text:
\section{Introduction}

Ice in natural land ice masses, such as polar ice sheets, ice
caps or glaciers, consists of zillions of individual hexagonal
crystals (``crystallites'' or ``grains'') with a typical
diameter of millimeters to centimeters. This length scale
stands in contrast with the size of the ice masses, which
ranges from 100's of meters to 1000's of kilometers. It has
long been known that, while the distribution of the
crystallographic axes (also known as optical axes or $c$-axes)
at the surface of an ice sheet is essentially at random, deeper
down into the ice, different types of anisotropic fabrics with
preferred orientations of the $c$-axes tend to develop.

Many models have been proposed to describe the anisotropy of
polar ice. On the one end of the range in complexity, a simple
flow enhancement factor is introduced in an \emph{ad-hoc}
fashion as a multiplier of the isotropic ice fluidity in order
to account for anisotropy and/or impurities. This is done in
most current ice-sheet models, often without explicitly
mentioning anisotropy \cite{greve_05a, huybrechts_etal_07,
saito_abeouchi_04}. In macroscopic, phenomenological models, an
anisotropic macroscopic formulation for the flow law of the
polycrystal is postulated. To be usable, the rheological
parameters that enter this law must be evaluated as functions
of the anisotropic fabric \cite{gillet_chaulet_etal_05,
gillet_chaulet_etal_06, morland_staro_98, morland_staro_03}.
The concept of homogenization models, also called micro-macro
models, is to derive the polycrystalline behaviour at the level
of individual crystals and the fabric \cite{azuma_94,
castelnau_etal_98, castelnau_etal_96, goedert_hutter_98,
ktitarev_etal_02, lliboutry_93, svendsen_hutter_96,
thorsteinsson_02}. As for the ``high-end'' complexity,
full-field models solve the Stokes equation for ice flow
properly by decomposing the polycrystal into many elements,
which makes it possible to infer the stress and strain-rate
heterogeneities at the microscopic scale
\cite{lebensohn_etal_04a, lebensohn_etal_04b, mansuy_etal_02,
meyssonnier_philip_00}. A very comprehensive, up-to-date
overview of these different types of models is given by
Gagliardini et~al.\ \cite{gagliardini_etal_09} (in this
volume). However, the more sophisticated models are usually too
complex and computationally time-consuming to be included
readily in a model of macroscopic ice flow.

Here, the Continuum-mechanical, Anisotropic Flow model, based
on an anisotropic Flow Enhancement factor (``CAFFE model''),
shall be described. It belongs to the class of macroscopic
models, and is laid down in detail in the study by Placidi
et~al.\ \cite{placidi_etal_09} (based on previous works by
Faria \cite{faria_06a, faria_06b}, Faria et~al.\
\cite{faria_etal_06}, Placidi \cite{placidi_04, placidi_05},
Placidi and Hutter \cite{placidi_hutter_06a}). The flow
enhancement factor is taken as a function of a newly introduced
scalar quantity called \emph{deformability}, which is
essentially a non-dimensional invariant related to the shear
stress acting on the basal plane of a crystallite, weighted by
the orientation-distribution function which describes the
anisotropic fabric of the polycrystal. Fabric evolution is
modelled by an orientation mass balance which accounts for
grain rotation and recrystallization processes.

The CAFFE model fulfills all the fundamental principles of
classical continuum mechanics (see also Placidi et~al.\
\cite{placidi_hutter_06b}), and it is a good compromise between
necessary simplicity on the one hand, and consideration of the
major effects of anisotropy on the other. In order to
demonstrate its performance, the model is applied to the site
of the EPICA (European Project for Ice Coring in Antarctica)
ice core in Dronning Maud Land, East Antarctica, for which data
on the ice flow as well as on the anisotropic fabric are
available.

\section{CAFFE model}

\subsection{Glen's flow law}
\label{sect_glen}

\begin{table*}[htb]
  \centering
  \begin{tabular}{ll} \hline
  \textbf{Quantity}\rule{0mm}{2.3ex} & \textbf{Value}\\ \hline
  Stress exponent, $n$\rule{0mm}{2.25ex} & $3$ \\
  Pre-exponential constant, $A_0$\rule{0mm}{2.5ex} &
  \hspace*{-0.8em} $\begin{array}[t]{ll}
    3.985\times{}10^{-13}\,\mathrm{s^{-1}\,Pa^{-3}}
    & \mbox{(for $T'\le{}263.15\,\mathrm{K}$)}
    \\
    1.916\times{}10^{3}\,\mathrm{s^{-1}\,Pa^{-3}}
    & \mbox{(for $T'>263.15\,\mathrm{K}$)}
  \end{array}$ \\
  Activation energy, $Q$\rule{0mm}{2.5ex} &
  \hspace*{-0.8em} $\begin{array}[t]{ll}
    60\,\mathrm{kJ\,mol^{-1}}
    & \hspace*{4.4em} \mbox{(for $T'\le{}263.15\,\mathrm{K}$)}
    \\
    139\,\mathrm{kJ\,mol^{-1}}
    & \hspace*{4.4em} \mbox{(for $T'>263.15\,\mathrm{K}$)}
  \end{array}$ \\ \hline
  \end{tabular}
  \caption{\emph{Physical parameters for Glen's flow law.}}
  \label{tab_physical_parameters}
\end{table*}

Let us briefly review the isotropic case, for which
polycrystalline ice is treated as an incompressible, viscous
fluid. The Cauchy stress tensor $\tenssu{T}$ is split up
according to
\begin{equation}
  \tenssu{T} = -p\tenssu{1} + \tenssu{S},
  \qquad
  p = -\frac{1}{3} \mbox{tr}\,\tenssu{T},
  \label{eq_stress_deviator}
\end{equation}
where $p$ denotes the pressure, and $\tenssu{S}$ is the
traceless stress deviator ($\mbox{tr}\,\tenssu{S}=0$). Due to the
incompressibility, the flow law only determines the stress
deviator $\tenssu{S}$ and reads
\begin{equation}
  \tenssu{S} = 2\eta\tenssu{D},
  \label{eq_viscous_flow_law}
\end{equation}
where $\tenssu{D}=\mbox{sym}\,\mbox{grad}\,\vecbu{v}$ is the strain-rate tensor
(symmetric part of the gradient of the velocity $\vecbu{v}$), and
the coefficient $\eta$ is the \emph{shear viscosity} (or simply the
\emph{viscosity}). Its inverse, the \emph{fluidity}, can be
factorized as
\begin{equation}
  \frac{1}{\eta} = 2EA(T')f(\sigma),
  \label{eq_fluidity}
\end{equation}
where
\begin{equation}
  \sigma = \sqrt{\mbox{$\frac{1}{2}$}\,\mbox{tr}\,(\tenssu{S}^2)}
  \label{eq_effective_stress}
\end{equation}
is the \emph{effective stress} (square root of the second invariant
of the stress deviator), and the \emph{creep function} $f(\sigma)$
is given by the power law
\begin{equation}
  f(\sigma) = \sigma^{n-1}
  \label{eq_power_law}
\end{equation}
(the parameter $n$ is called ``stress exponent''). Further, the
\emph{rate factor} $A(T')$ depends on the temperature relative
to pressure melting $T'=T-T_\mathrm{m}+T_0$ ($T$: absolute
temperature, $T_\mathrm{m}=T_0-\beta{}p\,$: pressure melting
point, $T_0=273.16\,\mathrm{K}\,$: melting point at zero
pressure, $\beta=9.8\times{}10^{-2}\,\mathrm{K\,MPa^{-1}}$:
Clausius-Clapeyron constant) via the Arrhenius law
\begin{equation}
  A(T') = A_0\,e^{-Q/RT'},
  \label{eq_arrhenius_law}
\end{equation}
where $A_0$ is the pre-exponential constant, $Q$ the activation
energy and $R=8.314\,\mathrm{J\,mol^{-1}\,K^{-1}}$ the
universal gas constant. The \emph{flow enhancement factor} $E$
is equal to unity for pure ice, and can be set to values
deviating from unity in order to account roughly for effects of
impurities and/or anisotropy (Paterson \cite{paterson_91}).

The isotropic flow law for ice is now obtained by inserting
Eq.~(\ref{eq_fluidity}) [with the specifications of
Eqs.~(\ref{eq_power_law}) and (\ref{eq_arrhenius_law})] in the
viscous flow law (\ref{eq_viscous_flow_law}). This yields
\begin{equation}
  \tenssu{D} = EA(T')f(\sigma) \, \tenssu{S},
  \label{eq_glens_flow_law}
\end{equation}
which is called \emph{Nye's generalization of Glen's flow law},
or \emph{Glen's flow law} for short (e.g., Greve and Blatter
\cite{greve_blatter_09}, Hooke \cite{hooke_05}, Paterson
\cite{paterson_94}, van der Veen \cite{vanderveen_99}).
Suitable values for the several parameters are listed in
Table~\ref{tab_physical_parameters}.

\subsection{Anisotropic generalization of Glen's flow law}

\subsubsection{Deformation of a crystallite}

In order to derive a generalization of Glen's flow law
(\ref{eq_glens_flow_law}) which accounts for general,
anisotropic fabrics of the ice polycrystal, we first consider
the deformation of a crystallite embedded in the
polycrystalline aggregate. Following Placidi et~al.\
\cite{placidi_etal_09}, only the dominant deformation along the
basal plane is accounted for, whereas deformations along
prismatic and pyramidal planes, which are at least 60 times
more difficult to activate, shall be neglected
(Fig.~\ref{fig_glide_planes.pdf}).

\begin{figurehere}
  \medskip
  \centering
  \noindent\includegraphics[width=75mm]{Greve_etal_PICR2_Fig01.pdf}
  \par\vspace*{-2mm}\par
  \caption{\emph{Basal, prismatic and pyramidal glide planes in the
  hexagonal ice crystal, sketched as a right hexagonal prism
  (Faria \cite{faria_03}).}}
  \label{fig_glide_planes.pdf}
  \medskip
\end{figurehere}

Let $\vecbu{n}$ be the normal unit vector of the basal plane
(direction of the $c$-axis), then $\tenssu{T}\vecbu{n}$ is the
resolved stress vector (Fig.~\ref{fig_stress_decomposition}).
Note that the tensor $\tenssu{T}$ is interpreted as the
\emph{macroscopic} stress which does not depend on the
orientation $\vecbu{n}$. It is reasonable to assume that only
the stress component $S_\mathrm{t}$ tangential to the basal
plane (resolved shear stress) contributes to its shear
deformation, while the component normal to the basal plane has
no effect.

\begin{figurehere}
  \medskip
  \centering
  \noindent\includegraphics[width=45mm]{Greve_etal_PICR2_Fig02.pdf}
  \par\vspace*{-2mm}\par
  \caption{\emph{Decomposition of the stress vector into a part
  normal and a part tangential to the basal plane.}}
  \label{fig_stress_decomposition}
  \medskip
\end{figurehere}

According to Fig.~\ref{fig_stress_decomposition}, the decomposition
of the stress vector reads
\begin{equation}
  \tenssu{T}\vecbu{n}
  = (\tenssu{T}\vecbu{n}\cdot\vecbu{n})\vecbu{n}
    + S_\mathrm{t}\vecbu{t},
  \label{eq_stress_decomposition_1}
\end{equation}
where $\vecbu{t}$ denotes the tangential unit vector. Inserting
the decomposition (\ref{eq_stress_deviator}) of the stress
tensor $\tenssu{T}$ readily eliminates the pressure $p$ and
leaves
\begin{equation}
  \tenssu{S}\vecbu{n}
  = (\tenssu{S}\vecbu{n}\cdot\vecbu{n})\vecbu{n}
    + S_\mathrm{t}\vecbu{t}.
  \label{eq_stress_decomposition}
\end{equation}
As mentioned above, deformation of the crystallite in the
polycrystalline aggregate is attributed to the tangential
component $S_\mathrm{t}$ only. Since we aim at a theory which
describes the effects of anisotropy by a \emph{scalar},
anisotropic flow enhancement factor, we define the scalar
invariant
\begin{equation}
  S_\mathrm{t}^2
  = \tenssu{S}\vecbu{n}\cdot\tenssu{S}\vecbu{n}
    - (\tenssu{S}\vecbu{n}\cdot\vecbu{n})^2.
  \label{eq_sc_st}
\end{equation}
This quantity has the unit of a stress squared, and so a
natural way to non-dimensionalize it is by the square of the
effective stress $\sigma$ [Eq.~(\ref{eq_effective_stress})],
which is also a scalar invariant. Thus, we introduce the
\emph{deformability} of a crystallite in the polycrystalline
aggregate, which is loaded by the stress $\tenssu{T}$, as
\begin{equation}
  \mathcal{A}^\star(\vecbu{n})
    = \frac{5}{2}\,\frac{S_\mathrm{t}^2(\vecbu{n})}{\sigma^2}
    = 5\,\frac{\tenssu{S}\vecbu{n}\cdot\tenssu{S}\vecbu{n}
               -(\tenssu{S}\vecbu{n}\cdot\vecbu{n})^2}
              {\mbox{tr}\,(\tenssu{S}^2)}.
  \label{eq_deformability_crystallite}
\end{equation}
The factor $5/2$ has been introduced merely for reasons of
convenience, as it will become clear below.

