text:
Returning Back Home can be Difficult
Heroes Remember
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Interviewer: And with all those experiences and those deployments, coming back home, is it difficult to return to civilian life? Because you have another job to do as soon as you get back here. Yes and no. Yeah, it takes a while. It just takes a while. It's difficult, but I guess achievable. You're so used to doing things on your own and when you come back, you've got other people there that depend on you and so forth and so on. And you just sort of want to, you've been on your own for the past six months or eight months whatever the case may be. You almost want that little space off to one side. Not that you don't want to see anybody, it's just that… leave me alone for awhile. And you know, I'll be good like that. Yeah, I can remember when I came home from, I think it was, Sierra Leone. Yeah, I had a fairly big frontyard and backyard and I got four loads of topsoil filled in to re-sod it and I was up 'til midnight spreading it all. And my wife, "Are you coming in tonight" and I said "No, I just want to get it done." You know, I wasn't finished. I wanted to stay out and do it. And something like that, yeah. It can be difficult. I guess it depends on your make-up. It just depends on what you did, what you've seen and how you've absorbed it all in.
Officer Hickey speaks about the sometimes difficult transition back to home life after deployments.
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text:
SheInspires
Michelle Beesley
Nanny Babe
Rachel Nitschke
Leonor Bodyplan
Smart Alex
Talking Modern Life
Reducing Fire Risk In Your Backyard
SheSociety
With a brutal bushfire season predicted for the weeks and months ahead, Landart Landscapes' Matt Leacy shares some tips for mitigating fire risks in your outdoor spaces.
"I love the Australian bush, and live near bushland myself, so I would never want to seem alarmist in my approach to fire-prepping. However, the reality is that we're already experiencing devasting fire conditions in many parts of Australia and signs are pointing to a long, dry summer – so we've got to be as proactive as possible when it comes to mitigating fire risks to our homes and outdoor spaces," says Matt, who is also resident garden guru on Channel Ten's The Living Room.
"While there's no way to entirely fire-proof your property, property owners shouldn't underestimate how much a good garden clean-up, prune and some clever plant choices can potentially make in reducing bushfire risks to your home," Matt adds.
Below, Matt shares his top tips for fire-proofing your outdoor spaces.
Tidy up and trim back
"As much as it may seem an obvious and tedious task, one of the best things you can do is to thoroughly prune and tidy up around your gardens and property," says Matt.
"Clean gutters, especially if your house is surrounded by large trees," adds Matt. "Also, ensure that all old dry leaves from autumn and winter are cleared out and away from your property – and that dead branches are cut away, and trees and other plants are trimmed right back away from your house."
"You might also consider installing some fire irrigation on the roof or some extra hose points. If a fire borders your property, it could make a critical difference to be able to wet your house down and put out spot fires from embers from multiple angles," says Matt.
Know what is in your garden
"It's useful to have at least some knowledge of how flammable the plants and trees on your property are – and if you're unsure and surrounded by lots of gardens and bushland, it might be worth engaging a professional to help inform you," says Matt.
"Trees that are known ignite quickly (and some will even explode) include tea tree, Cyprus, pines, eucalypts and various other natives," says Matt.
"Obviously, if you have a beautiful, well-established eucalyptus tree – which is also an important wildlife habitat, you aren't likely going to want to remove it entirely. But if you can prune it back and maintain it – especially the branches that are dying off – as well as control what's around it, you'll help to reduce associated fire risks."
"Just be sure to check with your local authority as to how much of the tree you can remove each year," adds Matt.
Landscaping choices
"When introducing new varieties into your outdoor spaces, choose plants that are fire retardant – that is, plants that don't ignite and therefore make areas less flammable," says Matt.
"These will help protect your property from falling embers and are usually plants that have a high moisture content in their leaves, as well as big thick leaves rather than fine hard leaves."
"Some of these plans include, saltbush, lavender, hydrangea, white cedar, succulents, grey or silver mulga, wattles, lilly pilly, kangaroo paw, palms, Moreton bay figs, Scaevola – fan flower, Cyathea, Dianella, Hymenopsermum – Native frangipani, Myoporum, Senecio, Syzygium viola and various species of flax and pigface.
"Keep in mind that if some of these plants dry out, they may then burn" cautions Matt.
"Vegetables (especially if you have a patch bordered by a pathway or pebbles) are also a great option," says Matt.
"It is also better to choose plants with smooth bark, rather than plants that have rough bark," adds Matt. "I recommend checking with your nursery to ensure the plants I'm suggesting are suitable to your specific area."
"Also, do your best when designing your garden to plant fire resistant trees and plants in a shield format, particularly if your property is bordered on any side by bushland" says Matt.
"Lower shrubs and groundcovers are a better choice than tall big trees or hedges."
"If you're mulching, consider using stones, gravel or pebbles rather than woodchips that will act as a fire fuel," says Matt.
"From a design perspective, if you are starting fresh with a new garden, or can adapt what you already have, I'd suggest planting trees at least 10 metres from you house," says Matt. "Also, include pebbled, paved, tiled or concrete pathways to help create fire breaks."
"If you can (and this is more so if your property backs onto or is surrounded by a National Park), look to create a design that integrates a pool, tennis courts or big stretches of lawn, between the bushland and the house," says Matt.
"Also, try to avoid clumping too many trees together; a tight canopy can carry fire."
"And, above all, try to avoid having trees that grow over or onto your house," emphasises Matt.
Lawns and water provision
"Lawns can also act as a physical barrier, if you've been able to keep them green during water restrictions and very dry conditions," says Matt.
"It's also a smart idea to pre-plan for upcoming rainfall and install water tanks now," suggests Matt "When we do eventually get rain, these tanks can be used to maintain a green garden, which can help to ward off the severity of bushfires later down the track."
"You might also look into the feasibility of sinking a bore for watering," says Matt. "You will, however, need to obtain the correct approval/licencing before doing so – and it can be a little costly, though worthwhile process."
"Drip watering systems are also a great, simple and cost-effective way to transport water into your garden in an eco-friendly manner," adds Matt.
Help local fauna find refuge
"If you're in the sad situation of being hit by fires (and hopefully it's just your garden you need to re-build), or you live in an area with bushland that's been ravaged by fires, look at how you can help support the animals in the area," says Matt.
"In most cases, this will mean a back-to-basics approach – leaving out buckets of water or incorporating water features with fresh water or bird baths into your garden design," he says.
"If you know what animals are in your region, you might look at establishing plants and garden features that wildlife could seek refuge in and use as a food source," Matt adds. "You could also purchase seed to feed birds and other animals in extreme situations."
"Note that if you're encouraging wildlife into your garden, you should be more vigilant with cats and other domestic pets that may hunt displaced fauna seeking refuge in your outdoor spaces," Matt cautions.
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redpajama_set_name: RedPajamaCommonCrawl


