text:
\section{Introduction}
An understanding of flow and transport processes in geologically disordered
media is necessary for the efficient extraction of fluids from underground
hydrocarbon reservoirs. Situations where flow proceeds through networks of
connected fractures are particularly attractive, because the throughput is
generally much higher than may be achieved through intergranular porosity alone
\cite{adler,berkowitz,dietrich,sahimi}.  An important feature of subsurface
fractures, which considerably
complicates the problem, is that the surfaces of naturally fractures rocks are
not smooth or even randomly rough, but rather are highly correlated self-affine
fractals \cite{bouchaud}. A second complication in the analysis is that typical
reservoir fluids are often complicated mixtures, which exhibit non-Newtonian
flow behaviors such as shear-thinning or shear-thickening.  Yet a third
difficulty is that the subsurface fracture flow often involves much higher
velocities than in the intergranular case, and the common simplification of
low-Reynolds number linear flow is inapplicable.

In this paper we use lattice Boltzmann calculations to elucidate the combined
effects of self-affinity, non-linear rheology and finite inertia in fluid flow
through a single fracture.  Previous authors have considered subsets of these
complications, but not all three simultaneously.  The flow of Newtonian fluids
in self-affine fractures at both low
\cite{drazer2000:permeability,drazer2002:transport} and finite \cite{skjetne1999:flow}
$Re$ has an extensive literature.
Some controlled experiments on shear-thinning fluids in self-affine fractures at
low $Re$ have been reported \cite{auradou}. Lastly, experiments and
phenomenological models for non-linear fluid motion in intergranular porous
media at various $Re$ are available \cite{chhabra2001:review}. We anticipate
that flow in a fracture can be characterized in a manner similar to the latter
problem, since in both cases the key effect is that the random solid boundary of
the flow domain causes streamlines to wind around. One simplification which we
{\em can} exploit, however, is to focus on two-dimensional flows.  It is well
known that the flow of a single fluid in a straight channel differs only in
detail between two and three-dimensional cases, and furthermore, in porous media
flow in the analogous intergranular case, one sees the same flow laws for both
two and three dimensional geometries.

The approach taken in the paper follows the lines of our previous studies of
permeability \cite{drazer2000:permeability} and transport
\cite{drazer2002:transport} in self-affine fractures based on the
lattice-Boltzmann method, along with a procedure for incorporating power-law
viscosity variation similar to that developed previously \cite{drazer2005:nn}.
The discussion of inertial effects is influenced by previous studies for the
case of a Newtonian fluid in intergranular porous media
\cite{skjetne1999:flow}.
The fracture surface is generated numerically by a Fourier transform algorithm
and discretized on the regular lattice used in the flow problem.  The upper and
lower fracture surfaces bound the allowed nodes in the flow domain, a bounce-back
condition enforces the no-slip boundary condition, and constant forcing
provides a pressure driven flow.  For power-law fluids, the lattice-Boltzmann
relaxation time is adjusted locally in space and time to provide the desired
relation between stress and strain.  The relation between imposed pressure drop
and total fluid flux provides the permeability, and the local flow fields are
analyzed to discuss the velocity, pressure and shear stress variations.
Some background on the flow geometry and calculational method is presented in
Section~\ref{sec:background}, the local analysis of the flow fields in
Sec.~\ref{sec:local}, the discussion of permeability is in Sec.~\ref{sec:perm},
and we summarize in Sec.~\ref{sec:concl}.

\section{Background}
\label{sec:background}

\subsection{Self-affine roughness}

In this subsection we review the characterization of self-affine fractures and
their numerical implementation. We consider a fracture surface without
overhangs, {\em i.e.}, the surface height $h(x,y)$ is a single-valued function
of the two coordinates $\mathbf{r}=(x,y)$ lying in the mean plane of the
surface. A {\em self-affine} fractal surface is one which displays different
scaling along the different spatial directions\cite{feder}, a statistical
self-similarity under the transformation
\begin{equation}
x \rightarrow \lambda x \mbox{ and } y \rightarrow \lambda y \Rightarrow
h(\mathbf{r}) \rightarrow \lambda^{\zeta} h( \mathbf{r} )
\end{equation}
where $\zeta$ is the Hurst or roughness exponent. Observations of a variety of
naturally fractured rock surfaces in different fracture modes yield just two
common values of $\zeta$, approximately 0.5 and 0.8. We further assume that the
surface has spatial isotropy in its mean plane. The surface is further
characterized by the amplitude of the roughness, or equivalently the prefactor
$C_0$ in the height-height correlation function,
\begin{equation}
\langle [h(\mathbf{r+\Delta})- h(\mathbf{r})]^2\rangle = C_0
(|\mathbf{\Delta}|/\ell)^{2\zeta}
\label{eq:cf}
\end{equation}
where the intrinsic length scale $\ell$ might be the grain size in experiment or
the lattice spacing in a calculation. In practice we generate self-affine
surfaces using the a Fourier synthesis method \cite{voss} as in
\cite{drazer2000:permeability}.

A self-affine fracture channel is made of two complementary self-affine surfaces
separated by a gap, and in some cases the surfaces are shifted relative to each
other parallel to the mean plane. The statistical properties of the fracture are
specified by the Hurst exponent, the mean aperture between two surfaces, the
shift distance, if any, and by the amplitude of the roughness. The height
fluctuations of a single self-affine surface increase with its lateral extent
$L$, so that the difference between the maximum and minimum heights scales as
$(L/\ell)^\zeta$, and we consider the limit $H\ll R < L$, as shown for a typical
fracture in Fig.~\ref{fig:saff-geom}.

\begin{figure}[htb]
\begin{center}
\includegraphics[width=0.8\linewidth]{velgeometry.ps}
\caption{Geometry of a typical self-affine fracture composed of two
complimentary self-affine surfaces with $\zeta$=0.8. \label{fig:saff-geom}}
\end{center}
\end{figure}

Note that the effective flow diameter of the fracture varies along its length
and can be much smaller than the mean aperture, due to the tortuosity of the
channel.  When a lateral shift is present, the aperture varies locally as well, and
furthermore if $H$ is too small the sides of the fracture may overlap.

\subsection{The lattice-Boltzmann method}
Since the flow domain is bounded by highly irregular surfaces, the lattice Boltzmann
method \cite{succi} is particularly convenient for fluid mechanical calculations, since
the excluded solid region may be simply specified by a mask.
If $f_i(\mathbf{x},t)$ is the velocity distribution function (VDF) for particles moving
in direction $i$ at lattice site $\mathbf{x}$ at time $t$, then the discrete Boltzmann
equation which evolves the distribution is
\begin{equation}
f_i(\mathbf{x}+\mathbf{e}_i, t+1)
=f_i(\mathbf{x},t)+\Omega_i(f(\mathbf{x},t)),
\label{eq:lbm}
\end{equation}
Here the $\mathbf{e}_i$ are unit lattice vectors, the lattice
spacing and the time step are both set equal to one,
$\Omega_i(f(\mathbf{x},t))$ is collision operator which
redistributes the VDF along different directions, and the spatial and temporal step
discretizes in single unit. To
recover the Navier-Stokes equation of fluid flow starting from
Boltzmann equation, moments of the VDF satisfy the constraints
\begin{equation}
 \rho=\Sigma_i f_i \quad  \rho\mathbf{u}=\sum_i f_i \mathbf{e}_i \quad
\mbox{\boldmath $\sigma$} = -\rho c_s^2\,\mathbf{I} -
(1-{1\over 2\tau})\sum_i f_i \mathbf{e}_i \mathbf{e}_i
\end{equation}
which relate the distribution function to the continuum density, velocity and stress fields,
and where $c_s$ is the sound speed.  The collision operator is treated in the
BGK approximation using a single characteristic relaxation time $\tau$,
\begin{equation}
 \Omega_i(f(\mathbf{x},t))=-\frac{1}{\tau}(f_i(\mathbf{x},t)-
f_i^{eq}(\mathbf{x},t)),
 \label{eq:bgk}
\end{equation}
where $f_i^{eq}(\mathbf{x},t)$ is equilibrium distribution function. The
relaxation time $\tau$ is related to the kinematic viscosity of the fluid  by
$\nu=(2\tau-1)/6$. To simulate a constant pressure gradient we add a
a constant body force term to the right hand side of eq.\ref{eq:lbm}.
equation eq.\ref{eq:lbm} and \ref{eq:bgk} to Navier-Stokes equation.
More details may be found in \cite{succi}, and a recent review of flow simulations in
this context is presented by Verberg and Ladd\cite{verberg2001:lbmreview}.

\subsection{Power-law fluids}
The basic idea in extending the lattice Boltzmann method to
power-law fluids was presented by Aharonov and Rothman
\cite{rothman1993:nonNewtonian}, and consists of adjusting the
relaxation time $\tau$ {\em locally} so as  to achieve the desired
ratio of stress to strain rate. Here we consider power-law fluids
using a generalized Newtonian model, as in
\cite{drazer2005:nn}, where the relation between the stress
tensor $\sigma_{\alpha\beta}$ and the strain rate tensor
$D_{\alpha\beta}=1/2((\partial_\beta u_\alpha+\partial_\alpha
u_\beta)$ is similar to that for Newtonian fluids,
$\sigma_{\alpha\beta}=2\mu D_{\alpha\beta}$, but the local viscosity
$\mu$ is a function of the invariants of the strain rate tensor. We
consider power-law fluids, $\mu=m \dot{\gamma}^{n-1}$, where the
case $0<n<1$ corresponds to shear-thinning,  $n>1$ corresponds to
shear-thickening, and $n=1$ recovers linear Newtonian fluids, where
the local shear rate $\dot\gamma$ is related to the second invariant
of $D_{ij}$ via $\dot\gamma=\left(2\mathbf{D:D}\right)^{1/2}$. The
procedure in \cite{drazer2005:nn} was to obtain the strain
rate tensor by numerical differentiation of the previously
calculated velocity field, then determine the appropriate local
viscosity and thence the local relaxation time. Here we adopt a
different procedure:  in the lattice Boltzmann method the strain
rate tensor is directly related to the velocity distribution
function by \cite{chen1998:lbm-review}
\begin{equation}
D_{\alpha\beta}= -
\frac{3}{2\rho\tau}\sum_i{(f_i- f_i^{eq})\mathbf{e}_{i\alpha}\mathbf{e}_{i\beta}};
\end{equation}
which should in turn equal $\sigma_{\alpha\beta}/2\mu$, there is a constraint on the
$f_i$ which is solved by iteration.