\subsubsection{Flow law for polycrystalline ice}

In polycrystalline ice, the crystallites within a control
volume (which is assumed to be large compared to the
crystallite dimensions, but small compared to the macroscopic
scale of ice flow) show a certain fabric. Extreme cases are on
the one hand the single maximum fabric, for which all $c$-axes
are perfectly aligned, and on the other hand the isotropic
fabric with a completely random distribution of the $c$-axes. A
general fabric, which is usually in between these cases, can be
described by the \emph{orientation mass density} (OMD)
$\rho^\star(\vecbu{n})$. It is defined as the mass per volume
and orientation, the latter being specified by the normal unit
vector (direction of the $c$-axis) $\vecbu{n}\in{}S^2$ ($S^2$
is the unit sphere). Evidently, when integrated over all
orientations, the OMD must yield the normal mass density
$\rho$, which leads to the normalization condition
\begin{equation}
  \int\limits_{S^2} \rho^\star(\vecbu{n})\,\mathrm{d}^2 n = \rho.
  \label{eq_omd_normalization}
\end{equation}
Alternatively, an \emph{orientation distribution function} (ODF)
$f^\star(\vecbu{n})$ can be defined as
\begin{equation}
  f^\star(\vecbu{n}) = \frac{\rho^\star(\vecbu{n})}{\rho},
  \label{eq_odf}
\end{equation}
which is normalized to unity when integrated over all orientations.

We use the ODF in order to define the \emph{deformability} of
polycrystalline ice by weighting the deformability of the
crystallite (\ref{eq_deformability_crystallite}),
\begin{eqnarray}
  \mathcal{A}
  &\!\!\!=\!\!\!& \int\limits_{S^2}
      \mathcal{A}^\star(\vecbu{n})\,f^\star(\vecbu{n})\,\mathrm{d}^2 n
  \nonumber\\[1ex]
  &\!\!\!=\!\!\!& \frac{5}{2} \int\limits_{S^2}
      \frac{S_\mathrm{t}^2(\vecbu{n})}{\sigma^2}
      f^\star(\vecbu{n})\,\mathrm{d}^2 n
  \nonumber\\[1ex]
  &\!\!\!=\!\!\!& 5 \int\limits_{S^2}
      \frac{\tenssu{S}\vecbu{n}\cdot\tenssu{S}\vecbu{n}
            -(\tenssu{S}\vecbu{n}\cdot\vecbu{n})^2}
           {\mbox{tr}\,(\tenssu{S}^2)}
      f^\star(\vecbu{n})\,\mathrm{d}^2 n.
  \label{eq_deformability}
\end{eqnarray}
Note that, for the isotropic case, the ODF is
$f^\star(\vecbu{n})=1/(4\pi)$, and from
Eq.~(\ref{eq_deformability}) we obtain a deformability of
$\mathcal{A}=1$ (Placidi et~al.\ \cite{placidi_etal_09}). For
that reason, the factor $5/2$ has been introduced in
Eq.~(\ref{eq_deformability_crystallite}).

\begin{figurehere}
  \medskip
  \centering
  \noindent\includegraphics[width=50mm]{Greve_etal_PICR2_Fig03.pdf}
  \caption{\emph{Uniaxial compression on single maximum \emph{(UC/SM)}
  and simple shear on single maximum \emph{(SS/SM)} for a small sample
  of polycrystalline ice. Stresses are indicated as black arrows,
  and the single maximum fabric is marked by the dark-grey arrows
  within the ice sample.}}
  \label{fig_stress_states}
  \medskip
\end{figurehere}

The envisaged flow law for anisotropic polar ice can now be
formulated. Essentially, we keep the form of the Glen's flow law
(\ref{eq_glens_flow_law}), but with a scalar, anisotropic
enhancement factor $\hat{E}(\mathcal{A})$ instead of the parameter
$E$,
\begin{equation}
  \tenssu{D} = \hat{E}(\mathcal{A})\,A(T')f(\sigma) \, \tenssu{S}.
  \label{eq_glens_flow_law_aniso}
\end{equation}
The function $\hat{E}(\mathcal{A})$ is supposed to be strictly
increasing with the deformability $\mathcal{A}$, and has the fixed
points
\begin{equation}
  \begin{array}{l}
    \hat{E}(0) = E_\mathrm{min}
    \\[1ex]
    \;\;\;\mbox{(uniaxial compression on single maximum)},
    \\[1ex]
    \hat{E}(1) = 1
    \\[1ex]
    \;\;\;\mbox{(arbitrary stress on isotropic fabric)},
    \\[1ex]
    \hat{E}(\frac{5}{2}) = E_\mathrm{max}
    \\[1ex]
    \;\;\;\mbox{(simple shear on single maximum)}.
  \end{array}
  \label{eq_aniso_enh_factor_values}
\end{equation}
The ``hard'' case (\ref{eq_aniso_enh_factor_values})$_1$ and
the ``soft'' case (\ref{eq_aniso_enh_factor_values})$_3$ are
illustrated in Fig.~\ref{fig_stress_states}. Note also that the
deformability cannot take values larger than $\mathcal{A}=5/2$
(Placidi et~al.\ \cite{placidi_etal_09}).

For the detailed form $\hat{E}(\mathcal{A})$ of the anisotropic
enhancement factor, in addition to
Eq.~(\ref{eq_aniso_enh_factor_values}), we demand that the
function is continuously differentiable, that is,
$\hat{E}\in{}C^1[0,\frac{5}{2}]$. Moreover, Azuma
\cite{azuma_95} and Miyamoto \cite{miyamoto_99} have
experimentally verified that the enhancement factor depends on
the Schmid factor (resolved shear stress) to the fourth power,
that is, on the square of the deformability $\mathcal{A}$. This
yields
\begin{equation}
  \hat{E}(\mathcal{A}) = \left\{
  \begin{array}{l}
    E_\mathrm{min} + (1-E_\mathrm{min}) \mathcal{A}^t,
    \\[3ex]
    \hspace*{3.5em}
    t = \bigfrac{8}{21}\,\bigfrac{E_\mathrm{max}-1}{1-E_\mathrm{min}},
    \\[3ex]
    \hspace*{9em}
    0 \le \mathcal{A} \le 1,
    \\[3ex]
    \bigfrac{4\mathcal{A}^2(E_\mathrm{max}-1)+25-4E_\mathrm{max}}{21},
    \\[3ex]
    \hspace*{9em}
    1 \le \mathcal{A} \le \bigfrac{5}{2}
  \end{array} \right.
  \label{eq_aniso_enh_factor}
\end{equation}
(for details see Placidi et~al.\ \cite{placidi_etal_09}).
Several investigations (e.g.\ Budd and Jacka
\cite{budd_jacka_89}, Pimienta et~al.\ \cite{pimienta_etal_87},
Russell-Head and Budd \cite{russell_head_budd_79}) indicate
that the parameter $E_\mathrm{max}$ (maximum softening) is
approximately equal to ten. The parameter $E_\mathrm{min}$
(maximum hardening) can be realistically chosen between zero
and one tenth, a non-zero value serving mainly the purpose of
avoiding numerical problems. The function
(\ref{eq_aniso_enh_factor}) is shown in
Fig.~\ref{fig_aniso_enh_factor}.

\begin{figurehere}
  \medskip
  \centering
  \noindent\includegraphics[width=60mm]{Greve_etal_PICR2_Fig04.pdf}
  \caption{\emph{Anisotropic enhancement factor $\hat{E}(\mathcal{A})$
  as a function of the deformability $\mathcal{A}$ according to
  Eq.~(\ref{eq_aniso_enh_factor}), for $E_\mathrm{max}=10$ and
  $E_\mathrm{min}=0$.}}
  \label{fig_aniso_enh_factor}
  \medskip
\end{figurehere}

\subsubsection{Inversion of the flow law}

As long as the creep function $f(\sigma)$ is given by the power law
(\ref{eq_power_law}), the anisotropic flow law
(\ref{eq_glens_flow_law_aniso}) can be inverted analytically. We
find
\begin{equation}
  \tenssu{S} = [\hat{E}(\mathcal{A})]^{-1/n}\,[A(T')]^{-1/n} \,
               d^{-(1-1/n)} \, \tenssu{D},
  \label{eq_glens_flow_law_aniso_inv}
\end{equation}
where
\begin{equation}
  d = \sqrt{\mbox{$\frac{1}{2}$}\,\mbox{tr}\,(\tenssu{D}^2)}
  \label{eq_effective_strain_rate}
\end{equation}
is the \emph{effective strain rate}. The deformability
$\mathcal{A}$ also needs to be expressed by strain rates
instead of stresses [see Eq.~(\ref{eq_deformability})]. In
analogy to Eq.~(\ref{eq_stress_decomposition}), we consider the
resolved strain-rate vector $\tenssu{D}\vecbu{n}$ in a
crystallite in the polycrystalline aggregate, and decompose it
according to
\begin{equation}
  \tenssu{D}\vecbu{n}
  = (\tenssu{D}\vecbu{n}\cdot\vecbu{n})\vecbu{n}
    + D_\mathrm{t}\vecbu{t},
  \label{eq_strain_rate_decomposition}
\end{equation}
where $D_\mathrm{t}$ is the resolved shear rate in the basal
plane (see also Fig.~\ref{fig_stress_decomposition}). As in
Eq.~(\ref{eq_sc_st}), we define the scalar invariant
\begin{equation}
  D_\mathrm{t}^2
  = \tenssu{D}\vecbu{n}\cdot\tenssu{D}\vecbu{n}
    - (\tenssu{D}\vecbu{n}\cdot\vecbu{n})^2.
  \label{eq_dc_dt}
\end{equation}
Owing to the collinearity of the tensors $\tenssu{S}$ and
$\tenssu{D}$ [see Eqs.~(\ref{eq_glens_flow_law_aniso}) and
(\ref{eq_glens_flow_law_aniso_inv})], the deformability of a
crystallite in the polycrystalline aggregate
[Eq.~(\ref{eq_deformability_crystallite})] can be readily
expressed by $D_\mathrm{t}$ and $d$,
\begin{equation}
  \mathcal{A}^\star(\vecbu{n})
    = \frac{5}{2}\,\frac{D_\mathrm{t}^2(\vecbu{n})}{d^2}
    = 5\,\frac{\tenssu{D}\vecbu{n}\cdot\tenssu{D}\vecbu{n}
               -(\tenssu{D}\vecbu{n}\cdot\vecbu{n})^2}
              {\mbox{tr}\,(\tenssu{D}^2)},
  \label{eq_deformability_crystallite_inv}
\end{equation}
and the deformability of polycrystalline ice
[Eq.~(\ref{eq_deformability})] yields
\begin{eqnarray}
  \mathcal{A}
  &\!\!\!=\!\!\!& \int\limits_{S^2}
      \mathcal{A}^\star(\vecbu{n})\,f^\star(\vecbu{n})\,\mathrm{d}^2 n
  \nonumber\\[1ex]
  &\!\!\!=\!\!\!& \frac{5}{2} \int\limits_{S^2}
      \frac{D_\mathrm{t}^2(\vecbu{n})}{d^2}
      f^\star(\vecbu{n})\,\mathrm{d}^2 n
  \nonumber\\[1ex]
  &\!\!\!=\!\!\!& 5 \int\limits_{S^2}
      \frac{\tenssu{D}\vecbu{n}\cdot\tenssu{D}\vecbu{n}
            -(\tenssu{D}\vecbu{n}\cdot\vecbu{n})^2}
           {\mbox{tr}\,(\tenssu{D}^2)}
      f^\star(\vecbu{n})\,\mathrm{d}^2 n.
  \label{eq_deformability_inv}
\end{eqnarray}
This completes the inversion of the anisotropic flow law.

