slappy Hours. Jesse Micheals and Operation Ivy were then thanked in Kerplunk.
The main character in American Idiot and is track 2 on American Idiot.
The type of underwear Billie Joe wears.
John Swett High School in Crockett, CA.
Billie Joe's eldest son who was born in March 1995.
What the guys call joints to get past censors on Tv.


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