To validate the formulation of power-law fluids given above, we calculate the
velocity profile for pressure-driven flow in a smooth-walled channel of constant
aperture (a Hele-Shaw cell), which may be compared to an analytic solution of the
Navier-Stokes equation. Applying a pressure gradient $\Delta P/L=-G$ in the
$x$-direction, the velocity for a power-law fluid with rheological parameters $m,n>0$
as above in a channel of width $H$ is
\begin{equation}
    u_x(y)=\frac{n}{n+1}\left(\frac{G}{m}\right)^{1/n} \left(
\left|\frac{H}{2}\right|^{(n+1)/n}-\left| \frac{H}{2}-y\right|^{(n+1)/n} \right),
    \label{eqn:vpower-law}
\end{equation}
We also record the mean velocity $\overline{u}$ and the fluid flux $Q$
(per unit length in the passive third direction), which will be useful below:
\begin{equation}
Q = H\overline{u}=\int_0^H dy\, u_x(y) =
{n\over 2n+1}\left({H^2\over 2}\right)\left(\frac{GH}{2m}\right)^{1/n}
    \label{eq:flux}
\end{equation}
In the simulation, we begin with zero velocity and integrate Eq. (\ref{eq:lbm})
to steady state, using the convergence criterion
\begin{equation}
    \epsilon=\sum_x \frac{\Vert u(\mathbf{x},t)-u(\mathbf{x},t-1) \Vert}{\Vert
u(\mathbf{x},t)\Vert}<1.0\times10^{-6},
\end{equation}

For power-law indices $n$=0.75, 1.0 and 1.25, $m$=0.01, and pressure
gradient $G=1\times 10^{-6}$ we obtain the profiles shown in
Fig.~\ref{fig:vvalid-n75}, which agree with theory. In practice, as
with any numerical method, computational instabilities may occur for
substantially different values of the pressure gradient and fluid
index, but the algorithm could be extended there using techniques
such as multi-time step relaxation for the local shear viscosity
\cite{sullivan2006:porous}.
\begin{figure}[htb]
\begin{center}
\includegraphics[scale=.2,angle=-90.]{valid-2pw-n-0.75.ps}
\includegraphics[scale=.2,angle=-90.]{valid-2pw-n-1.0.ps}
\includegraphics[scale=.2,angle=-90.]{valid-2pw-n-1.25.ps}
\caption{Velocity profiles of power-law fluids with $m=0.01,n=0.75,1.0,1.25$
in a Hele-Shaw cell with pressure gradient $G=1\times 10^{-6}$.
The points are simulation results while the solid lines are the analytical solution
in (\ref{eqn:vpower-law}).  The maximum velocities for the three fluids are
$u_{max}=0.006,0.048,0.169$, respectively.}
\label{fig:vvalid-n75}
\end{center}
\end{figure}

\section{Local analysis of the flow field}
\label{sec:local}
We wish to examine how the local flow behavior varies with the
rheology of the fluid, at different geometrical features of a
self-affine channel.  We focus on a single realization of the
fracture, shown in Fig.~\ref{fig:saff-geom}, and vary the power law
index $n$ and the pressure gradient $G$.  The complete simulation
box has length $L=256$ in the flow direction and width $W=80$, in
terms of the (unit) lattice spacing, and the (constant) vertical
aperture is $H=20$. A uniform pressure gradient is
applied everywhere along the channel, as above, and periodic
boundadry conditions are applied in the flow direction. Local
minimum in the effective width (normal to the average flow) occur
around $x$=55, 110, and 240 where mass conservation implies the velocity magnitude
will be a maximum, irrespective of the rheology of the fluid.  In
Fig.~\ref{fig:vstream-75}, we show velocity fields and streamlines
for the three fluids along a segment of the fracture channel
$20\lesssim x\lesssim 100$ in Fig.~\ref{fig:saff-geom} which
includes a constriction, for applied pressure gradient $G=1\times
10^{-6}$. As we see, the streamlines are tortuous and very roughly
follow the channel walls, although recirculating eddies (closed
vortices) {\em may} occur where the channel exhibits side branches
or dead-end regions.  Indeed, at the present flow rate an eddy
appears in the shear-thickening case but not the others, presumably
because the velocites are higher in that case.

\begin{figure}[htb]
\begin{center}
\includegraphics[scale=.15]{vstream-n75-p1e-6.ps}
\includegraphics[scale=.15]{vstream-n100-p1e-6.ps}
\includegraphics[scale=.15]{vstream-n125-p1e-6.ps}
\caption{Segment of Velocity vector field with streamlines of the flow for
power-law fluid with $m=0.01, n=0.75(top),1.0(middle),1.25(bottom)$ and the
pressure gradient applied is $G=1\times 10^{-6}$. The segment extends from
$x=20$ to $x=100$.}
\label{fig:vstream-75}
\end{center}
\end{figure}

\subsection{Velocity field}

First we examine the variation of maximum absolute velocity along the channel, in
order to show how the fluid rheology influences the earlier results of Skjetne {\em et
al}. \cite{skjetne1999:flow} for the Newtonian case.  More precisely, for
each $x$ along the channel we compute the maximum over $y$ of $|\mathbf{u}(x,y)|$,
although we would have reached the same qualitative conclusions had we considered the
maximum over $y$ of $u_x(x,y)$.  Calculations were performed for three values
of the pressure gradient, $G=1\times 10^{-6}$, $5\times 10^{-5}$ and
$2\times 10^{-4}$, which correspond to Reynolds numbers $Re=0.95$, 37.0 and 92.7,
respectively, for the
Newtonian fluid.  Since the viscosity varies within the channel for the shear thinning
and thickening fluids, there is no unique definition of $Re$ in those cases, although
a convenient choice will be introduced in Section~\ref{sec:perm} for scaling purposes.

The resulting plots of maximum velocity are shown in Fig.~\ref{fig:maxv-n}, where each
velocity is normalized by the average streamwise flow velocity $\overline{u_x}$
(referred to as
the interstitial velocity $u^*$ in \cite{skjetne1999:flow}), which equals the
flux divided by the channel width.
Obvious peaks appear at the positions of the visible constrictions in the channel near
$x=55$, 110 and 240, reflecting the narrowed aperture there. The normalized
peak heights are
fairly insensitive to the Reynolds number, although away from the peaks the trend is
for maximum velocity to increases with $Re$.  Note that for a flat  channel, the
the normalized maximum absolute velocity would equal 1.5, so the values of 5 or more
seen here are a substantial enhancement.  The peaks are not {\em all} closely correlated
with channel constrictions, however:  near $x=70$ and 130 maximum velocity peaks occur,
but at these locations the channel is expanding just downstram of a constriction.
It is also possible to calculate a ``maximum velocity trajectory'', following
\cite{skjetne1999:flow}, as the set of $(x,y)$ gridpoints which at each $x$ has the
$y$-value corresponding to the position where the maximum velocity occurs.  For
the most part our observations concerning the behavior of these trajectories is
similar to that reported in this reference, but
we do not observe the line-length of this trajectory decreasing
monotonically with $Re$.
\begin{figure}[htb]
\begin{center}

\includegraphics[scale=.2,angle=-90.]{norm-vmagmax-n-0.75.ps}
\includegraphics[scale=.2,angle=-90.]{norm-vmagmax-n-1.0.ps}
\includegraphics[scale=.2,angle=-90.]{norm-vmagmax-n-1.25.ps}
\caption{Maximum absolute velocity along the fracture channel for shear-
thinning({\em top}, $n$=0.75),Newtonian({\em middle}, $n=1.0$), and shear-
thickening({\em bottom}, $n$=1.25) fluids for various applied pressure
gradient $G$. Each maximum velocity curve is normalized by the corresponding
$\overline{u_x}$,
the average flow velocity in the $x$-direction.}
\label{fig:maxv-n}
\end{center}
\end{figure}

Comparing the other fluids to the Newtonian case, we see in Fig.~\ref{fig:maxv-n} that
the global maximum absolute velocity always occurs at the narrowest constriction near
$x=110$  and the other primary peaks always occur at the same positions, $x=55$ and
240, as well.  Furthermore, each peak has roughly the same (normalized) velocity
value.  In the shear-thinning case, both the variation in $x$ away from the
peaks/constrictions and the variation with pressure gradient are weaker than in the
other cases, which may be attributed to the fact that typical velocities in the
fracture are smaller in this case, and inertial effects play a weaker role.
In the shear-thickening case, where typical
velocites are larger, the maximum velocity values are larger off the peaks values,
and furthermore exhibits rather more variation with $x$ and $Re$ than the other fluids.