\subsection{Evolution of anisotropy}

\subsubsection{Orientation mass balance}

The anisotropic flow law in the form
(\ref{eq_glens_flow_law_aniso}) or
(\ref{eq_glens_flow_law_aniso_inv}) needs to be complemented by
an evolution equation for the anisotropic fabric. This is done
by formulating the \emph{orientation mass balance} for the OMD
$\rho^\star(\vecbu{n})$.

\par\rule{0mm}{5mm}\par

\begin{figurehere}
  \medskip
  \centering
  \noindent\includegraphics[width=55mm]{Greve_etal_PICR2_Fig05.pdf}
  \caption{\emph{Orientation transition rate
  $\vecbu{u}^\star(\vecbu{n})$ on the unit sphere $S^2$.}}
  \label{fig_otr}
  \medskip
\end{figurehere}

We are not going to enter the detailed formalism of orientation
balance equations here (see Placidi et~al.\
\cite{placidi_etal_09}, and references therein). Instead, we
rather motivate the form of the orientation mass balance by
generalizing the ordinary mass balance. The difference is that,
in addition to the dependencies on the position vector
$\vecbu{x}$ and the time $t$, the density and velocity fields
also depend on the orientation vector $\vecbu{n}\in{}S^2$,
which is indicated by the notation $\rho^\star(\vecbu{n})$ and
$\vecbu{v}^\star(\vecbu{n})$. The velocity, which describes
motions in the physical space, is complemented by an
\emph{orientation transition rate}
$\vecbu{u}^\star(\vecbu{n})$, which describes motions on the
unit sphere, that is, changes of the orientation due to grain
rotation (Fig.~\ref{fig_otr}). Also, an \emph{orientation flux}
$\vecbu{q}^\star(\vecbu{n})$ is considered, which allows
redistributions of the OMD due to rotation recrystallization
(polygonization). Consequently, the orientation mass balance
reads
\begin{equation}
  \pabl{\rho^\star}{t} + \mbox{div}\,(\rho^\star\vecbu{v}^\star)
   + \mbox{div}\,\!_{S^2}(\rho^\star\vecbu{u}^\star+\vecbu{q}^\star)
  = \rho^\star \Gamma^\star.
  \label{eq_omb_1}
\end{equation}
The first two terms on the left-hand side are straightforward
generalizations of the terms in the ordinary mass balance. The
third term on the left-hand side is the equivalent of the
second term for the orientation transition rate
$\vecbu{u}^\star(\vecbu{n})$ and the orientation flux
$\vecbu{q}^\star(\vecbu{n})$, where $\mbox{div}\,\!_{S^2}$ is the
divergence operator on the unit sphere. On the right-hand side,
a source term appears which allows that certain orientations
can be produced at the expense of others. The quantity
$\Gamma^\star(\vecbu{n})$ is therefore called the
\emph{orientation production rate}. Physically, it describes
migration recrystallization and all other processes in which
the transport of mass from one grain, having a certain
orientation, to another grain, having a different orientation,
cannot be neglected.

\par\vspace*{2ex}\par

In the following, we will make the reasonable assumption that
the spatial velocity does not depend on the orientation, that
is, $\vecbu{v}^\star(\vecbu{n})=\vecbu{v}$. Therefore, the
orientation mass balance (\ref{eq_omb_1}) simplifies to
\begin{equation}
  \pabl{\rho^\star}{t} + \mbox{div}\,(\rho^\star\vecbu{v})
   + \mbox{div}\,\!_{S^2}(\rho^\star\vecbu{u}^\star+\vecbu{q}^\star)
  = \rho^\star \Gamma^\star.
  \label{eq_omb}
\end{equation}
Integration over $S^2$ (all orientations) gives the classical
mass balance
\begin{equation}
  \pabl{\rho}{t} + \mbox{div}\,(\rho\vecbu{v}) = 0,
  \label{eq_mass_balance}
\end{equation}
with the use of the Gauss theorem and the mass-conservation
requirement
\begin{equation}
  \int\limits_{S^2} \rho^\star(\vecbu{n})\,\Gamma^\star(\vecbu{n})
  \,\mathrm{d}^2 n = 0.
  \label{eq_mass_conservation}
\end{equation}

\par\vspace*{1ex}\par

In order to solve the orientation mass balance (\ref{eq_omb}),
constitutive relations for the orientation transition rate
$\vecbu{u}^\star(\vecbu{n})$, the orientation flux
$\vecbu{q}^\star(\vecbu{n})$ and the orientation production
rate $\Gamma^\star(\vecbu{n})$ need to be provided as closure
conditions.

\par\vspace*{2.5ex}\par

\subsubsection{Constitutive relation for the orientation transition
rate}

As mentioned above, the orientation transition rate corresponds
physically to grain rotation. Since grain rotation is induced
by shear deformation in the basal plane, we argue that it is
controlled by the resolved shear rate $D_\mathrm{t}\vecbu{t}$
[Eq.~(\ref{eq_strain_rate_decomposition})], and use the
relation
\begin{eqnarray}
  \vecbu{u}^\star(\vecbu{n})
  &=& -\iota \, D_\mathrm{t}\vecbu{t} + \tenssu{W}\vecbu{n}
  \nonumber\\[0.5ex]
  &=& \iota \cdot
      [(\tenssu{D}\vecbu{n}\cdot\vecbu{n})\vecbu{n}-\tenssu{D}\vecbu{n}]
      + \tenssu{W}\vecbu{n}
  \label{eq_otr}
\end{eqnarray}
(see, e.g., Dafalias \cite{dafalias_01}). The parameter $\iota$
is assumed to be a positive constant. The additional term
$\tenssu{W}\vecbu{n}$ with the spin tensor
$\tenssu{W}=\mbox{skw}\,\mbox{grad}\,\vecbu{v}$ (skew-symmetric part of the
gradient of the velocity $\vecbu{v}$) describes the
contribution of local rigid-body rotations.

In the special case $\iota=1$, the basal planes are material
area elements, that is, they carry out an affine rotation.
However, due to geometric incompatibilities of the deformation
of individual crystallites in the polycrystalline aggregate, an
affine rotation is not plausible, and we expect realistic
values of $\iota$ to be less than unity.

\subsubsection{Constitutive relation for the orientation flux}

The orientation flux is supposed to describe rotation
recrystallization (polygonization). Following the argumentation
by G\"odert \cite{goedert_03}, it is modelled as a diffusive
process,
\begin{equation}
  \vecbu{q}^\star(\vecbu{n})
  = -\lambda\,\mbox{grad}\,\!_{S^2}
     [\rho^\star(\vecbu{n})\mathcal{H}^\star(\vecbu{n})],
  \label{eq_ofl}
\end{equation}
where the parameter $\lambda>0$ is the orientation diffusivity,
$\mbox{grad}\,\!_{S^2}$ is the gradient operator on the unit sphere,
and the ``hardness'' $\mathcal{H}^\star(\vecbu{n})$ is a
monotonically decreasing function of the crystallite
deformability $\mathcal{A}^\star(\vecbu{n})$ [see
Eq.~(\ref{eq_deformability_crystallite})]. A simple choice for
the hardness function would therefore be
\begin{equation}
  \mathcal{H}^\star(\vecbu{n})
  = \frac{1}{\mathcal{A}^\star(\vecbu{n})+\epsilon},
  \label{eq_hardness_1}
\end{equation}
the offset $\epsilon\ll{}1$ being introduced in order to
prevent a singularity for $\mathcal{A}^\star=0$. However,
recent results by Durand et~al.\ \cite{durand_etal_08} suggest
that rotation recrystallization is an isotropic process not
affected by the orientation. In this case, the choice
\begin{equation}
  \mathcal{H}^\star(\vecbu{n}) \equiv 1
  \label{eq_hardness_2}
\end{equation}
is indicated, which renders Eq.~(\ref{eq_ofl}) equivalent to
Fick's laws of diffusion on the unit sphere.

\subsubsection{Constitutive relation for the orientation production
rate}

The driving force for the orientation production rate, which
models essentially migration recrystallization, are macroscopic
deformations of the polycrystal, which can be more easily
followed on the microscopic scale by grains oriented favourably
for the given deformation. Therefore, it is reasonable to
assume that the orientation production rate for a certain
orientation $\vecbu{n}$ is related to the crystallite
deformability $\mathcal{A}^\star(\vecbu{n})$
[Eqs.~(\ref{eq_deformability_crystallite}),
(\ref{eq_deformability_crystallite_inv})]. In the CAFFE model,
the linear relation
\begin{equation}
  \Gamma^\star(\vecbu{n})
  = \Gamma\,[\mathcal{A}^\star(\vecbu{n})-\mathcal{A}]
  \label{eq_opr}
\end{equation}
is proposed. Subtraction of the polycrystal deformability
$\mathcal{A}$ is required in order to fulfill the
mass-conservation condition (\ref{eq_mass_conservation}). The
parameter $\Gamma$ is assumed to be positive, which guarantees
a positive mass production for favourably oriented grains, and
a negative production for unfavourably oriented grains
(Fig.~\ref{fig_opr}).

\begin{figurehere}
  \medskip
  \centering
  \noindent\includegraphics[width=55mm]{Greve_etal_PICR2_Fig06.pdf}
  \caption{\emph{Orientation production rate according to
  Eq.~(\ref{eq_opr}).}}
  \label{fig_opr}
  \medskip
\end{figurehere}

The CAFFE model is now formulated completely. Equation
(\ref{eq_glens_flow_law_aniso}) is the actual flow law, which
replaces its isotropic counterpart (\ref{eq_glens_flow_law}).
Anisotropy enters via the enhancement factor
$\hat{E}(\mathcal{A})$ [Eq.~(\ref{eq_aniso_enh_factor})], which
depends on the deformability $\mathcal{A}$ defined in
Eq.~(\ref{eq_deformability}). Computation of the deformability
requires knowledge of the orientation mass density
$\rho^\star$, which is governed by the evolution equation
(\ref{eq_omb}) and the constitutive relations (\ref{eq_otr}),
(\ref{eq_ofl}) and (\ref{eq_opr}).

\section{Application to the EDML ice core}

\subsection{Methods}

We have developed a one-dimensional flow model, including the
CAFFE model, for the site of the EPICA ice core at Kohnen
Station in Dronning Maud Land, East Antarctica (``EDML core'',
$75^\circ{}00'06''\mathrm{S}$, $00^\circ{}04'04''\mathrm{E}$,
2892 meters above sea level; see
http://www.awi-bremerhaven.de/Polar/Kohnen/). For this core
with an overall length of 2774~m, preliminary fabric data are
available from 50~m until 2570~m depth (I.\ Hamann, pers.\
comm.\ 2006). The fabric is essentially isotropic down to
approximately 600~m depth, and shows a gradual transition to a
broad girdle fabric between 600 and 1000~m depth. Further down,
the girdle fabric narrows until approximately 2000~m depth. The
fabric then experiences an abrupt change towards a single
maximum, which prevails below 2040~m depth. Tendencies of
secondary or multiple maxima are observed at several depths.
The complete data set and a detailed interpretation will be
presented elsewhere (Hamann et~al.\ \cite{hamann_etal_09}).

The location of the EDML site on a flank (rather than a dome
like most other ice cores) allows deriving a one-dimensional
flow model based on the shallow-ice approximation (Hutter
\cite{hutter_83}, Morland \cite{morland_84}), with which the
performance of the CAFFE model can be tested. We define a local
Cartesian coordinate system such that Kohnen Station is located
at the origin, the $x$-axis points in the $260^\circ$ (WSW)
direction, the $y$-axis in the $170^\circ$ (SSE) direction, and
$z$ (depth) points vertically downward
(Fig.~\ref{fig_coordinate_system}).

\begin{figurehere}
  \medskip
  \centering
  \noindent\includegraphics[width=60mm]{Greve_etal_PICR2_Fig07.pdf}
  \caption{\emph{Local coordinate system for the EDML site. Underlaid
  topography map by Wesche et~al.\ \cite{wesche_etal_07}.}}
  \label{fig_coordinate_system}
  \medskip
\end{figurehere}

\begin{figure*}[htb]
  \centering
  \includegraphics[width=110mm]{Greve_etal_PICR2_Fig08.pdf}
  \caption{\emph{Dansgaard-Johnsen type distributions of
  the vertical strain rate \emph{(left panel)} and the temperature
  at the EDML site \emph{(right panel)}.
  The depth of the kinks is at two-thirds of the local ice thickness.
  The strain rate at the surface has been chosen such that the
  downward vertical velocity equals the accumulation rate, and
  the surface and basal temperatures match the ice-core data.}}
  \label{fig_dansgaard_johnsen}
\end{figure*}

According to the topographical data by Wesche et~al.\
\cite{wesche_etal_07}, the $x$-axis is approximately aligned
with the downhill direction, and the gradient of the free
surface elevation, $h$, is
\begin{equation}
  \pabl{h}{x} = -9 \times 10^{-4} \pm 10\%,
  \quad
  \pabl{h}{y} = 0.
\end{equation}
Thus, in the shallow-ice approximation, the only non-vanishing
bed-parallel shear-stress component is $T_{xz}$
\linebreak
($=S_{xz}$), given by
\begin{equation}
  T_{xz} = S_{xz} = \rho g z \pabl{h}{x},
  \qquad
  \label{eq_txz}
\end{equation}
where $g$ is the acceleration due to gravity. Combination with
the $x$-$z$-component of the Glen's flow law
(\ref{eq_glens_flow_law}) yields the isotropic horizontal
velocity,
\begin{equation}
  v_x = -2\rho g \pabl{h}{x}
         \int\limits_{z}^{H}
         A(T')\,\sigma^{n-1}\,\bar{z}\,\mathrm{d}\bar{z}
  \label{eq_vxy_iso}
\end{equation}
(e.g., Greve \cite{greve_97a}, Greve and Blatter
\cite{greve_blatter_09}), where $H$ is the ice thickness, the
rate factor $A(T')$ and stress exponent $n$ are chosen as
listed in Sect.~\ref{sect_glen}, and the enhancement factor $E$
has been set to unity. Similarly, for anisotropic conditions
and the corresponding flow law (\ref{eq_glens_flow_law_aniso}),
the horizontal velocity is
\begin{equation}
  v_x = -2\rho g \pabl{h}{x}
         \int\limits_{z}^{H}
         \hat{E}(\mathcal{A})\,A(T')
         \,\sigma^{n-1}\,\bar{z}\,\mathrm{d}\bar{z},
  \label{eq_vxy_aniso}
 \end{equation}
with the enhancement factor function $\hat{E}(\mathcal{A})$ of
Eq.~(\ref{eq_aniso_enh_factor}). Note that no-slip conditions
have been assumed at the ice base, that is, $v_x(z\!=\!H)=0$.

The unknowns in Eq.~(\ref{eq_vxy_aniso}) are the normal
deviatoric stresses ($S_{xx}$, $S_{yy}$, $S_{zz}$) which are
required together with the shallow-ice shear stress
(\ref{eq_txz}) for computing the deformability $\mathcal{A}$ by
Eq.~(\ref{eq_deformability}), and then the enhancement factor
$\hat{E}(\mathcal{A})$ by Eq.~(\ref{eq_aniso_enh_factor}). The
normal deviatoric stresses are computed by application of the
inverse anisotropic flow law
(\ref{eq_glens_flow_law_aniso_inv}) with the deformability in
the form (\ref{eq_deformability_inv}). The latter is evaluated
with the calculated shallow-ice deformations and an assumed
vertical strain rate $D_{zz}$ in the form of a
Dansgaard-Johnsen type distribution
\cite{dansgaard_johnsen_69}, which consists of a constant value
of $D_{zz}$ from the free surface down to two thirds of the ice
thickness, and a linearly decreasing value of $D_{zz}$ below. A
similar distribution is employed for the temperature profile
(see Fig.~\ref{fig_dansgaard_johnsen}). We also assume
extension in the $x$-direction only, so that the only non-zero
horizontal strain rate entering the evaluation of
Eq.~(\ref{eq_deformability_inv}) is $D_{xx}=-D_{zz}$. The
vertical velocity $v_z$ results from integrating the prescribed
vertical strain rate $D_{zz}$, which gives a linear/quadratic
profile (e.g., Greve et~al.\ \cite{greve_etal_02}).

For the ODF, we use the preliminary data of the EDML fabric
described above. However, since during the drilling process the
orientation of the core is not fixed, the horizontal
orientation of the non-circularly symmetric girdle fabric
(between approximately 600 and 2040~m depth) relative to our
coordinate system, i.e., the direction of ice flow, is unknown.
For this reason, we need to assign an orientation for the
fabric when computing the enhancement factor. We consider two
limiting cases by rotating the initial data such that the
girdle fabric at all depths is aligned with the $x$-axis (case
``R13'') and with the $y$-axis (case ``R23''), respectively.
This is illustrated in Fig.~\ref{fig_fabric_rotate}.

\begin{figurehere}
  \medskip
  \centering
  \noindent\includegraphics[width=52mm]{Greve_etal_PICR2_Fig09.pdf}
  \caption{\emph{Sketch of the rotation of the girdle fabrics in
  order to align with the $x$-axis (case ``R13'') and with the
  $y$-axis (case ``R23'') in the Schmidt projection.}}
  \label{fig_fabric_rotate}
  \medskip
\end{figurehere}

At the surface, we assume isotropic conditions, so that
$\mathcal{A}_\mathrm{s}=1$, and for the maximum softening and
hardening parameters, we use the values $E_\mathrm{max}=10$ and
$E_\mathrm{min}=0$, respectively.

In a second step, we attempt at solving the fabric evolution
equation (\ref{eq_omb}). For the lack of better knowledge, we
neglect recrystallization, that is, we set $\lambda=0$ and
$\Gamma=0$ in the constitutive relations (\ref{eq_ofl}) and
(\ref{eq_opr}), respectively. By allowing only a dependency of
the orientation mass density $\rho^{\star}$ on the vertical
coordinate $z$ (one-dimensional steady-state problem) and on
the orientation $\vecbu{n}$, the orientation mass balance
(\ref{eq_omb}) yields an equation which governs the fabric
evolution along the EDML ice core,
\begin{equation}
  \pabl{\rho^{\star}}{z} v_{z} + \partial_{i}(\rho^{\star}u_{i}^{\star}) = 0,
  \label{eq_omb_1d_1}
\end{equation}
where the orientational gradient operator $\partial_{i}$ and the
orientation transition rate $u_{i}^{\star}$, respectively, read
in index notation as
\begin{equation}
  \partial_{i} = \pabl{}{n_{i}} - n_{i}n_{j} \pabl{}{n_{j}}
  \label{div_op_index}
\end{equation}
and, due to Eq.~(\ref{eq_otr}),
\begin{equation}
  u^{\star}_{i} = \iota D_{hk}n_{h}n_{k}n_{i}-\iota
  D_{ij}n_{j}+W_{ij}n_{j}.
  \label{eq_otr_index}
\end{equation}
With Eq.~(\ref{div_op_index}), and by inserting the
constitutive relation Eq.~(\ref{eq_otr_index}) in
Eq.~(\ref{eq_omb_1d_1}), it follows
\begin{equation}
  \begin{array}[b]{l}
    \bigpabl{\rho^{\star}}{z} v_{z}
    + u_{i}^{\star}\partial_{i}\rho^{\star}
    + \rho^{\star}\partial_{i}u_{i}^{\star}
    \\[2.5ex]
    = \bigpabl{\rho^{\star}}{z} v_{z}
      + (W_{ij}-\iota D_{ij})n_{j}\partial_{i}\rho^{\star}
    \\[2ex]
    \hspace*{14mm}
      +\;3 \iota \rho^{\star}D_{hk}n_{k}n_{h}
    = 0.
  \end{array}
  \label{eq_omb_1d_2}
\end{equation}
We assume that the local flow field consists of vertical
compression with the compression rate (negative vertical strain
rate) $\varepsilon=-\partial{}v_{z}/\partial{}z$ according to
Fig.~\ref{fig_dansgaard_johnsen}, horizontal extension in
$x$-direction, and the horizontal, bed-parallel shear rate
\begin{equation}
  \gamma = \pabl{v_x}{z}
         = 2 \rho g \pabl{h}{x}\,
             \hat{E}(\mathcal{A})\,A(T')\,\sigma^{n-1}\,z
  \label{eq_shear_rate_aniso}
\end{equation}
that results from Eq.~(\ref{eq_vxy_aniso}). The velocity
gradient $\tenssu{L}=\mbox{grad}\,\vecbu{v}$ then reads
\begin{equation}
  \tenssu{L} = \matdd{\varepsilon}{0}{\gamma}
                     {0}{0}{0}
                     {0}{0}{-\varepsilon}.
\end{equation}
Consequently, we obtain for the strain-rate tensor $\tenssu{D}$
and the spin tensor $\tenssu{W}$
\begin{equation}
  \tenssu{D} = \matdd{\varepsilon}{0}{\mbox{$\frac{1}{2}$}{}\gamma}
                     {0}{0}{0}
                     {\mbox{$\frac{1}{2}$}{}\gamma}{0}{-\varepsilon}
\end{equation}
and
\begin{equation}
  \tenssu{W} = \matdd{0}{0}{\mbox{$\frac{1}{2}$}{}\gamma}
                     {0}{0}{0}
                     {-\mbox{$\frac{1}{2}$}{}\gamma}{0}{0}.
\end{equation}
With these expressions and the introduction of spherical
coordinates, Eq.~(\ref{eq_omb_1d_2}) reduces to
\begin{equation}
  \begin{array}[b]{l}
    4 \bigpabl{\rho^{\star}}{z} v_{z}
    \\[2.5ex]
     +\;3 \iota \rho^{\star}
        \big[ \varepsilon
          (2\sin^{2}{\theta}\cos{2\varphi}-1-3\cos{2\theta})
    \\[2.5ex]
    \hspace*{11mm}
     +\;2 \gamma \sin{2 \theta} \cos{\varphi} \big]
    \\[2ex]
     +\;2 \bigpabl{\rho^{\star}}{\varphi}
      \Big[\varepsilon \iota \sin{2\varphi}
     +\;\gamma(-1+\iota)\,\bigfrac{\sin{\varphi}}{\tan{\theta}}
      \Big]
    \\[2.5ex]
     +\;2 \bigpabl{\rho^{\star}}{\theta}
        \Big[ -\bigfrac{1}{2}\iota \varepsilon
        \sin{2\theta}\,(\cos{2\varphi}+3)
    \\[2.5ex]
    \hspace*{14.5mm}
     +\;\gamma(1-\iota \cos{2\theta}) \cos{\varphi}
     \Big]
     = 0,
  \end{array}
  \label{eq_omb_1d_3}
\end{equation}
where $\theta$ and $\varphi$ are the polar angle (co-latitude)
and azimuth angle (longitude), respectively. Note that, due to
Eq.~(\ref{eq_shear_rate_aniso}), the shear rate $\gamma$
depends on the fabric via the deformability $\mathcal{A}$.