The probablity distribution of velocity magnitudes is also of interest
\cite{skjetne1999:flow},
since the presence of low and high velocity components strongly influences mixing
processes and transport of passive tracers and suspended particles \cite{guyon}.
Histograms of the observed absolute value of the velocity for the three fluids at
various pressure gradients are shown in Fig.~\ref{fig:velfreq}.  In all cases there is
a peak near the origin, which reflects the numerous low-velocity zones in the
crevasses at the fractures walls, along with a higher-velocity peak resulting from the
rapid flow in the channel constrictions.  The latter moves out to higher values as the
pressure gradient increases (note the normalization by $\overline{u_x}$ in the figure)
Once again, the shear-thickening case behaves somewhat differently than the other two
fluids, showing a less prominent and broader ``constriction peak,'' and more variation
with $G$.
\begin{figure}[htb]
\begin{center}
\includegraphics[scale=.2,angle=-90.]{velfreq-nonNw-p1e-6.ps}
\includegraphics[scale=.2,angle=-90.]{velfreq-nonNw-p5e-6.ps}
\includegraphics[scale=.2,angle=-90.]{velfreq-nonNw-p1e-5.ps}
\caption{Distribution of normalized absolute velocity in the whole self-affine
fracture flow domain for different power-law fluids with pressure gradients
$G=1.0e-6$, $5.0e-6$ and $1.0e-5$ (top to bottom).}
\label{fig:velfreq}
\end{center}
\end{figure}

\subsection{Pressure and stress field}
The distribution of pressure and stress in the fluid are important for non-Newtonian
rheology, and in considering possible erosive processes on the fracture walls.
To contrast the behavior of the different fluids, Fig.~\ref{fig:p-diff-n} shows the
pressure ``fluctuations'' along the channel for the three power-law fluids $n=0.75$,
1.0 and 1.25. The fluctuation $p'$ is the deviation in pressure from the imposed
linear gradient, which would vanish identically in a Hele Shaw geometry. In the
figure, the fluctuation has been normalized by the imposed pressure difference,
$\Delta p = GL$, and averaged over the channel width.
For all three fluids, the pressure fluctuation are most significant in the vicinity of
the main constrictions in the channel where the fluid accelerates, rising just before
each constriction's location
and dropping rapidly as it is traversed.  Some additional structure arises at
positions $x$ of bends in the flow path, another source of fluid acceleration.
Again, the shear-thinning and Newtonian
fluids behave somewhat similarly, while the variation is strongest in the
shear-thickening case.
\begin{figure}[htb]
\begin{center}
\includegraphics[scale=.3,angle=-90.]{pressurefluct-p1e-5-norm.ps}
\caption{Normalized pressure fluctuation along the channel for different power-law
fluids, at pressure gradient $G=1.0e-5$.}
\label{fig:p-diff-n}
\end{center}
\end{figure}

The variation in fluctuation with imposed gradient is shown in
Fig.~\ref{fig:p-n}, and indicates the expected general increase in magnitude with $G$
along the channel.
\begin{figure}[htb]
\begin{center}
\includegraphics[scale=.2,angle=-90.]{pressurefluct-n-0.75-norm.ps}
\includegraphics[scale=.2,angle=-90.]{pressurefluct-n-1.0-norm.ps}
\includegraphics[scale=.2,angle=-90.]{pressurefluct-n-1.25-norm.ps}
\caption{Pressure fluctuations of different fluids with power $n=0.75, 1.0,
1.25$ and $m=0.01$ along a self-affine fracture channel under different applied
pressure gradients.}
\label{fig:p-n}
\end{center}
\end{figure}

To assess the effects of the flow on the fracture wall, we first calculate the average
force exerted by the fluid on the wall,
\begin{equation}
\mathbf{F} = {1\over L}\int d\ell\, \mbox{\boldmath $\hat{n}\cdot\sigma$}
\end{equation}
where the integral runs over the fracture surface (a curve in this two-dimensional
calculation), and $\mathbf{\hat{n}}$ is the local normal to the wall. The force is
then decomposed into $x$ and $y$ components, representing the average drag and thrust on
the wall, respectively, and then normalized by a typical inertial pressure $\rho
\overline{u}^2/2$ times the nominal surface area $L\times 1$, to give drag and thrust
coefficients
\begin{equation}
 d=\frac{F_x}{L\rho \overline{u}^2/2}, \qquad t=\frac{F_y}{L\rho \overline{u}^2/2}.
\end{equation}
Note that aside from the (reasonable) use of the inertial pressure, the remainder of the
normalization is somewhat arbitrary but a fixed constant for each fracture, and
mainly serves to provide dimensionless drag and thrust coefficients.
The drag and thrust forces for the lower and upper walls of the channel are similar
but not identical because of the asymmetry of the fluid-solid boundary, and for
definiteness we present only the forces on the lower wall.

The results of calculating the drag and thrust coefficients is shown in
Figs.~\ref{fig:drag} and \ref{fig:thrust} for the three fluids with exponents
$n=0.75,1.0,1.25$.  In all cases, the coefficients exhibit simple power-law behavior,
provided $G$ is not too large,
and the transition to a different behavior at larger $G$ may be associated with the
onset of inertial effects (see the following section).
This form of scaling behavior result is consistent with the experimental results
reported in
\cite{chhabra2001:review}, and the values of the slopes found in the log-log plots in
the low-$G$ range,
-1.67, -1.02, -0.62 for $n=0.75$, 1.0 and 1.25, respectively, for {\em both} drag and
thrust, may be understood from the following argument.

If inertial effects are absent, one expects the scaling behavior in a rough channel
to be the same as in a straight channel.  In that case, from Eq. (\ref{eqn:vpower-law})
one has $u\sim G^{1/n}$, and therefore $\nabla u \sim G^{1/n}$
as well, so that $\mu\sim|\nabla u|^{n-1}\sim G^{(n-1)/n}$.  The drag and thrust
forces are
proportional to the stress, $\sigma\sim \mu\nabla u\sim G^{(n-1)/n+1/n}\sim G^1$.
The drag and thrust {\em coefficients} are then
$d,t\sim F_{x,y}/\overline{u}^2\sim \sigma/u^2\sim G^{1-2/n}$,
giving exponents -5/3, -1 and -3/5, respectively, for the three fluids.

\begin{figure}[htb]
\begin{center}
\includegraphics[scale=.3,angle=-90.]{drag-friction-factor.ps}
\caption{Drag factor $d$ for power-law fluids in a self-affine fracture channel
as a function of applied pressure gradient.}
\label{fig:drag}
\end{center}
\end{figure}
\begin{figure}[htb]
\begin{center}
\includegraphics[scale=.3,angle=-90.]{thrust-factor.ps}
\caption{Thrust factor $t$ for power-law fluids in a self-affine fracture channel
as a function of applied pressure gradient.}
\label{fig:thrust}
\end{center}
\end{figure}

\section{Permeability}
\label{sec:perm}
Next we consider global behavior -- the permeability of a self-affine fracture channel.
Our discussion is colored by analogies to flow in intergranular porous media,
so we first recall the situation in that system \cite{bear}.
For Newtonian fluids in the low Reynolds number limit, the definition of intergranular
permeability is given by Darcy's law, $\langle\mathbf{u}\rangle = -(k/\mu) \nabla p$, where
$\langle\mathbf{u}\rangle$ is the average flow velocity and $p$ the average pressure.
The average
in question could be a volume average or an ensemble average, and for a flow which is
macrosopically unidirectional, an operational definition of permeability is
$k=\mu Q L/A\Delta p$ where $Q$ is the flux through a sample of cross-sectional area
$A$ and length $L$.  In a two-dimensional situation, the area is replaced by the width
$W$, and $Q$ is the flow per unit length in the third direction.  A definition identical
to the latter case may be used for the permeability of low Reynolds number Newtonian
flow in a fracture.  Both finite Reynolds number flow and non-Newtonian fluid rheology
modify this description.  We first consider the effects of inertia, and then examine
how permability relates to the fracture morphology.

\subsection{Inertial effects}

At higher flow rates when inertial effects appear, the
relation between pressure difference and average velocity or flux becomes nonlinear
and one may write
\begin{equation}
\Delta p = \alpha Q + [\,\beta Q^2\mbox{  or }\gamma Q^3]
\label{eq:forch}
\end{equation}
where $\alpha$ incorporates the Darcy permeability, and the term in brackets is
the inertial correction, with $\alpha,\beta >0$.  At high $Q$ the quadratic
or ``Forchheimer'' term applies,
but in the transitional region where the Reynolds number is small but finite, a
cubic dependence is
found. This picture is supported by experiments, analytic calculations, and numerical
simulations \cite{koch}.

The flow of a Newtonian fluid in a self-affine fracture can be described in identical
terms, as
shown by the numerical simulations of Skjetne {\em et al}. \cite{skjetne1999:flow}
which exhibit the same transitions between flow regimes indicated in
Eq.~(\ref{eq:forch}).
In extending the discussion to power-law fluids, the first issue is to choose the
appropriate power of $Q$.
The exact solutions for Hele Shaw flow given in Eq.~(\ref{eq:flux}) have the scaling
behavior $G\sim Q^n$ where $G$ is the applied pressure gradient (the relevant pressure
for macroscopic behavior) and $n$ the power-law index.  In a rough fracture, one would
naturally expect an identical relation, albeit with a modified coefficient, at
low $G$, and then at larger $G$ inertial effects would be expected to produce
(positive) terms involving higher powers of $Q$.  To test this idea, note that
we are concerned here with the statistical
behavior of self-affine fractures, rather than the details of flow in one particular
geometry which was relevant in the previous section, so
an ensemble average over six realizations of the fracture surface is used.
The simulation results are shown in Fig.~\ref{fig:trans-1}
\begin{figure}[htb]
\begin{center}
\includegraphics[scale=.3,angle=-90.]{transition-n-0.75.ps}
\includegraphics[scale=.3,angle=-90.]{tran-valid-n-1.0.ps}
\includegraphics[scale=.3,angle=-90.]{transition-n-1.25.ps}
\caption{Relation between imposed pressure gradient and fluid flux for power law
fluids:  $n=0.75$, 1.0 and 1.25 (top to bottom).
\label{fig:trans-1}}
\end{center}
\end{figure}
and indeed show a $G\sim Q^n$ scaling behavior at low $G$.  The Newtonian $n$=1 plot
shows this behavior clearly since $G/Q^n$ is constant at low $Q$, whereas in the other
cases, the expected behavior is present at sufficently small $Q$ as indicated in the
alternative plots in the insets of $G$ {\em vs}. $Q$.
The need for different plotting variables arises becuase in the non-Newtonian cases,
the flow rate fluctuates substantially at low $G$ and division by $Q^n$ is numerically
unstable.  Beyond the quasi-linear regime, the Newtonian case shows the expected
trasition to a Forchheimer flow regime $G\sim Q^2$ at larger forcing, and the
shear-tickening fluid shows a somewhat analogous behavior $G\sim Q^{2n}$.  The
shear-thinning fluid is not described by a simple power law at large $G$, and we are
not aware of any theoretical treatment of this problem, so we simply report the
numerical results.

To understand the numerical coefficient in the flow results, the fracture-modified
Darcy permeability, we again refer to the Hele Shaw case and define
\begin{equation}
k=\frac{m^{1/n} \overline{u}}{G^{1/n}}.
    \label{eq:k-power-law}
\end{equation}
Since the roughness and tortuosity of the fracture cause the stramlines to bend and
viscous dissipation to increase, the permeability should be reduced compared to a
smooth and flat Hele Shaw geometry of the same aperture.  In Table I, the various
permeabilites are compared, and a reduction by a factor 6-7 is found.

\begin{table}
\begin{center}
\begin{tabular}{|l|c|c|} \hline
fluid index &   $k_0$   &   $k$ \\ \hline
$n=0.75$    &   2.99    &   0.373   \\ \hline
$n=1.0$     &   33.2    &   4.73    \\ \hline
$n=1.25$    &   142 &   20.6    \\ \hline
\end{tabular}
\end{center}
\caption{Effect of roughness and tortuosity on the low Reynolds number permeabilty:
$k_0$ and $k$ are the permeabilitites (defined in Eq.~(\ref{eq:k-power-law}) for a
Hele Shaw cell and a self-affine fracture of the same mean aperture, respectively.}
\end{table}

So far, we have expressed the pressure gradient $G$ in terms of the flux $Q$,
because these quantities are well defined in the present simulations.  However, for
general purposes It is preferable to use a dimensionless quantity such as the Reynolds
number as the independent variable, but the definition of $Re$ for power-law fluids is
not entirely obvious for power-law fluids because the
the viscosity varies over the flow domain.  One way to combine the results for
different fluids is based on an analogy to the friction factor scaling laws for flow
in pipes originally due to Nikaradze \cite{schlichting}, which can be extended to
non-Newtonian fluids as shown by Metzner \cite{metzner}.  Recall that
for unidirectional flow of a Newtonian fluid of viscosity $\mu$ in a pipe of diameter
$D$, the mean velocity is $\overline{u} = GD^2/32\mu$ and the shear stress at the wall is
$\tau_w = GD/4$, so if one defines the conventional friction factor as
$f=\tau_w/{\scriptstyle {1\over 2} }\rho\overline{u}^2$, then one finds $f=16/Re$
where $Re=\rho\overline{u}D/\mu$.
Experiments follow this scaling law up to a value of $Re$ that depends on the roughness
of the pipe, and at larger values of $Re$, $f$ levels off.  An analogous calculation
for Hele Shaw flow using the aperture $H$ instead of the diameter $D$ gives
$\tau_w=GH/2$ and
$f=12/Re$.  The power-law generalization is to use the latter form for $\tau_w$,
along with Eq.~(\ref{eq:flux}) to express the pressure gradient in terms of the mean
velocity, and yields
\begin{equation}
f={12\over Re}\qquad\mbox{if}\quad Re \equiv 6\rho \overline{u}^{2-n}H^n/m',
\label{eq:re}
\end{equation}
where $m'=m (2(2n+1)/n)^n$.  This choice of variables is not the last word,
because in the analogous interganular porous medium case where a similar approach
has been taken \cite{chhabra2001:review}, extra constant factors such as functions of
the porosity or the ``dynamic specific surface area'' are introduced into the friction
factor and Reynolds number definitions to promote data collapse.  It is not clear how
such ad hoc factors might be interjected here, so instead we collapse the data using
a simple constant factor which varies from fluid to fluid, and the result is shown in
Fig.~\ref{fig:re-f-zeta-n}.  Two different values of the Hurst exponent are shown, and
in both cases we see an $F\sim 1/Re$ scaling at low $Re$, a transition at $Re\sim 1-10$
and perhaps a constant friction factor at larger $Re$.  Unfortunately, the
calculations cannot be extended into the latter regime using the present
method (a particluar implementation of the lattice Bolzmann technique) becuase
numerical instabilites arise.
\begin{figure}[htb]
\begin{center}
\includegraphics[scale=.3,angle=-90.]{zeta-collapse-re-f.ps}
\caption{Friction factor of self-affine fracture channels of Hurst exponent
$\zeta=0.5$ and $0.8$ as a function of Reynolds number defined as in \ref{eq:re}
for power-law fluids with $n=0.75,1.0,1.25$. \label{fig:re-f-zeta-n}}
\end{center}
\end{figure}

\subsection{Morphology effects}
We now consider how the geometry of the fracture effects the (low-Reynolds number)
permeability for the various fluids considered.
First we investigate the effect of the Hurst exponent $\zeta$ on the permeability,
and to simplify the analysis we consider
a fracture channel with one self-affine wall and one flat wall, as in
\cite{drazer2000:permeability}. For a fixed presure gradient $G$, we compute the flux
as a function of the channel length $L$ for the three fluids, and
in Fig.~\ref{fig:pw-saff-p}, we first show the flow rate depletion $(Q_0-Q)/Q_0$
{\em vs}. $L$ for a fracture with $\zeta=0.8$.  Here $Q_0$ is the flux through a
flat-walled channel fo the same mean aperture.  Increasing the length allows for more
fluctuation in the channel width (see Eq.~(\ref{eq:cf}) which increases the tortuosity
and tends to decrease the flux.  If the Hurst exponent of the channel's rough wall is
instead $\zeta=0.5$, the three fluids again behave quite similarly, so it suffices to
compare the behavior of different Hurst exponents for a single case,
and in the lower panel of the figure we plot the flux depletions for the two exponents
for the shear-thinning case.  The fact that the flux depletion is greater for the
$\zeta=0.8$ channel may be explained by noting that this exponent value corresponds to
more fluctuation as a function of $L$ than the 0.5 case, and therefore to a more
tortuous channel.
\begin{figure}[htb]
\begin{center}
\includegraphics[scale=.3,angle=-90.]{rel-saff-pw-zeta-0.8.ps}
\includegraphics[scale=.3,angle=-90.]{rel-n-0.75-diff-zeta.ps}
\caption{Flux variation with length in a channel with one self-affine and one flat
wall for different fluids and Hurst exponents.  The maximum aperture of the channel
is $H_{\rm max}=64$, and the applied pressure gradient is $G=1.0\times 10^{-6}$. Top:
flux depletion for different fluids confined in a channel with $\zeta=0.8$. Right:
flux depletion for a shear-thinning fluid in channels of different $\zeta$.
\label{fig:pw-saff-p}}
\end{center}
\end{figure}

To relate the flux to the channel aperture, we imagine dividing the channel into a
sequence of nearly-straight sections, each of length $\ell_i$,
and writing the total pressure difference as the sum of the pressure drops in each
section, using Eq.~\ref{eq:flux} for each.  This reasoning yields
\begin{equation}
 \Delta P=\sum _i \Delta P_i=\sum_i \left[ Q \cdot \frac{2n+1}{n} \cdot b_i^{-
\frac{2n+1}{n}} \right]^{n} \cdot m \cdot 2^{n+1} \cdot l_{i},
 \label{eqn:dpsegment}
\end{equation}
where the summation is over the sections, and $b_i$ is the effective aperture and
$l_i$ is the length along the local flow direction in
section $i$, and we have noted that $Q$ is a the same in all sections.
If $\theta_i$ is the angle between the orientation of channel section $i$ and the mean
flow direction, then $b_i=H \cos \theta_i$ and
$l_i=l_i^\Vert/\cos \theta_i$, where $H$ is the aperture and $l^\Vert$ is the
projected length of section $i$ in the mean flow direction, assumed to be the same for
all sections.  Using these relations in Eq.\ref{eqn:dpsegment} we have
\begin{equation}
 \Delta P=2mQ\,l^\Vert\left[2 \frac{2n+1}{n} H^{-\frac{2n+1}{n}} \right]^{n}
\sum_i (\cos \theta_i)^{-(2n+2)}.
 \label{eqn:dpseg1}
\end{equation}
This result generalizes
Eq.~26 in \cite{drazer2000:permeability} to power-law fluids, and if we proceed as in
that reference to evaluate the average over angles $\theta_i$ we obtain
\begin{equation}
 Q-Q_0 \sim H^{(2\zeta-2)/\zeta+(2n+1)/n}
 \label{eqn:qdiff}
\end{equation}
where again $Q_0$ is the flux in a flat channel of the same aperture $H$.