\begin{figure*}[htb]
  \centering
  \includegraphics[width=165mm]{Greve_etal_PICR2_Fig10.pdf}
  \caption{\emph{Variation of
  the enhancement factor \emph{(left panel)},
  the ice fluidity \emph{(middle panel)} and
  the horizontal velocity \emph{(right panel)}
  along the EDML ice core.
  ``Data R13'' and ``Data R23'' represent the solutions
  obtained with the measured girdle fabrics rotated to align
  with the $x$- and $y$-direction, respectively, and
  ``Isotropy'' represents isotropic conditions.}}
  \label{fig_enh_flui_vel}
\end{figure*}

The shear flow at the EDML station leads to the transport of
ice particles over significant horizontal distances. Huybrechts
et~al.\ \cite{huybrechts_etal_07} estimate, based on
three-dimensional flow modelling, that particles at 89\% depth
of the core originate from $\approx{}184\,\mathrm{km}$
upstream. This is not taken into account in our spatially
one-dimensional model. However, the variation of the shear
upstream of the drill site is likely small due to the small
variation of the surface gradient
(Fig.~\ref{fig_coordinate_system}), so that the error resulting
from the neglected horizontal inhomogeneity should be limited.

In this study, we restrict the solution of
Eq.~(\ref{eq_omb_1d_3}) to the simplified case of a
transversely isotropic (circularly symmetric) fabric, so that
the OMD $\rho^{\star}$ is only a function of the depth $z$ and
the polar angle $\theta$. Then Eq.~(\ref{eq_omb_1d_3}) becomes,
after integration over the azimuth angle $\varphi$,
\begin{equation}
  \begin{array}[b]{l}
    4 \bigpabl{\rho^{\star}}{z} v_{z}
    - \bigpabl{\rho^{\star}}{\theta} 3 \iota \varepsilon \sin{2\theta}
    \\[2.5ex]
    \hspace*{12mm}
    -\;3 \iota \rho^{\star}\varepsilon (1+3\cos{2\theta}) = 0.
  \end{array}
  \label{eq_tranverse}
\end{equation}
Equation (\ref{eq_tranverse}) is solved by using a
finite-difference discretization with the parameter
$\iota=0.6$.

\subsection{Results}

Figure~\ref{fig_enh_flui_vel} shows the variation of the
enhancement factor, the ice fluidity and the horizontal
velocity along the ice core, computed with the ODF based on the
fabric data described above. For both limiting cases R13 and
R23, the enhancement factor is close to unity in the upper
600~m, which reflects the nearly isotropic fabrics in that part
of the EDML core. Further down, in the girdle fabric regime,
the case R13 is characterized by a moderate increase of the
enhancement factor to an average value of about two, whereas
the case R23 exhibits a strong decrease of the enhancement
factor to values close to zero. This demonstrates clearly that
the girdle fabrics produce a significantly different mechanical
response depending on the orientation relative to the ice flow.
Case R23 is probably closer to reality, because in the girdle
fabric regime above 2000~m depth the deformation is essentially
pure shear (vertical compression, horizontal extension in
$x$-direction only). For this situation, a simple
``deck-of-cards'' model illustrates that the $c$-axes turn away
from the $x$-axis and towards the $z$-axis, whereas nothing
happens in $y$-direction, so that in the Schmidt projection a
concentration perpendicular to the $x$-axis (flow direction)
results.

\begin{figure*}[htb]
  \centering
  \includegraphics[width=110mm]{Greve_etal_PICR2_Fig11.pdf}
  \caption{\emph{Variation of
  the enhancement factor \emph{(left panel)} and
  the horizontal velocity \emph{(right panel)}
  along the EDML ice core.
  ``Model'' represents the solutions based on the fabric
  evolution equation (\ref{eq_tranverse}) for transverse
  isotropy. For ``Data R13'', ``Data R23'' and ``Isotropy''
  see the caption of Fig.~\ref{fig_enh_flui_vel}.}}
  \label{fig_transverse}
\end{figure*}

Below 2000~m depth, where the fabric switches to a single
maximum, the difference between the cases R13 and R23
essentially vanishes. The crystallite basal planes are
favourably oriented for the now prevailing simple-shear
deformation, which leads to large deformabilities.
Consequently, the enhancement factor shows a sharp increase to
a maximum value of about eight, which is close to the
theoretical maximum of $E_\mathrm{max}=10$.

The variabilities of the enhancement factor and the effective
stress, as well as the increase of the temperature with depth,
contribute to the fluidity profiles shown in
Fig.~\ref{fig_enh_flui_vel}b. Since the fluidity is very small
above 2000~m depth and increases only further down, the
difference between the cases R13 and R23 in absolute values is
surprisingly small. At 2563~m depth, the fluidity is about 200
times higher than the fluidity at 1000~m depth for the case R23
due to the counteracting contributions from the favourably
oriented $c$-axes, the higher temperature and the smaller
effective stress. The latter is somewhat surprising; it is
caused by the normal deviatoric stresses $S_{xx}$ and $S_{zz}$,
which decrease strongly below 2000~m depth and outweigh the
influence of the increasing shear stress $S_{xz}$ in the
effective stress.

Owing to the large enhancement factors close to the bottom, the
anisotropic flow law predicts significantly larger horizontal
velocities compared to the isotropic flow law for the entire
depth of the ice core (Fig.~\ref{fig_enh_flui_vel}c). At the
surface, the anisotropic horizontal velocities are by
approximately a factor 3.5 larger than their isotropic
counterparts, and the absolute value of
$\approx{}0.7\,\mathrm{m\,a^{-1}}$ agrees very well with
measurements (H.~Oerter, pers.\ comm.\ 2005; Wesche et~al.\
\cite{wesche_etal_07}). The difference between the cases R13
and R23 amounts to $\approx{}10\%$, the larger values
being obtained for the case R23 owing to the slightly larger
enhancement factors below 2000~m depth. Interestingly, these
differences show that the fabrics are not perfectly
transversely isotropic below 2000~m depth, even though they are
very close to the single-maximum type.

Let us now turn to the simulation in which the fabric evolution
is computed by solving Eq.~(\ref{eq_tranverse}) for a
transversely isotropic fabric. Although this assumption is not
consistent with the observed girdle fabric between
approximately 600 and 2000~m depth and is therefore a gross
simplification, it is interesting to study the mechanical
response of such a simplified system and the differences to the
ice flow resulting from applying the measured fabrics.

Figure~\ref{fig_transverse}a shows the comparison between the
enhancement factors resulting from the computed, transversely
isotropic fabric (which will be referred to as ``modelled
enhancement factor'' in the following) and from the fabric
data. Evidently, the agreement is good despite the assumption
of transverse isotropy. Down to 1800~m depth, the modelled
enhancement factor lies in between the cases R13 and R23, which
are the limiting cases for the orientation of the measured
girdle fabric with respect to the ice-flow direction. Between
1800 and 1900~m depth, the modelled enhancement factor is very
close to the low values of the case R23, for which the girdle
fabric is aligned perpendicular to the flow direction. Below
2000~m depth, the sharp increase is also well reproduced;
however, the maximum of the modelled enhancement factor is more
pronounced and lies closer to the bottom than for the cases R13
and R23.

For that reason, the modelled enhancement factor leads to
larger near-basal shear rates than the enhancement factor based
on the cases R13 and R23. Consequently, the horizontal velocity
resulting from the modelled enhancement factor is larger by
about a factor two than the velocities for the cases R13 and
R23 (Fig.~\ref{fig_transverse}b). At the surface, a value of
$\approx{}1.5\,\mathrm{m\,a^{-1}}$ is reached, which is twice
the measured surface velocity. This highlights the great
sensitivity of the ice dynamics to the processes near the
bottom, which are most difficult to model precisely. Beside the
assumption of transverse isotropy, a weak point in that context
is the neglection of recrystallization processes, which are
expected to become important for the fabric evolution in the
lower part of the ice core. This point requires further
attention.

\section{Conclusions}

The newly developed CAFFE model (Continuum-mechanical,
Anisotropic Flow model, based on an anisotropic Flow
Enhancement factor), which comprises an anisotropic flow law as
well as a fabric evolution equation, was presented in this
study. It is a good compromise between physical adequateness
and simplicity, and is therefore well suited for being used in
flow models of ice sheets and glaciers.

The CAFFE model was successfully applied to the site of the
EDML ice core in East Antarctica. Two different methods were
employed, (i) computing the anisotropic enhancement factor and
the horizontal flow based on fabrics data, and (ii) solving the
fabric evolution equation under the simplifying assumption of
transverse isotropy. Method (i) demonstrated clearly the
importance of the anisotropic fabric in the ice column for the
flow velocity, and better agreement with the measured surface
velocity was achieved compared to an isotropic computation. The
anisotropic enhancement factor produced with method (ii) agreed
reasonably well with that of method (i), despite the fact that
the measured fabric is not transversely isotropic in large
parts of the ice core.

A solution of the fabric evolution equation (\ref{eq_omb_1d_3})
for the EDML ice core without the assumption of transverse
isotropy has been presented elsewhere (Seddik et~al.\
\cite{seddik_etal_08}). Further, the CAFFE model has already
been implemented in the three-dimensional, full-Stokes ice-flow
model Elmer/Ice (Seddik \cite{seddik_08}, Seddik et~al.\
\cite{seddik_etal_09a}) in order to simulate the ice flow in
the vicinity within $100\,\mathrm{km}$ around the Dome Fuji
drill site (Motoyama \cite{motoyama_07}) in central East
Antarctica.