To test the relation \ref{eqn:qdiff},
we calculate the flow for fracture channels of length $L=256$ with
varying apertures $H=8,12,16,20,24$, for fluid with $m=0.01$, $n$=0.75, 1.0 and 1.25,
all at a pressure gradient $\Delta P/L=1.0e-6$. Figure~\ref{fig:saff-law} shows the
flux depeltion $(Q_0-Q)$ as a function of aperture.  The points are the numerical
results and the solid lines are fitted curves, based on the expected power-law
exponents obtained from Eq.\ref{eqn:qdiff}, which are 2.83, 2.5, and 2.3 for the
three fluids.  We see that the theoretical analysis is in excellent agreement with the
data for the shear-thinning and Newtonian fluids ($n$=0.75 and 1.0), but the agreement
is less statisfactory for the shear-thickening fluid, whose numerical exponent is
closer to 2.5.  A possible interpretation is that in the shear-thickening case,
for the same pressure gradient the average velocity is larger than that for the other
fluids, so that fluid inertia comes into play.
\begin{figure}[htb]
\begin{center}
\includegraphics[scale=.3,angle=-90.]{saff-256.ps}
\caption{Log-log plot of flow rate variations versus the aperture of self-affine
channel for different fluids with power $n=0.75,1.0$ and $1.25$.
\label{fig:saff-law}}
\end{center}
\end{figure}

Finally, we consider an additional effect, a lateral shift between the two sides of a
fracture, which might arise in practice due to geological processes.
We begin with a fracture channel with complimentary sides and constant initial
aperture $H$, and then shift one side along the mean plane by a distance $d$.
The fracture aperture is now a function of position, $H_d(x)$, and effectively
a spatial random function.  We again compute the flux depletion relative to a flat
channel having the same initial aperture, using six
realizations of a self-affine fracture wall with Hurst exponent $\zeta=0.8$.
As shown in Fig.~\ref{fig:saff-shift} the flux decreases somewhat faster than
linearly with shift, by producing narrow gaps when proturbances on the two sides are
brought closer to one another.  The shear-thinning and Newtonian fluids have a fairly
similar behavior, while the reduction is twice as large in the shear-thickening case,
perhaps again as a result of inertial effects.  As in the previous discussion, using a
different value $\zeta=0.5$ for the Hurst exponent gives the same trends.
\begin{figure}[htb]
\begin{center}
\includegraphics[scale=.3,angle=-90.]{xshift-flowrate.ps}
\caption{Flow rate reduction due to lateral shift along the mean plane of
fracture channel for different fluids with power $n=0.75,1.0$ and $1.25$, and
the Hurst exponent used here is $\zeta=0.8$.
\label{fig:saff-shift}}
\end{center}
\end{figure}

\section{Conclusion}
\label{sec:concl}
Using a new implementation of the lattice Boltzmann method for power-law fluids,
we have investigated their flow in two-dimensional
self-affine fracture channels as a function of applied pressure gradient.
Generally, fluids with different power-law index behave in a similar manner
when their flow parameters are properly scaled, using standard results for flow in
constant-thickness channels.  Many previous results for Newtonian fluids in
self-affince fractures  are found to generalize in a straightforward manner.
However, shear-thickening fluids, which have higher velocities for the same
pressure gradient than Newtonian or shear-thnning counterparts, are more
susceptible to inertial effects.

With regard to the local flow fields, we first considered the maximum absolute velocity
as a function of distance along the mean flow direction, which was found to
fluctuates along the fracture channel due to its tortuosity and the variable
effective aperture along the channel. The local maxima of this maximum
absolute velocity occur at points of narrowing or minimal effective aperture,
and the range of maximum absolute velocity relative to the global mean velocity
ranges from about 1.5 to 5.5.
With increasing inertia, this normalized maximum absolute velocity
increases for all power-law fluids to different degrees, with shear-thickening
fluids having the largest effect and shear-thinning the least.
As the pressure gradient increases, the normalized maximum velocities near
the constrictions are relatively constant but outside these points velocities
tend to increase.  The variation in velocity is greatest for a shear-thickening
fluid and lest for shear-thinning.  Pressure fluctuations along the
channel increase with forcing for all fluids, and for a given pressure gradient
increase with the power-law index $n$.

The relationship between pressure gradient and flux is found to have the same
functional form as for flow in a flat channel, $\Delta p\sim Q^n$, when inertial
effects are absent.  At higher $\Delta p$, Newtonian fluids behave in the same way
as in intergranular porous media, and shear-thinning fluids behave analogously, but
the shear-thickening case does not show simple power-law behavior. It is possible to
collapse all of the data on flux {\em vs}. pressure gradient into a universal
friction factor curve.  The variation of flux with system length was  shown to scale
with system length with an exponent algebraically related to the Hurst exponent,
in a manner which generalizes the Newtonian case.

The most interesting question raised by these results is the form of the flux-pressure
gradient relationship in the regime of strong inertia in the non-Newtonian case.
In this work, we were limited in the range of accessible pressure gradients by
numerical instabiliites, and it is desirable to improve the algorithm so as to
consider higher pressure gradients and further
explore the dynamics of the inertial regime.  An extension of these considerations to
viscoelastic fluids is likewise highly desirable, but new ideas beyond the methods
used here are needed.

\begin{acknowledgments}
This work was supported by the NSF CREST Center for Mesoscopic Modeling and
Simulation at CCNY, and the Geosciences Program of the Office of Basic Energy
Sciences, U. S. Department of Energy. We thank German Drazer and Jean-Pierre
Hulin for helpful discussions and suggestions.
\end{acknowledgments}

redpajama_set_name: RedPajamaArXiv


Larry David, the "social assassin" of Curb Your Enthusiasm and Seinfeld fame, just made the decision for Democratic presidential candidate easier, if for no other reason than we would get four more years of David impersonating Bernie Sanders on Saturday Night Live.
During a parody of the Democratic debate, David stood alongside Alec Baldwin as Jim Webb and Kate McKinnon as Hillary Clinton as he nailed every Bernie-ism from the New York accent ("An-da-sen"), facial expressions and hand gestures. He touched on Clinton's emails, the fact that he's not a billionaire and, of course, the banks. Even Sanders thought the impersonation was spot on.


text:
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Children of the Corn II: The Final Sacrifice (1993)
Belated sequel to the '84 film. 8 years after the first, authorities discover the mutilated bodies of adults in the secluded town of Gatlin, Nebraska and children hiding in the corn. Enter John Garrett and son Danny, who head for Gatlin on a story and get caught up in this mess when an orphan named Micah is possessed by "He Who Walks Behind The Rows".
A witch put to death in 1692 swears vengeance on her persecutors and returns to the present day to punish their descendants.
A new family moves into the house on Elm Street, and before long, the kids are again having nightmares about deceased child murderer Freddy Krueger. This time, Freddy attempts to possess a teenage boy to cause havoc in the real world, and can only be overcome if the boy's sweetheart can master her fear.
Clown (2014)
A loving father finds a clown suit for his son's birthday party, only to realize the suit is part of an evil curse that turns its wearer into a killer.
The 13th Floor (1988)
As a child, a girl witnesses her father electrocute a young boy. When she grows into an adult, the ghost of the murdered boy appears to her, and together they set out to expose the crimes of her father.
Snuff: A Documentary About Killing on Camera (2008)
This documentary examines the existence of films in which people are murdered on camera and the culture surrounding them. Through interviews with former FBI Profilers, Cultural Academics, and Film Historians the documentary delves into the disturbing history and myth of Snuff Films. The FBI claims there is no evidence to prove the existence of Snuff and, therefore, Snuff Films are a myth. This documentary analyzes the relationships between war, cult films, serial killers and pornography to prove whether or not this pervasive myth is, in fact, reality.
Beware: Children At Play (1989)
It's ten o' clock, do you know who your children are slaughtering? God fearing parents are in a panic as their children mysteriously disappear! Little do they know that the only thing worse than their children disappearing would be them coming back! After the youngsters of Tromaville fall under the ruthless control of a cult leader, they turn on their parents with gruesome results. Cannibalism, Parenticide and heartstopping gore explode from the screen in a movie that dares you to breed! Don't miss the last ten gut-wrenching minutes, which have made Beware! Children at Play a modern day classic! This exclusive DVD release features a director's commentary, introduction by Troma President and creator of the Toxic Avenger, Lloyd Kaufman, and it comes to you in an uncensored director's cut! Beware, you may never look at your children the same way again!
Hansel & Gretel (2013)
In this modern retelling of the classic horror tale, teen siblings are enslaved by a psychotic recluse within her gruesome house of horrors in the woods.
Exte: Hair Extensions (2007)
An aspiring hair dresser (Kuriyama) becomes the infatuation of a tricophilic man who sells hair extensions to nearby hair salons. The source of the hair is the corpse of a girl whose dead body continues to grow beautiful, voluminous, black hair that comes alive, driving those who use the extensions insane or killing them.
Child 44 (2015)
Set in Stalin-era Soviet Union, a disgraced MGB agent is dispatched to investigate a series of child murders -- a case that begins to connect with the very top of party leadership.
Counter Investigation (2007)
A cop investigates whether the man convicted of murdering his daughter is really guilty.
True Crime (1996)
Mary Giordano is a bright, intelligent student who goes to a catholic school. She also has a addiction to mystery novels and detective magazines (hence the title of the movie), which inspire her to do her own detective work. When she starts snooping around on the case of a murderer of teenage girls, it gets her in hot water with her mentor Detective Jerry Gunn. But it also starts a team up with police cadet Tony Campbell. The two work together to find the murderer. But the closer Mary gets to solving the murder, the more danger she puts herself in of being the next victim.
Domestic Disturbance (2001)
A divorced father discovers that his 12-year-old son's new stepfather is not what he made himself out to be.
Looper (2012)
In the futuristic action thriller Looper, time travel will be invented but it will be illegal and only available on the black market. When the mob wants to get rid of someone, they will send their target 30 years into the past where a looper, a hired gun, like Joe is waiting to mop up. Joe is getting rich and life is good until the day the mob decides to close the loop, sending back Joe's future self for assassination.
Standoff (2016)
A troubled veteran gets a chance at redemption by protecting a girl from an assassin after she witnesses a murder. Holding a shotgun with a single shell, he engages in physical and psychological warfare in a desperate fight for the girl's life.
Still Small Voices (2007)
A 911 operator receives a ghostly call from a child murdered thirty years before and becomes obsessed with unraveling the crime. What she discovers shatters her.
Defekt (1977)
Gedeon is a young, ambitious detective. Three women have disappeared and he strongly believes that there's direct connection between them. All three of them were driving lonely and have disappeared in the same region. After a lenghty discussion Gedeon gets the permission from his boss for going on patrol with his colleague in that area.

redpajama_set_name: RedPajamaCommonCrawl


NEW YORK--Michael Sullivan, North American consumer practice leader at MSLGroup, has passed away.
Sullivan joined MSLGroup in June 2010 after heading his own firm, SullivanBremer. He had previously served as a president at DeVries Public Relations.
A respected consumer marketing specialist, Sullivan's 20 years of PR experience included a particularly long relationship with P&G. He had recently been due to transfer to MSLGroup's London office for a special assigment with the FMCG company.
In a post on MSLGroup's website, chief client officer Renee Wilson paid tribute to Sullivan's effect on the firm.
"Michael changed the game for us in consumer – he let us know that what we were doing could be so much better. What had been acceptable no longer was, if you were working with Michael. He pushed our teams – HARD. And not everyone liked it, but no one can dispute he made us better public relations strategists. I see his effect on many of you, and it's inspiring."
Details of the memorial service can be found here.


This appendix presents SAS programs for the creation of variables related to the respondent's family background, household, marriage/cohabitation, and fertility. Unless otherwise noted, the programs presented are for round 14. Except for minor hand edits to account for inconsistencies in the raw data, variable creation code remains generally constant from round to round. However, users who need code for a specific round not included here may contact NLS User Services.


Bussani Mobilityprovides economical, safe & maneuverable wheelchair rental vans for those in and around the New York area. In addition to your handicap accessible van rental, we can also provide hand controls and transfer seats on some of our rental vehicles. Though a smaller town, Bethpage still offers many attractions to wheelchair bound visitors. You will be able to play modified golf at one of the five golf courses in the area, and the Bethpage State Park has some wheelchair accessible trails. The central downtown area has navigable sidewalks and a number of historical boutiques for local shopping. Made over from a school, the Island Trees Library is also worth a visit.


text:
// Copyright (C) 2018 The Android Open Source Project
//
// Licensed under the Apache License, Version 2.0 (the "License");
// you may not use this file except in compliance with the License.
// You may obtain a copy of the License at
//
// http://www.apache.org/licenses/LICENSE-2.0
//
// Unless required by applicable law or agreed to in writing, software
// distributed under the License is distributed on an "AS IS" BASIS,
// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
// See the License for the specific language governing permissions and
// limitations under the License.

package com.google.gerrit.acceptance.rest.binding;

import static java.nio.charset.StandardCharsets.UTF_8;

import com.google.common.collect.ImmutableList;
import com.google.gerrit.acceptance.AbstractDaemonTest;
import com.google.gerrit.acceptance.GerritConfig;
import com.google.gerrit.acceptance.rest.util.RestApiCallHelper;
import com.google.gerrit.acceptance.rest.util.RestCall;
import com.google.gerrit.common.RawInputUtil;
import com.google.gerrit.extensions.api.plugins.InstallPluginInput;
import com.google.gerrit.extensions.restapi.RawInput;
import org.junit.Test;

/**
 * Tests for checking the remote administration bindings of the plugins REST API.
 *
 * <p>These tests only verify that the plugin REST endpoints are correctly bound, they do no test
 * the functionality of the plugin REST endpoints.
 */
public class PluginsRemoteAdminRestApiBindingsIT extends AbstractDaemonTest {
  /**
   * Plugin REST endpoints to be tested, each URL contains a placeholder for the plugin identifier.
   */
  private static final ImmutableList<RestCall> PLUGIN_ENDPOINTS =
      ImmutableList.of(
          RestCall.put("/plugins/%s"),

          // For GET requests prefixing the view name with 'gerrit~' is required.
          RestCall.get("/plugins/%s/gerrit~status"),

          // POST (and PUT) requests don't require the 'gerrit~' prefix in front of the view name.
          RestCall.post("/plugins/%s/gerrit~enable"),
          RestCall.post("/plugins/%s/gerrit~disable"),
          RestCall.post("/plugins/%s/gerrit~reload"),

          // Plugin deletion must be tested last
          RestCall.delete("/plugins/%s"));

  private static final String JS_PLUGIN = "Gerrit.install(function(self){});\n";
  private static final RawInput JS_PLUGIN_CONTENT = RawInputUtil.create(JS_PLUGIN.getBytes(UTF_8));

  @Test
  @GerritConfig(name = "plugins.allowRemoteAdmin", value = "true")
  public void pluginEndpoints() throws Exception {
    String pluginName = "my-plugin";
    installPlugin(pluginName);
    RestApiCallHelper.execute(adminRestSession, PLUGIN_ENDPOINTS, pluginName);
  }

  private void installPlugin(String pluginName) throws Exception {
    InstallPluginInput input = new InstallPluginInput();
    input.raw = JS_PLUGIN_CONTENT;
    gApi.plugins().install(pluginName + ".js", input);
  }
}

redpajama_set_name: RedPajamaGithub


Practical and sophisticated, this simple Columbian leather shoulder bag will help elevate your looks and keep you organized. Wear it with distressed denim and ankle boots for a more casual look, or dress things up with a pretty A-line dress.
Measurements: 13" x 11" x 5"


text:
"""Offer template automation rules."""
import logging

import voluptuous as vol

from homeassistant import exceptions
from homeassistant.const import CONF_FOR, CONF_PLATFORM, CONF_VALUE_TEMPLATE
from homeassistant.core import callback
from homeassistant.helpers import config_validation as cv, template
from homeassistant.helpers.event import (
    TrackTemplate,
    async_call_later,
    async_track_template_result,
)
from homeassistant.helpers.template import result_as_boolean

# mypy: allow-untyped-defs, no-check-untyped-defs

_LOGGER = logging.getLogger(__name__)

TRIGGER_SCHEMA = IF_ACTION_SCHEMA = vol.Schema(
    {
        vol.Required(CONF_PLATFORM): "template",
        vol.Required(CONF_VALUE_TEMPLATE): cv.template,
        vol.Optional(CONF_FOR): cv.positive_time_period_template,
    }
)

async def async_attach_trigger(
    hass, config, action, automation_info, *, platform_type="template"
):
    """Listen for state changes based on configuration."""
    value_template = config.get(CONF_VALUE_TEMPLATE)
    value_template.hass = hass
    time_delta = config.get(CONF_FOR)
    template.attach(hass, time_delta)
    delay_cancel = None

    @callback
    def template_listener(event, updates):
        """Listen for state changes and calls action."""
        nonlocal delay_cancel
        result = updates.pop().result

        if delay_cancel:
            # pylint: disable=not-callable
            delay_cancel()
            delay_cancel = None

        if not result_as_boolean(result):
            return

        entity_id = event.data.get("entity_id")
        from_s = event.data.get("old_state")
        to_s = event.data.get("new_state")

        @callback
        def call_action(*_):
            """Call action with right context."""
            hass.async_run_job(
                action,
                {
                    "trigger": {
                        "platform": "template",
                        "entity_id": entity_id,
                        "from_state": from_s,
                        "to_state": to_s,
                        "for": time_delta if not time_delta else period,
                        "description": f"{entity_id} via template",
                    }
                },
                (to_s.context if to_s else None),
            )

        if not time_delta:
            call_action()
            return

        variables = {
            "trigger": {
                "platform": platform_type,
                "entity_id": entity_id,
                "from_state": from_s,
                "to_state": to_s,
            }
        }

        try:
            period = cv.positive_time_period(
                template.render_complex(time_delta, variables)
            )
        except (exceptions.TemplateError, vol.Invalid) as ex:
            _LOGGER.error(
                "Error rendering '%s' for template: %s", automation_info["name"], ex
            )
            return

        delay_cancel = async_call_later(hass, period.seconds, call_action)

    info = async_track_template_result(
        hass,
        [TrackTemplate(value_template, automation_info["variables"])],
        template_listener,
    )
    unsub = info.async_remove

    @callback
    def async_remove():
        """Remove state listeners async."""
        unsub()
        if delay_cancel:
            # pylint: disable=not-callable
            delay_cancel()

    return async_remove


i'm pretty obsessed with nail polish. i barely ever have naked nails.
i also really love blogger package swaps. i've always been really lucky with partners and made some of my best bloggy friends through swaps.
when i saw this swap for nail polish i was super excited.
the rules were pretty simple...buy at least 2 polishes worth a certain dollar amount and send. i once again got super lucky with my partner. i was paired with maria from agapelovedesigns. she totally hooked me up.
i was at dinner with some friends talking about how i need a decent gold polish. i came home to my polish package and about died. i am so obsessed with this gold.
thanks maria for all the fun polish.
if this sounds like fun, stay tuned for a blue polish swap in april for autism awareness month.
I have been wanting a gold polish, that looks like a good color and I love Essie! One of my friend's just tried the magnet polish on her daughter and said it was a little weird, but they had fun with it.
Looks like you had an awesome partner!!
I think I got that same magnetic polish for Christmas. I loved the color, need to practice my "magnet" skills some more. Oooh and gold polish, love!
that seems like such a cute idea!
Visiting from the swap linkup :-) These colors look so fun! I love the Sally Hansen magnetic, especially in that color. I'd love to hear how you like it!
Love Essie!!! You got some great shades!
I own that gold too! I didn't get it through the swap, I bought it at Target a couple months ago! Wearing it right now- SO GOOD!


text:
const _ = require(`lodash`)
const { getNode, getNodes } = require(`./nodes`)

/**
 * Map containing links between inline objects or arrays
 * and Node that contains them
 * @type {Object.<(Object|Array),string>}
 */
const rootNodeMap = new WeakMap()

const getRootNodeId = node => rootNodeMap.get(node)

/**
 * Add link between passed data and Node. This function shouldn't be used
 * directly. Use higher level `trackInlineObjectsInRootNode`
 * @see trackInlineObjectsInRootNode
 * @param {(Object|Array)} data Inline object or array
 * @param {string} nodeId Id of node that contains data passed in first parameter
 */
const addRootNodeToInlineObject = (data, nodeId) => {
  if (_.isPlainObject(data) || _.isArray(data)) {
    _.each(data, o => addRootNodeToInlineObject(o, nodeId))
    rootNodeMap.set(data, nodeId)
  }
}

/**
 * Adds link between inline objects/arrays contained in Node object
 * and that Node object.
 * @param {Node} node Root Node
 */
const trackInlineObjectsInRootNode = node => {
  _.each(node, (v, k) => {
    // Ignore the node internal object.
    if (k === `internal`) {
      return
    }
    addRootNodeToInlineObject(v, node.id)
  })

  return node
}
exports.trackInlineObjectsInRootNode = trackInlineObjectsInRootNode