\vspace*{1ex}

\begin{center}
\includegraphics[scale=0.33]{Snowflake.pdf}
\hspace*{2em}
\includegraphics[scale=0.33]{Snowflake.pdf}
\hspace*{2em}
\includegraphics[scale=0.33]{Snowflake.pdf}
\end{center}

\section*{Acknowledgements}

The authors wish to thank Dr.\ S\'ergio H.\ Faria (University
of G\"ottingen, Germany), Dr.\ Olivier Gagliardini (Laboratory
of Glaciology and Environmental Geophysics, Grenoble, France)
and Professor Kolumban Hutter (Swiss Federal Institute of
Technology, Zurich) for their collaboration in developing the
new model for anisotropic polar ice. Thanks are further due to
Ms.\ Ilka Hamann and  Dr.\ Sepp Kipfstuhl for kindly providing
the preliminary fabric data of the EDML ice core, to Dr.\ Hans
Oerter for communicating the measured surface velocity, to Ms.\
Christine Wesche (all at Alfred Wegener Institute for Polar and
Marine Research, Bremerhaven, Germany) for allowing us to use
the topographic map of the vicinity of the drill site, and to
an anonymous reviewer whose comments helped improving the
clarity of the paper.

This work was supported by a Grant-in-Aid for Creative
Scientific Research (No.\ 14GS0202) from the Japanese Ministry
of Education, Culture, Sports, Science and Technology, and by a
Grant-in-Aid for Scientific Research (No.\ 18340135) from the
Japan Society for the Promotion of Science. We would like to
express our gratitude for the efficient management of the
Creative Research project by the leader, Professor Takeo
Hondoh, and the project assistant, Ms.\ Kaori Kidahashi.

\clearpage

\input{Greve_etal_PICR2_MS7.bbl}

\end{multicols}
\end{document}

redpajama_set_name: RedPajamaArXiv


> and both are different for indexing and querying.
> custom analyzer, I've to use it anyway.
> change the order of applying the filters as you said.
> > KK, you got the right idea.
> > before the porter stem filter... otherwise it might not work correctly.
> > >  * Analyzer for Indian language.
> > > and indic texts. let me try out the delimiter. Will update you on that.
> > > > you want.
> > > > > stop filter, is this the default one?
> > > > > Does this sound OK? I think it will do the job...let me try it out..
> > > > > > codebase.
> > > > > > See how it combines a specified tokenizer with various filters?
> > > > > > filters.
> > > > > > > Thanks Muir.
> > > > > > > Thanks for letting me know that I dont need language identifiers.
> > > > > > >  I'll have a look and will try to write the analyzer.
> > > > > > > wont be that difficult.
> > > > htere?
> > > > > > > let me know.
> > > > > > > > whether fragments are english or not.
> > > > > > > > neither will the LowerCaseFilter.
> > > > > > > > > Thank you all.
> > > > fly.
> > > > > > > > > in Solr, Solr is based on Lucene only, right?
> > > > > > > > > content.
> > > > > > > > > WordDelimiteFilter to do my job.
> > > > > > > > > mix of non-english and engish words.
> > > > > > > > > to document.
> > > > > > > > > index.
> > > > > > > > > I would like some one to guide me in this direction.
> > > > > > > > > to some tutorials for the same.
> > > > > > coding.
> > > > > > > > > Thank you very much.
> > > > > > > > > --KK.
> > > > > > > > > > characters such as ZWJ/ZWNJ.
> > > > > > > > > > > > mixed with non-english content?
> > > > > > > good.
> > > > > > > > > > > > 3. lowercase the english.
> > > > > > > > > > > > 4. stem the english.
> > > > > > > > > > > > > Muir, thanks for your response.
> > > > > > > > > > .
> > > > > > > > > > > content].
> > > > > > > > > > > > > english word say "Detection"
> > > > > > > same.
> > > > > > > > > > that?
> > > > > > > > > > > > > russian etc].
> > > > > > thoughts!
stuff like marathi mixed in?
> > > > filed.
> > > > > > > > > > > > > > > non-english content.
> > > > > > this.
proceed for fixing this issue.
> > > > > > > > > > > > > > > KK.


I was the Chapter president of the University of Washington chapter for two years (2015-2017). I was also the Zone 17 AZC for 2016-2017. Currently, I am a physics graduate student at Louisiana State University.
I am enrolled in graduate program at LSU. I am involved in a research group and frequently teach/grade for classes in the physics department.


text:
Ari Hoenig (Mastering Odd Times)
Ari Hoenig (Mastering Odd Times) quantity
SKU: N/A Categories: Bass, Drums & Percussion, Guitar, Horns, Keyboards, Rhythm Section, Videos
Artist: Ari Hoenig
Subtitles: Chinese, English, French, Italian, Korean, Spanish
Description: In this mastering odd times lesson, acclaimed drummer Ari Hoenig shows you how to become fluent and free when playing in odd time signatures. Ari breaks down a series of exercises, so that you can become a master of odd times regardless of your instrument. If you want to learn to hear, feel and play some more advanced rhythmic content in odd meters, this masterclass video is for you.
Topics Covered: Odd Time Training, Displacement, Groupings, Clave, Exercises, Melody Independence, Long 5, Short 5, Sixteenths, etc.
Ari Hoenig
Born on November 13, 1973 in Philadelphia, Ari Hoenig, was exposed at an early age to a variety of musical experiences. His father is a conductor and classical singer, his mother a violinist and pianist. Accordingly, at 4 years of age, Ari began studying the violin and piano. He began playing drums at age twelve, and by age fourteen he was honing his skills with other young jazz musicians at Philly clubs such as Ortlieb's Jazz Haus.
Ari attended the prestigious University of North Texas for three years, where he studied with Ed Soph while playing with the "One O'Clock" Lab Band. Wanting to be closer to New York City, in 1995 Ari transferred to William Patterson College in northern New Jersey. He soon found himself playing for legendary Philadelphia organist Shirley Scott and working regularly in New York City.
Shortly thereafter, Ari moved to Brooklyn and began playing extensively with a variety of groups, including Jean Michel Pilc Trio, Kenny Werner Trio, Chris Potter Underground, Kurt Rosenwinkel Group, Joshua Redman Elastic Band, Jazz Mandolin Project and bands led by Wayne Krantz, Mike Stern, Richard Bona, Pat Martino, Dave Leibman and Bojan Z. He has also shared the stage with such artists as Herbie Hancock, Ivan Linz, Wynton Marsalis, Toots Theilmans, Dave Holland, Joe Lovano, Pat Metheny and Gerry Mulligan, although he got kicked off the stage by security shortly thereafter.
Both of Ari's self-produced solo drum CDs, "Time Travels" (2000) and "The Life Of A Day" (2002), document his exploratory nature. They represent an ambitious tribute to the melodic possibilities of the drum set. Today, Ari continues to build on the concepts of these two records by playing largely improvised solo concerts using a regular four piece drum kit and no percussion.
The Ari Hoenig Quartet was formed at the end of 2002 while playing every Monday night at the New York Village jazz club Fat Cat. This band featured Jacques Schwarz-Bart on tenor sax, Jean Michel Pilc on piano and Matt Penman on bass. They released two records on the Smalls Records label: "The Painter" (2004) and the DVD "Kinetic Hues" (2005).
In 2006 Ari signed a multi record deal with Dreyfus Records and released his first record for them called "Inversations." "Inversations" (2006) features the trio with Jean Michel Pilc and Johannes Weidenmueller. "Bert's Playground" (2008), Ari's second record for Dreyfus, features Ari's Punk Bop Band joined by Chris Potter. Highlights of this record include Chris's solo on Moments Notice and Ari jumping around in red pants on the cover. Jonathan Kreisberg, Matt Penman, Will Vinson, Gilad Hekselman and Orlando le Fleming also represent on this one.
Ari's next record project was for "Smalls Live," a record label set up in 2009 to document some of the music being performed at the "Smalls Jazz Club" in New York where Ari has had a residency since 2003. Ari chose his Punk Bop Band to make the record "Punk Bop Live at Smalls." The Punk Bop Band features Will Vinson on alto, Jonathan Kreisberg on guitar and fellow Jazz Mandolin Project alumni Danton Boller on bass. Tigran Hamasyan is a special guest on 4 tracks as well.
Ari's Quartet with Tigran Hamasyan, Gilad Hekselman, Orlando le Fleming and Chris Tordini released "Lines of Oppression" (2011) on the Naïve label. This record represents a culmination of Ari's bandleading, composing and accounting skills.
Currently Ari leads three groups that play his original music. Besides the Ari Hoenig Quartet and "Punk Bop," Ari also leads the Ari Hoenig Trio, with Jonathan Kreisberg or Gilad Hekselman covering guitar duties and Matt Penman or Orlando plucking on the bass. He also co-leads a variety of projects, including Pilc, Moutin, Hoenig ("the three headed monster"), Oscillations Quartet and various duo's with Chris Potter, Edmar Casteneda or Dan Weiss.
As an educator, Ari teaches privately and is on faculty at New York University and the New School for Social Research in New York. He gives clinics and lectures at music schools and universities worldwide, and writes a regular educational column for Modern Drummer magazine. In collaboration with bassist Johannes Weidenmueller, Ari released "Intro to Polyrhythms Vol 1", and "Metric Modulations, Expanding and Contracting Time within Form Vol 2". (Mel Bay 2009, 2012)
Website: http://arihoenig.com/
Content By Ari Hoenig
Ari Hoenig (Rhythm Training) – All 3 Videos
Ari Hoenig (Rhythm Training) – Micro-Credential
Ari Hoenig (Drums: Jazz Coordination)
Ari Hoenig (Micro Timing) – BUNDLE
Ari Hoenig (Complete Brush Perspective)
Ari Hoenig (Mastering Odd Times) – Micro-Credential
Blair Sinta (Drum Sounds for the Studio and Stage)
Adam Small (Bass) – Videos 1 & 2 Bundle
Adam Small 1 (Bass)
Al Street 1 (Guitar)

redpajama_set_name: RedPajamaCommonCrawl


Arnie Pie's full length show, following its debut at the Edinburgh Fringe 2012. Arnie Pie takes you through a wacky account of his travels as a stand-up comic, his dad's "wise" words, his random thought process and the crap he did and came across … because he felt like it.
General Admission are $10. Opening Night/Concession/Cheap Tues tix are $5. Show starts at 11pm at The Austral, 205 Rundle St.
"If you can leave every politically correct part of you at the door, you'll enjoy this act" – Broadway Baby.


You want to cut your chickens feed bill producing high quality compost, raising at the same time happy healthy chickens in your permaculture center?
Simple, raise them on manure, they love earthworms!
When you will incorporate chickens into your composting system, you will be very pleased not just with the daily egg production but you will discover the usefulness of them as our compost helpers.
This is a way to minimize effort in your permaculture garden.
Composting with Chickens: which are the benefits?
Composting is a process that works to speed up the natural decay of organic material by providing the ideal conditions for detritus-eating organisms to thrive. The end-product of this concentrated decomposition process is nutrient-rich soil that can help your entire permaculture system.
The key to effective composting is to create an ideal environment for the microorganisms to thrive warm temperatures, nutrients, moisture and plenty of oxygen.
When chickens have access to manure, they eat the bad bugs, parasites, and larvae out of the manure. This stops the bad bugs from reproducing and possibly making your animals or pasture sick.
Properly managed manure with chickens will help cut your chickens' feed bill!
Bugs, parasites, and larvae are all a good source of food. The protein and minerals in them are great for their health and help produce strong eggshells.
Chickens also find and eat any undigested food. Grains and any other foods other animals didn't fully digest—the chickens will gladly eat them.
This is free chicken food! You save tons of money on chicken feed.
The quality of your egg production increases, and the health of your chickens is exceptional.
Benefits for the composting process!
They also love working on the compost, and it keeps them busy during the day. In the winter, the pile provides added heat to their area.
The compost decomposes more quickly because the continued efforts of the chickens facilitate the composting process. They scratch and tear and work at the pile all day long. While doing so, they also add their own droppings to the pile, which is an additional bonus.
Getting Started Composting with Chickens!
1. Create a composting area in your chicken coop where you can easily dump your organic material.
2. Add organic material to the compost and don't worry about mixing the pile — your chickens will tear into this naturally and do the work for you.
After you obtain your base organic materials, heap it into a pile and work on adding your kitchen scraps. As you add material to the pile, the chickens quite instinctively will head for the pile and began working it.
4. Cleaning the chicken coop: When cleaning your chicken coop, you can now just dump the droppings into the compost pile and the chickens will mix all that organic material right into the pile.
At Edible Acres, chickens generates about 4 wheelbarrow loads of compost a week during the summer. Chickens give them 12-16 eggs a day and they cost them about a penny per bird per day. Their main expense is buying in millet and sunflower seeds. The other whole grains they barter for, and they collect compost scraps from local organic sources, as well as hay and wood chips to make the basic bulk mix.
Be sure to share this post to inspire your friends and family to cut your chickens feed bill producing high quality compost!