/**
 * Finds top most ancestor of node that contains passed Object or Array
 * @param {(Object|Array)} obj Object/Array belonging to Node object or Node object
 * @param {nodePredicate} [predicate] Optional callback to check if ancestor meets defined conditions
 * @returns {Node} Top most ancestor if predicate is not specified
 * or first node that meet predicate conditions if predicate is specified
 */
const findRootNodeAncestor = (obj, predicate = null) => {
  // Find the root node.
  let rootNode = obj
  let whileCount = 0
  let rootNodeId
  while (
    (!predicate || !predicate(rootNode)) &&
    (rootNodeId = getRootNodeId(rootNode) || rootNode.parent) &&
    ((rootNode.parent && getNode(rootNode.parent) !== undefined) ||
      getNode(rootNodeId)) &&
    whileCount < 101
  ) {
    if (rootNodeId) {
      rootNode = getNode(rootNodeId)
    } else {
      rootNode = getNode(rootNode.parent)
    }
    whileCount += 1
    if (whileCount > 100) {
      console.log(
        `It looks like you have a node that's set its parent as itself`,
        rootNode
      )
    }
  }

  return !predicate || predicate(rootNode) ? rootNode : null
}

function trackDbNodes() {
  _.each(getNodes(), node => {
    trackInlineObjectsInRootNode(node)
  })
}

/**
 * @callback nodePredicate
 * @param {Node} node Node that is examined
 */
exports.findRootNodeAncestor = findRootNodeAncestor
exports.trackDbNodes = trackDbNodes


Twenty-two years after a Swedish radio station first suggested that the Bofors howitzer gun deal involved the payment of "kroners to cronies" in the Rajiv Gandhi government and the Congress party, the controversy is still an occasional "breaking news". Yet, to those who have grown to adulthood after that 1987 broadcast, the scam is a curious leftover of the past.
First, the sum involved — Rs.64 crore ($1.3 million) — is too paltry by today's standards to justify the continuing media interest.
Second, nearly all those implicated in the underhand transactions are dead. They include former prime minister Rajiv Gandhi, who paid the ultimate political price of squandering a two-thirds parliamentary majority in the post-Bofors elections of 1989.
Though the Congress did find its way back to power two years later — mainly because of dissension among its opponents — the party has never really been able to regain its earlier, confident pre-Bofors self. Even today it is dependent on restive allies for survival at the centre.
Why has Bofors had such a long-lasting impact? For a start, for many people in the seventies and eighties, the scam confirmed the Congress's reputation as a cynical and corrupt organisation, which had lost the halo of the freedom movement. While much of the belief in its degeneration was based on speculation, the Bofors affair seemingly provided the first concrete evidence. Although nothing has ever been proved, the mud has stuck for two reasons.
One is that the Rajiv Gandhi government never appeared serious about unearthing the truth despite its promises to do so. A joint parliamentary committee which it set up to probe the deal was widely believed to have conducted a whitewash, helped by the opposition's unwise decision to boycott it.
The other reason was the relentless efforts of several journalists, of whom The Hindu's Chitra Subramaniam deserves special mention, which kept the spotlight on the deal. They were helped by the intriguing entries in the diary of Martin Ardbo, the Bofors president, which referred to "Q", "Nero" and "Gandhi trustee lawyer" in connection with the scam.
Since "Q" was believed to refer to Ottavio Quattrocchi, the Italian businessman, who was known to be close to the Nehru-Gandhi family, and "Nero" to Arun Nehru, then an influential minister in the Rajiv Gandhi government, it did not take long for most people to jump to unflattering conclusions about political skullduggery.
The misgivings about the government's, and specifically the Congress's, dubious role were also substantiated to a large extent by the Central Bureau of Investigation's (CBI) seeming unwillingness to pursue the available leads on Quattrocchi with sufficient purposefulness.
The doubts about the government's intentions were heightened, for instance, by its decision to unfreeze Quattrocchi's London bank account, the inability to extradite him from Argentina, where he was arrested because of an Interpol notice, and finally the latest move to withdraw the cases against him.
Although it isn't only the Congress regimes which failed to make any headway in clearing the mists about the scandal — the non-Congress governments fared no better — it is now reasonably clear that the taint will persist for India's Grand Old Party.
It must be all the more regrettable for it at present when it is again trying to recover some of its lost aura by reaching out to the people — as Rahul Gandhi is doing — and focussing more on good governance via people of integrity and efficiency like Manmohan Singh and P. Chidambaram.
The Congress's chances of recapturing its lost glory are also fairly bright at the moment because of the disarray in the ranks of its adversaries, such as the BJP and the Left.
The Congress must be ruing the fact, therefore, that an echo from its unsavoury past should continue to resonate in the political arena. Even if the ordinary people are apparently willing to forget the issue — or, at least, no longer penalise the party for it — as is evident from the Congress's recent electoral successes, the opposition parties and the media are unlikely to bury the scam in the foreseeable future.


text:
Hasiakowa Skała (1232 m n.p.m.) – najdalej na wschód wysunięta kulminacja Połoniny Wetlińskiej w Bieszczadach, położona na północ od Przełęczy Wyżnej i na zachód od doliny potoku Prowcza. Na północ odchodzi ze szczytu boczny grzbiet Jawornika i Dwernika Kamienia, ciągnący się aż do doliny Sanu. Od wysokości ok. 1100 m n.p.m. stoki pokrywa połonina. Kilka metrów na południe od najwyższego punktu znajduje się schronisko "Chatka Puchatka", najwyżej położone w Bieszczadach.

Przez wierzchołek prowadzi znakowany na czerwono Główny Szlak Beskidzki Smerek – Berehy Górne, z którym łączy się szlak żółty z Przełęczy Wyżnej. Do niego z kolei (w dolnej części) dochodzi czarny szlak z kempingu "Górna Wetlinka".

Szlaki turystyczne
  czerwony:
 z Berehów Górnych 1.40 h (↓ 1.10 h)
 ze wsi Smerek 4.50 h (z powrotem 4.05 h), z Przełęczy Orłowicza 1.50 h (z powr. 1.35 h),z Osadzkiego Wierchu 0.50 h (z powr. 0.50 h)
  żółty:
 z Przełęczy Wyżnej 1 h (↓ 0.35 h)
   czarny i żółty:
 z kempingu "Górna Wetlinka" 1.45 h (↓ 1 h)

Przypisy

Bibliografia

Szczyty Bieszczadów Zachodnich
Szczyty w Bieszczadzkim Parku Narodowym

redpajama_set_name: RedPajamaWikipedia


text:
Football Jordan
Player Profile: Jordan Football Captain Elijah Jones
August 26, 2021 August 26, 2021 JJ FiddlerComments Off on Player Profile: Jordan Football Captain Elijah Jones
It's no surprise that Elijah Jones has a propensity for leadership.
The Jordan football team captain is the oldest of four siblings and he helps take care of his immobile great grandmother Cilla Morales who lives with his family. Jones makes food for her, goes to the store for her and sometimes he'll just sit there and watch television with her after he gets home from practice.
"We watch Walker Texas Ranger on TV," Jones said. "She loves the old shows. I wanted to be a firefighter (when I was younger) because I like helping people."
Lately, Morales has been giving Jones an hour everyday to read the Bible, and he said he's really enjoyed reading and discussing verses with her. It's also no surprise that his favorite verse is Isaiah 41:10 which reads, ""Fear thou not; for I am with thee: be not dismayed; for I am thy God: I will strengthen thee; yea, I will help thee; yea, I will uphold thee with the right hand of my righteousness."
"He's a good, bright kid and a good role model who has a lot of responsibility," Jordan coach Tim Wedlow said of Jones. "Every time I see him he's got a smile on his face and he's ready to work. I wish I had 10 more of him."
Jones has been playing exclusively at the Varsity level for Jordan since he was a sophomore, and this year the senior team captain is playing wide receiver and defensive back. That experience and leadership helped on both sides of the ball last week when Jordan edged Kennedy in overtime.
Football: Jordan Wins Emotional Overtime Opener Against Kennedy
"We feel good and I feel like we can carry this into the rest of the season," Jones said. "We've got the size and people who are willing to try to win. We're willing to fight. We're tired of losing."
The home opening win was the first in nine years for the Panthers, and Jones knows the pain of losing at Jordan. He said sometimes he'll go back and watch the 2019 loss to Cabrillo for motivation.
"We're willing to fight (this year) because we're tired of losing," Jones said.
Jones added that the Jordan coaches deserve a lot of credit for the team being ready for this season after all of the COVID-19 complications.
"The coaches care," he said. "Even though we've had bad years they're still with us and fighting with us. I like that."
Jones grew up in Carson where he was a great Little League shortstop on his baseball team. But once he started flag football at 6 years old, and then tackle football when he was 11, Jones knew his true sports love was football as a wide receiver.
"When someone tries to hit you and break for 50 yards… making guys miss is still the best part," Jones said. "I like catching passes and getting the ball in my hands."
Jones is also a ball hawk in the defensive secondary where he's getting better every week. The senior wants to continue his playing career, and said he's willing to attend a junior college to make that happen.
"He's working really hard to get a scholarship so he's playing every play like it's his last play," Wedlow said of Jones.
We caught up with Jones this week before Jordan travels to JW North for its second game of the season…
Q: Are you excited to go back to school in person?
A: Yeah. I struggled so much online. You have nobody to keep you in check. I feel like if I'm in the classroom I have the will power to concentrate because it's like a competition.
Q: What are your favorite classes?
A: I like science, English and history. To know about the people who came before us, a long time before us is very interesting. Even like fossils and stuff. Some people weren't living past 30. Now some people live to like 106. That's crazy.
Q: Do you have any favorite TV shows?
A: I like watching Anime on Hulu. My favorite character is Yusuke. He's a leader and he doesn't give up.
Q: Who is your favorite superhero?
A: Batman. Everybody else has powers, but not him. He's just the Dark Knight.
Q: If you could have any superpower what would it be?
A: Super speed. Like Red Hood.
Q: What's your favorite food?
A: Domino's Pizza. The BBQ pizza.
Q: What does your mom get mad at you for the most?
A: Leaving stuff open, like the cabinets. I just forget. And eating late, like cereal at 3am. I'm just watching TV. I try to go to sleep but I just can't.
Q: What kind of music do you listen to?
A: I like everything except for rock. Pop, jazz, rap and even gospel music. Take me to the King. That's a song, but I forgot who sings it.
Q: Whose album are you more excited for: Kanye or Drake?
A: Kanye. Drake gets on my nerves and Kanye is soulful. He's just a different artist compared to others.
Q: Who is the funniest person on your team?
A: Damien Henderson because he just throws random jokes out of nowhere. Even when we're in the huddle he'll just say something stupid.
Q: Which teammate can eat the most?
A: Jeremie McGurn.
Q: Which teammate would you not let date your sister?
A: Jacob Hernandez because he's too cocky.
Q: You said you're a Green Bay Packers fan, so what do you think about the whole Aaron Rodgers situation?
A: He gets on my nerves sometimes. The decisions he makes are poor. Put in Jordan Love sometimes, with the way (Rodgers) plays."
Cabrillo Compton Jordan Lakewood Long Beach City College Long Beach Poly Long Beach State Millikan Podcast St. Anthony Wilson
PODCAST: How Important Is Winning/Losing In High School Sports?
July 21, 2022 July 21, 2022 JJ Fiddler
We interview Jordan High alum and NFL wide receiver John Ross about hosting a youth football camp in Long Beach. How important is winning and losing in high school sports? What's it like to go to the NBA Summer League in Las Vegas? Why are there so many Long Beach guys at MLB All-Star Weekend […]
Baseball Cabrillo Compton COVID-19 Jordan Lakewood Long Beach City College Long Beach Poly Long Beach State Millikan Podcast St. Anthony Wilson
PODCAST: Talking Baseball With Tai & Ricky Tiedemann
April 30, 2020 April 30, 2020 JJ Fiddler
This week on the podcast Mike and JJ talk to the baseball player brothers Tai and Ricky Tiedemann. Tai also played football at Long Beach Poly, and is currently a minor league baseball player. Ricky is a senior at Lakewood and is about to get drafted. 08:30 Interview With The Brothers Tiedemann 28:00 Quarantine Recommendations […]
LIVE UPDATES: Long Beach High School Football Games
We'll have live updates from Long Beach Poly vs. Corona Centennial, Millikan vs. Jordan, Wilson vs. Compton, Lakewood vs. Cabrillo, and all the local games. Click here for our previews. Click here if you can't see the updates. Tweets by 562sports
PODCAST: Long Beach State Changing Game Concessions
LIVE UPDATES: Cabrillo vs Jefferson, High School Football
Get ready: Long Beach's best sports coverage is coming back to a screen near you. Thanks to John Martin for the video, visit the562.org to find out how you c…