Whilst wandering around cyberspace with no particular place to go, I stumbled across the Wikipedia entry for the sci-fi author Robert Silverberg, which contained this odd phrase: "In 1959, the market for science fiction collapsed..."
Yes, collapsed. Like October 1929, but for science fiction, not money, although they are, arguably, both abstract and immaterial concepts.
Something about this statement, the unequivocal nature of it, piqued my interest, and I thought that I'd dig a bit deeper and blog my findings. Except, of course, an explanation far more eloquent - and possibly a tad more embittered - than any I could construct has already been written by Barry N Malzberg at baen.com detailing the various factors at play, not least the forced divestiture of the magazine distribution arm of American News Service.
That last point provides the explanation for the cliff edge nature of events of 1959, but there's a plethora of context to be taken into account as well. One is that the parallels between 1959 and 1929 don't seem so far fetched: in both cases we're dealing with bubbles with an unrecognised oversupply or overvaluation leading to a market correction. 1929 is well documented; in 1959 it was the belief that the readership of science fiction could continue to grow exponentially whereas, in reality, it was made up of spotty youths who were just filling in the years until the family acquired a TV.
Which led me to wonder why the market for science fiction hadn't moved to television and cinema, rather than "collapsing". Perhaps part of the reason was that, by Malzberg's account at least, the writers had become somewhat fat and lazy, needing to churn out a mere thousand words, derivative words at that, each day before indulging in whiskey and "wife exchanging". TV would have demanded more, much more, and the market only actually collapsed for the dinosaurs. Perhaps it was because, for Malzberg, the market is defined narrowly, as anthology and magazine publishing, and this marketplace was in New York whilst television and cinema was based on the opposite coast. Perhaps it came down to personalities: the need to collaborate on a TV production doesn't sit well with a person who takes on a blank sheet of paper in single combat.
But I think there's another angle to this. Compare, say, Melies' Le Voyage dans la Lune with something modern, for example The Martian or Gravity (both of which score virtually the same on IMDB, albeit with Melies' classic ahead by a nose). There's a sense of utter joyful, ridiculous fantasy to Melies' classic, whilst the modern yarns labour the accuracy of the science and technology. Sure, there's plenty of cartoon fantasy courtesy of Marvel and DC, but it ain't science fiction in the sense that magic powers ain't science, even when science gone bad is supposed to have endowed them. Melies takes science - a rocket - and creates a fiction. And in 1902 that fiction could take us almost anywhere; today we know that a rocket can't realistically take us anywhere other than our nearest neighbours, and they're all barren rocks anyway. We've lost a lot of the freedom of movement in constructing a story whilst retaining a straight face.
Malzberg alludes to this when he says, "Sputnik in 1957 had made science fiction appear, to the fringe audience, bizarre, arcane, irrelevant.". However, I don't buy this. If anything, Sputnik should have moved science fiction up the agenda: it showed we could really leave the confines of Mother Earth without suggesting the impending failure to find anything out there. That all came later.
Classic science fiction up to, say, Star Trek, exists in a Goldilocks zone between technology being invented for us to explore the stars and us discovering that there's nothing out there to find. The joyful youth of sci-fi, I think, ran until roughly the same time that Neil Armstrong stepped on the moon unwatched by native fauna - because there isn't any. That's a full decade after 1959's "collapse".
Curiously, I found this extended timeline supported by some wonderfully unscientific research by Castalia House. It makes an interesting read, even if you feel unable to sign up to its findings.
So where does this leave us? Science fiction is dead? Not at all. It's just that the genre has moved on from stories that just happen to be set in space. Think about how many spaceships are really just sea-going vessels with a different view out of the portholes, or aliens who are just re-employed redskins. Science fiction in its cynical middle age has had to find stranger stories than a man wearing a goldfish bowl on his head wrestling a sentient octopus. And, whilst that may make for the niche, cult, and distinctly un-populist, I think it's rather good at it.


text:
Dad of missing New Jersey teen says his boy died 'horrible death' in frozen lake
By: Rolando Pujol , PIX11 Web Team
"imagine screaming and knowing you're going to die," Clyde Schimanski Jr. said about his son.
A New Jersey dad said his son died a "horrible death" in a New Jersey lake, where his son and another boy disappeared Monday.
A body Tuesday afternoon has been pulled from the lake, according to a report , while the search continues for a second teenager who disappeared into Budd Lake.
"Imagine screaming and knowing you're going to die," Clyde Schimanski Jr. told the Star Ledger, about the death of his son, Clyde Schimanski III. "He died a horrible death."
Police, fire and rescue teams resumed the search for the boys at 7 a.m. Tuesday at the Morris County lake Monday night, according to Mt. Olive police. The boy's body was found around 1 p.m. Tuesday
Around 6:19 p.m. Monday, multiple people called 911 reporting someone calling for help from the ice on the lake. Responders broke through roughly 100 feet of ice where they believed the victims were, but were unable to find either of the missing teens.
During the search state police helicopters circled the lake while responders below used flashlights to try and spot any bodies below the ice.
It is not clear what the two missing teenagers were doing on the ice.


text:
MESS, emulatore multipiattaforma di console e personal computer
Mess, fiume lussemburghese
Mess, gruppo musicale italiano
Mess, gruppo musicale austriaco che ha partecipato all'Eurovision Song Contest 1982
Mess, album dei Liars del 2014

redpajama_set_name: RedPajamaWikipedia


The forging process is of course completely different from the casting process. With forging, the steel is preheated in a furnace to a point at which it can be easily plastically deformed. It is then pressed into a steel die which has an upper and a lower half. Deep cavities are not possible using this process which is of course a major limitation compared to casting.
However, a large advantage of forging compared to casting is the cost. Forging is a lot cheaper than cast steel. Another advantage is the excellent weldability.
We supply forgings from 20 grams up to approximately 30kgs unit weight.


text:
Portrait of Helen (Berkovic) Goldberger, Eugene Goldberger and their sons Milan and Leo taken shortly before the family moved to Denmark.
Photograph | Photograph Number: 90001
October 1933 - 1934
Opava, [Silesia; Ostrava] Czechoslovakia
Variant Locale
Troppau
[Sudetenland]
Photo Designation
LIFE BEFORE THE HOLOCAUST -- Czechoslovakia -- Family/Friends/Portraits
United States Holocaust Memorial Museum, courtesy of Gus Goldberger
Lavoslav (Leo) and Gustav (Gus) Goldberger are the sons of Eugene (Jeno) and Helen (Berkovic) Goldberger, who grew up in small towns in Czechoslovakia. They met in Vienna, where Jeno was studying music at the conservatory and attending cantorial school. Following their marriage, Jeno and Helen moved to Vukovar (Croatia), where he was offered a cantorial position. The two oldest children, Emanuel (Milan) and Lavoslav (Leo) were born there. In 1932 Jeno accepted a new positon as chief cantor in Troppau (Opava, Czechoslovakia), where Gustav (Gus) was born two years later. Fearing the rising tide of Nazism, Jeno moved his family once again, this time to Denmark, where he assumed the position of chief cantor of Copenhagen. The family quickly integrated into their new surroundings, and in 1938 a fourth son was born, Erik (Chaim). The German occupation of Denmark did not significantly change the lives of the Goldbergers during its first years. However, in the late summer of 1943 the situation altered suddenly. Seeking retaliation for the activities of the Danish resistance, the Germans seized Jeno and a number of other prominent Jewish citizens. Fortunately, a sympathetic Danish neighbor was able to prevent his formal arrest. Several weeks later, on October 1, 1943, plans for the imminent arrest and deportation of Danish Jewry were leaked to the Danes, who immediately rallied to the rescue of their Jewish compatriots, ferrying over 7,000 of them to Sweden. The Goldbergers were among those Jews who were carried to safety. For the remainder of the war the family lived in Goteborg, Sweden, where Jeno served as cantor. In June 1945 the Goldbergers returned to Copenhagen, where Jeno resumed his former post.
Keywords and Subjects
FAMILIES (PREWAR JEWISH)
JEWS (CZECH)
Copyright: United States Holocaust Memorial Museum
Provenance: Gus Goldberger
Record last modified: 2002-12-03 00:00:00
This page: https://collections.ushmm.org/search/catalog/pa1099601
Available for Research
Recognize Someone?


Online Word Counter is a word counter that provides an extensive statistics about the word count, character count, the number of characters without spaces. All results are immediately shown and it is ridiculously easy to use and of course, the service is completely free.
Online word counters are a perfect tool for anyone who needs to keep a count of their words and characters, but does not use Microsoft Word or other editors. Imagine writing a piece and having to manually count the words! Not only will it take forever, but there is a chance you won't be wholly accurate.
Who is this word counting tool for?
You can paste your text with the characters to count in the text area above, or you can type your characters and words. The counter will be updated instantly, displaying the amount of characters, words, sentences, paragraphs and whitespace in your text.


A design entity which has a well defined functional specifications and performing distinct tasks independently is considered as a block verifiable at block or module level. Bigger blocks constituting such interconnected design units performing another set of well defined tasks will also be verified using block or module level verification techniques.
A System on Chip (SoC) will constitute many design blocks working in sync to accomplish a final function or operation. Full chip verification of a design will need well defined requirements at top/ chip level as well as at constituent block level. All constituent blocks of a chip will be verified first using a block level testbench and a seperate top system verification environment will be created for full chip level verification. System level verification environment may reuse some block level verification components.
We have a set of VIPs under development, which are flexibly re-configurable and have well documented user manuals.
When design is considerably big in size and complex in function resulting in multi million gates, it is advisable to go for acceleratable verification environment using a reliable emulator platform. Hardware emulation platforms accelerate design testing thus reducing verification time by many folds.
Avinya Technology provides skilled engineers to customers on contract basis, which can work either on-site or at off-shore as per demand. For specific long term requirement Avinya Technology facilitates fully equipped Off-shore Development Centers (ODCs).
Client gets a set of skilled engineering HR as per its requirement.
World class infrastructure and equipments are provided and maintained by Avinya Technology.
Client is free from every HR and infrastructure overhead without compromising the quality of engineering services.
Client gets best engineering services at the cost much less than employing HR at their own site.
•Block or Module level functional verification of design.
•System on Chip (SoC) or full chip level functional verification from block level up to system level.
•Verification Intellectual Property (VIP) development and integration in testbench.
•Development of acceleratable testbenches compatible to any advance emulator platform.
•Providing skilled engineering HR and Setting up of Offshore Development Center (ODC) with a set of skilled engineers for customer.
1.Designing and hoisting of web site – this service is provided in three categories with different features for different type of businesses/ clients.
2.Annual maintenance of web site designed by company – this service is also available in three categories as per above features.


RSS stands for "Really Simple Syndication" - and is a new way for you to quickly access and read online content from the City of Chilliwack. By using an RSS Reader, or by merging the RSS feed into your online BLOG.
The first step to access an RSS feed is to install a RSS reader. After you have installed an RSS reader, simply paste one of the links below into the RSS reader.