Intel® Software Guard Extensions technology adds powerful, built‑in protection for Sticky Password users on Intel- powered PCs.
Password management software provider Lamantine Software announced today that they have partnered with Intel to integrate Software Guard Extensions (Intel® SGX) technology into Sticky Password's software to provide hardware-enhanced security and increased ease-of-use.
Intel® SGX is a new security technology built into most 6th and 7th Gen Intel® Core processors that allows applications to store sensitive data inside encrypted enclaves at the very core of your PC—the silicon CPU.
Inside the sealed Intel® SGX enclave, the data is out of reach to advanced malware and threats, even if your computer has already been compromised or stolen.
Hardware Encryption: CPU-hardened enclaves isolate, encrypt, and store sensitive data — closing the door to advanced threats, even if your PC is compromised.
Built-in Protection: Unlike software-based security, Intel® SGX extends protection to the deepest level of your PC: the hardware.
Zero-Hassle Security: Silicon-assisted security offers a powerful new protection environment without sacrificing ease-of-use.
If your PC uses a 6th or 7th Gen Intel® Core processor, it's likely that you can start enjoying the added protection of Intel® SGX by updating Sticky Password today. If you're not sure if your PC supports SGX, ask your PC vendor or visit the Intel website to get the latest information about upgrading, and take advantage of hardware-enhanced security.
Intel® SGX, is a new Intel technology built in to Core processors that allows developers to add the power of hardware-based security to their apps. Traditional security solutions use software to protect security credentials, opening the door to many potential vulnerabilities and exploits. Intel® Software Guard Extensions stores credentials in the hardware enclaves instead of the operating system or 3rd party software. Critical data is captured, encrypted, matched, and stored in hardware, closing the door and making it harder for even the most advanced threats to reach it.
When it comes to application security, software-only solutions are no longer the limit of what's possible. The 6th and 7th Gen Intel® Core processors with Intel® Software Guard Extensions enable cutting-edge hardware-enhanced ID theft protection.


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Ohio City é uma vila localizada no estado norte-americano de Ohio, no Condado de Van Wert.

Demografia
Segundo o censo norte-americano de 2000, a sua população era de 784 habitantes.
Em 2006, foi estimada uma população de 775, um decréscimo de 9 (-1.1%).

Geografia
De acordo com o United States Census Bureau tem uma área de
1,2 km², dos quais 1,2 km² cobertos por terra e 0,0 km² cobertos por água.

Localidades na vizinhança
O diagrama seguinte representa as localidades num raio de 16 km ao redor de Ohio City.

Ligações externas

Vilas do Ohio


The year 2005 was the hottest on record. The average global surface temperature of 14.77 degrees Celsius (58.6 degrees Fahrenheit) was the highest since recordkeeping began in 1880. January, April, September, and October of 2005 were the hottest of those months on record, while March, June, and November were the second warmest ever.
In fact, the six hottest years on record have all occurred in the last eight years. After 2005, 1998 was the second warmest, with an average global temperature of 14.71 degrees Celsius. But there was an important difference between 1998 and 2005: the strongest El Niño of the past 100 years lifted the average 1998 temperature 0.2 degrees Celsius, whereas the record warmth last year was not buoyed by such an effect.
Rising temperatures are due primarily to the buildup of greenhouse gases in the atmosphere, particularly carbon dioxide (CO2) from the burning of fossil fuels. Once released into the atmosphere, CO2 traps heat that would otherwise escape back into space. Emissions of CO2 have been rising since the start of the Industrial Revolution in 1760, causing temperatures to climb.
Two recent reports demonstrate the exceptional levels of current global temperature and atmospheric CO2. Using records stored in ice, tree rings, and fossils, scientists have estimated that the northern hemisphere is warmer now than at any time in the past 1,200 years. Another study reported that atmospheric levels of CO2 and methane, another greenhouse gas, are higher today than at any time in the last 650,000 years.
As greenhouse gas emissions continue to increase, so too will the pace of climate change. By 2100 the average global temperature is projected to rise 1.4‑5.8 degrees Celsius relative to the 1990 level, according to the Intergovernmental Panel on Climate Change, a global body of more than 1,500 scientists.
There is little question that a global temperature increase in the upper range of predictions would be highly disruptive. As global temperatures continue to rise, so do the health risks from heat waves, failing crops, infectious diseases, and other environmental changes. People already facing food insecurity could be particularly distressed because with each 1-degree-Celsius increase in temperature above optimal levels, wheat, rice, and corn yields fall by 10 percent. Even at the lowest projected temperature increases, climate change models predict more frequent and more severe storms, floods, heat waves, and droughts—all of which would affect biodiversity, human health, and economic security.
Such effects may have already begun to occur. In 2005, for example, parts of Brazil's Amazon rainforest experienced the worst drought in over a century, thought to have been precipitated in part by abnormally high temperatures in the North Atlantic Ocean. With less rainfall, tropical forests dry out and burn more easily. Less moisture evaporates from these drier forests, leading to less precipitation, which perpetuates the problem.
The rise in sea surface temperature has also contributed to a record-breaking Atlantic hurricane season, with 27 named storms and 15 hurricanes in 2005. In August, Hurricane Katrina ravaged the U.S. Gulf Coast, leading to more than 1,100 deaths and displacing approximately 1 million people. The United States suffered an estimated $75 billion in damage due to the hurricane—the costliest natural disaster in U.S. history.
A report by the Pew Center on Global Climate Change analyzing the results of 40 previous studies found a clear link between increased temperatures and numerous changes in natural systems across the United States. Warmer winters, increased precipitation, and earlier springs are causing certain plant species to bloom several weeks earlier, which is disrupting insect food supplies and plant pollination cycles. Temperature changes have led to shifts in many species' habitats as populations move north and to higher elevations in search of cooler temperatures. Scientists estimate that about half of all wild species in the United States have already been affected by climate change.
Warming in the Arctic—the area around the North Pole, including parts of Russia, Alaska, Canada, Greenland, and Scandinavia—has occurred at nearly twice the global average rate. Indeed, a snapshot of 2005 shows that the greatest warming last year occurred in the Arctic Circle. Warming there is enhanced by a positive feedback mechanism. Snow and ice reflect some 80 percent of solar radiation. When they melt, more heat is absorbed by the underlying surface, which in turn melts more snow and ice. From 2002-2005, summer Arctic sea ice has covered 20 percent less area than its 1978-2000 summer average. The Arctic could be ice-free in summers by the end of this century, threatening the fate of the polar bear as melting ice shrinks its habitat and compromises access to food.
In addition, in Western Siberia, an area of permafrost spanning a million square kilometers—the size of France and Germany combined—has recently begun to melt for the first time since it was formed over 11,000 years ago at the end of the last ice age. This permafrost covers the world's largest frozen peat bog. Scientists warn that if warming trends continue it will release billions of tons of stored carbon into the atmosphere, accelerating global warming.
The temperature data for 2005 provide further evidence of what some scientists are calling a new geological epoch, the Anthropocene, in which human activities are the main driver of the global climate system. The amount that temperatures increase depends on what we do from now on to curb emissions of CO2 and other greenhouse gases. We can continue to use climate-disrupting fossil fuels or we can choose to shift to renewable energy sources and more-energy-efficient technologies.