Among this year's contenders determined to make their food dreams a reality is New South Wales' travel agent Jess Hall, who has an all-or-nothing approach to the kitchen. This 28-year-old wears her heart on her sleeve, she has a vivacious spirit and she is pedantic in making sure everything is perfect for the judges. Will it be a resounding yes? Get a feel for Jess' energy here.
33-year-old Victorian cooking and garden educator Tim Bone may look like a prince, but can he serve up a dish fit for a king? Tim may have been told countless times of his uncanny resemblance to Prince Harry but he is still on the hunt for his crowning achievement in the kitchen. See here for yourself whether Tim does have a touch of the Royals about him.
MasterChef Australia Season 11. Coming Soon To 10 and WIN Network.


text:
namespace inet {

namespace power {

W EpEnergySinkBase::computeTotalPowerGeneration() const
{
    W totalPowerGeneration = W(0);
    for (auto energyGenerator : energyGenerators)
        totalPowerGeneration += check_and_cast<const IEpEnergyGenerator *>(energyGenerator)->getPowerGeneration();
    return totalPowerGeneration;
}

void EpEnergySinkBase::updateTotalPowerGeneration()
{
    totalPowerGeneration = computeTotalPowerGeneration();
}

void EpEnergySinkBase::addEnergyGenerator(const IEnergyGenerator *energyGenerator)
{
    EnergySinkBase::addEnergyGenerator(energyGenerator);
    auto module = const_cast<cModule *>(check_and_cast<const cModule *>(energyGenerator));
    module->subscribe(IEpEnergyGenerator::powerGenerationChangedSignal, this);
    updateTotalPowerGeneration();
}

void EpEnergySinkBase::removeEnergyGenerator(const IEnergyGenerator *energyGenerator)
{
    EnergySinkBase::removeEnergyGenerator(energyGenerator);
    auto module = const_cast<cModule *>(check_and_cast<const cModule *>(energyGenerator));
    module->unsubscribe(IEpEnergyGenerator::powerGenerationChangedSignal, this);
    updateTotalPowerGeneration();
}

} // namespace power

} // namespace inet

redpajama_set_name: RedPajamaGithub


Dinner on Grand Day in Middle Temple Hall, Feliks Topolski.
Topolski's Chronicles contain over 2300 drawings, depicting his interpretation of the many current affairs of the time.
A renowned portrait artist, he used tangled dynamic lines to bluntly portray his models, at times in an almost caricatural manner. Drawing was his expression of choice. He usually worked with pencils, crayons, and ink, drawing using a thick entanglement of lines, which made up exquisitely characterised personalities and scenes. He always drew his works on the run, quickly and on-site and he never redrew them. Thus, they can be treated as quick, seemingly chaotic, yet always clever and authentic notes.


Welcome to BarneyRedoms free chat!
Bookmark BarneyRedoms free chat page.
BarneyRedoms turn on: temptations like you deserve sins like me... risk to live this moment in which my desire is to listen to you, to please you, to pamper you, and to give you the best experience. dare yourself!


At Sphinx Home Health Care, we have highly-skilled home care nurses who are passionate and dedicated to giving all of their patients the absolutely best treatment. We hold all of our staff members to the highest standards so that you can rest assured that the professional administering your treatment is one you can trust completely. Your home care nurse is matched specifically to you based on a personality assessment, lifestyle, and needs. Your care program will be designed to improve or maintain your health.
Our skilled in-home nursing care is available to our Sterling Heights clients all day, every day, seven days a week. Call us today to ask about our availability or to schedule an appointment for a more detailed discussion of how we can meet your home care needs.


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De Golf van Amundsen is een golf nabij de Canadese Northwest Territories, tussen Bankseiland, Victoria-eiland en het vasteland.  De Golf van Amundsen kan beschouwd worden als een uitloper van de Beaufortzee.

Zeestraat in Canada


Through local historians, scholars, and media initiatives, Washington Street Historical Society develops and offers educational resources about the history of the Washington Street neighborhood and its prominent figures. We continue to document oral histories of last survivors and descendants of the former Arab speaking community, offer historical walking tours of the area, host conferences and exhibits, and can offer educators, scholars and local historians to interested outside parties. For more information on these projects, contact us.
The first report of the Washington Street Historical Society is the commissioned architectural and historical analysis of two historic buildings of the neighborhood whose landmark designation we are seeking from the Landmarks Preservation Commission. Please read the report here.


Here's what people have said about working and interviewing at Seacoast HVAC (2004) Limited.
Listen to their concerns and stop blindly following everything that the managers say. The managers lie constantly to cover themselves. If you care about your employees, stop treating them like they don't matter.


I'm not precisely certain what brought on this onslaught of stressful thought. It is true that we are expecting a spate of company in the next few weeks. And, it is also true that the stains and spots on the carpet have been glaring up at me for some time and the furniture has gone far beyond my mother's claim that "old houses need a little patina of dust." But under usual circumstnces I am successful at ignoring such annoying nudges.


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Cottage Grove City Council raises development charges
Serena Markstrom
COTTAGE GROVE � The cost of new construction in Cottage Grove will go up immediately after the City Council on Monday approved an update to the city�s fee schedule that ties so-called systems development charges to a national index.
The charges, known as SDCs, will go up by 2.24 percent because that is how much infrastructure construction costs are believed to have increased in the past year.
The council amended the fee schedule to increase SDCs using calculations published in Engineering News-Record, based on averages in 20 U.S. cities.
The News-Record is a weekly magazine that provides news, analysis, data and opinion for the construction industry.
The city charges the fee with building permits for residential and commercial projects � mainly new construction but also expansions and remodels, city engineer Ron Bradsby said. The fee is intended to help recover the city�s costs in extending services to new and upgraded developments.
Based on a residential unit of less than 2,650 square feet, the SDC fee for parks will go from $1,901 to $1,944; for storm drainage, it will go from $694 to $710; and for street infrastructure, it will bump from $1,663 to $1,700.
The fee for street infrastructure varies, in part based on how much traffic a new structure is expected to generate during peak afternoon hours, Bradsby said. Small convenience stores, gas stations and grocery stores all have a different rate attached to them, he said.
SDCs for water and wastewater are based on the number of fixtures such as toilets, sinks and hose bibs. The SDC rate for water now will climb from $237 to $242, and the rate for wastewater will bump up a buck, from $48 to $49.
The amount paid is based on 2,650-square-foot increments for residential and commercial, but commercial projects do not have to pay SDCs for parks, Bradsby said.
Bradsby, who presented the SDC fee amendment to the council, said certain construction costs decreased in recent years, only to inflate in the past year.
�It�s gone up more because we are starting to see more work,� Bradsby said before the council meeting.
The Engineering News-Record calculates its inflation rates based on the cost of such materials as concrete, rock, pipe and asphalt, as well as on building costs.
The city last approved changes to its SDCs in February of last year.
In another matter, the council on Monday decided against going into an agreement with the state Department of Transportation to spend federal money to expand Gateway Boulevard at the Interstate 5 southbound offramp.
Bradsby said the city got $90,000 in federal appropriations to buy land to widen the street on its south side, in order to add a northbound right-turn lane.
The transportation department last made improvements to the area in 2004, but opted for a less expensive design that did not include the extra lane, even though it had been deemed the best way to make traffic more efficient, Bradsby said.
Because the project would have been an add-on to the transportation department project, the city would have needed to fund it, to the tune of $210,000 in construction costs above the $90,000 in federal funds. The city has already spent about $10,000 on the project for preliminary design, consultant fees for a traffic study and environmental analysis.
In voting to not go forward with the project, the city will return the $90,000, including the $10,000 it has already spent, City Manager Richard Meyers said during the meeting.
The council consensus was that there are higher-priority traffic projects and that to take the $90,000 in order to spend $210,000 in city funds would be a waste of money.
Mayor Thomas Munroe noted that the Department of Transportation already has rebuilt the area twice.
�It sounds like, pardon the expression, a boondoggle,� he said.


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Q: Conflict in fold settings with filetype plugins I am trying to configure vim to properly fold both html and javascript. Both are working the way I'd like them to when I only open javascript files or html files, but if I open an html file, then open a javascript file, then open another html file, the indentation settings seem to have been overwritten and there is no folding in the html file.
Relevant code:
~/.vimrc
filetype plugin indent on
syntax on

~/.vim/after/ftplugin/html.vim
setlocal shiftwidth=2
setlocal softtabstop=2
setlocal foldmethod=indent

~/.vim/after/ftplugin/javascript.vim
setlocal foldmethod=syntax
setlocal shiftwidth=2
setlocal softtabstop=2
let foldlevelstart=1
let javaScript_fold=1

I am opening two files like this:
vim ./thing.html ./thing.js

Initially the html file is open and folded as I expect, then I switch to the javascript file with :b thing.js and it is also folded as i expect. Then I switch back to my html file :b thing.html and there is no folding any more. Checking :set foldmethod? shows that the foldmethod of the html file has been changed to syntax. Why is this? The problem is adding this "let javaScript_fold=1" Having this line seems to be responsible for changing my html folding method, but without it my javascript wont fold properly.

redpajama_set_name: RedPajamaStackExchange


text:
Sugarcult Start Static (20th Anniversary Edition)
20th ANNIVERSARY LP WITH 3 BONUSTRACKS
Start Static is American rock band Sugarcult's debut studio album. Originally released in 2001, the delivered three hit radio singles: "Bouncing Off The Walls," "Pretty Girl" and "Stuck in America." These singles drove the album to mainstream success, with songs featured across MTV's Laguna Beach and support tours with Blink-182, Jimmy Eat World and Green Day.
Sugarcult's debut album avoids settling into the comfortable, predictable territory of a single genre. Instead, the band brings together the universal qualities from all the music they love. While the record subscribes to the don't-bore-us-get-to-the-chorus approach of power pop, it's the don't-give-a-fuck attitude of seminal punk rock that forms the backbone of Start Static.
START STATIC is anything but pop-punk by numbers. It has a spikey anthemic edge to it that hasn't been heard in many a year, which when mixed alongside the more classic songwriting style that front man Tim Pagnotta adopts, combines to come up with some of the most bouncy tracks you'll hear all year. It also makes for a record which is as chaotic as it is sane. In short it's bloody essential." – Punktastic
This release celebrates the 20th anniversary of the album and features three bonus tracks.
Stuck In America
Hate Every Beautiful Day
Bouncing Off The Walls
Daddy's Little Defect
Lost In You
Pretty Girl (The Way)
Crashing Down
How Does It Feel
I Changed My Name
Say I'm Sorry
Bouncing Off The Walls (Live)


The Department Head Certification Training (DHCT) is held in conjunction with the Summer Leadership Development Workshop.
The 2019 Department Head Certification Training (DHCT) face-to-face workshop will meet on Monday, June 17 from 9:00 am - 4:00 pm. It is held in conjunction with the Summer Leadership Development Workshop (LDW) that will meet on Tuesday, June 18 from 9:00-4:00, and on Wednesday, June 19 from 9:00-12:00 noon. Both the DHCT and the LDW are pre-conference events for the AIESEP 2019 International Conference (https://aiesep2019.adelphi.edu/).
Add 2019 Department Head Certification Training to my calendar.


Sensolus worked hard to achieve the deadline of the product launch of Sensolus SNT Trackers at the Mobile World Congress 2015. After a serious team effort of long days and short nights, the Sensolus SNT service was launched in Barcelona. And yes, the first customers already signed up. At the same conference, the roll out of the communication network in Belgium was announced. This opens great opportunities for new Internet of Things applications in our backyard.