text:
\section{Introduction}

The combination of a thin disk and collimated jet is a common
structure that is created in the vicinity of a massive object
\cite{bib:bland1-2,bib:begelman4,bib:livio,bib:ferrari,bib:livio2}.
Beneath a large variety of scales, constituents, and local
processes of such systems, there must be a simple and universal
principle that dictates the remarkably similar geometry;
see Fig.\,\ref{fig:streamline}.
Here we show that the collimated structure of jet is a natural
consequence of the \emph{alignment} of the flow velocity and the
vorticity, i.e. so-called \emph{Beltrami condition} determines the structure.
On a Keplerian thin disk, the
vorticity becomes a vertical vector with a magnitude $\propto
r^{-3/2}$ ($r$ is the radius from the center of the disk), which
appears as a spindle of the disk. Then, the alignment is the
unique solution for avoiding singularity of Coriolis force near the center.
However, we need to generalize the
``vorticity'' to deal with the
strong heterogeneity of the disk-jet system,
as well as to account for the dissipation that causes accretion.
The mission of this study is to
formulate an appropriate \emph{generalized vorticity}
to which the disk-jet flow aligns.

Let us start by a short review of the Beltrami vector field
which has wide applications as a model
of various \emph{vortex structures} found in nature.
The Beltrami condition, demanding the alignment of flow and its
vorticity, forces the total \emph{energy density} (consisting of thermal energy, kinetic energy,
and other energies of coupled fields such as gravitational or electromagnetic) to
distribute homogeneously (so called Bernoulli condition); the
Beltrami-Bernoulli condition, thus, fits the notion of
``relaxed state.''
While a Beltrami field was discovered
by many researchers as a particular type of equilibrium
state\,\cite{bib:ChandrasekharKendall1957,bib:low}, or \emph{free decay}
solution\,\cite{bib:vanKampen}, in fluids or
plasmas, its relation to the \emph{helicity}
was noticed in the study of ``force-free magnetic
fields'' in plasmas; Woltjer\,\cite{bib:Woltjer1958} invoked the
helicity as a constraint in minimizing the magnetic energy;
Taylor\,\cite{bib:JBT1974} considered that the ``relaxed
state'' is the energy minimizer under the lugged constancy of the total helicity;
the corresponding Euler-Lagrange equation
becomes the eigenvalue problem of the curl operator;
see \cite{bib:yoshida-giga} for the mathematical characterization of the curl operator
and its eigenfunctions.
We can actually observe Taylor relaxed states on various experiments\,\cite{bib:JBT-RMP},
as well as in some astronomical systems;
e.g. \cite{bib:Heyvaerts-Priest1984,bib:Kusano1995}.
The helicity constraint causes a finite \emph{vorticity}
in the relaxed state, resulting in interesting topological properties
of field-lines\,\cite{bib:Moffatt}.
In the context of Hamiltonian mechanics,
the helicity is regarded as a Casimir element representing the
defect of the governing symplectic geometry\,\cite{bib:Morrison};
a Beltrami field is an equilibrium point on a \emph{helicity leaf}.

The Beltrami fields constitute an interesting, widely-applied class of
vectors (or axial vectors) with ``twisted'' field-lines;
e.g. \cite{bib:Cantarella,bib:Dritschel,bib:Tang}.
Not only for describing equilibrium states,
they are applied to analyze waves\,\cite{bib:Yoshida1991,bib:Gonzalez},
instabilities\,\cite{bib:Yoshida2003}, and turbulence\,\cite{bib:Montgomery,bib:Ito,bib:Yang} (here we can
cite only a short list of references).

A variety of generalizations have been proposed.
Including the cross helicity as an
additional constraint, we obtain a flow parallel to
the magnetic field and the resultant hydrodynamic pressure balancing with a
static pressure\,\cite{bib:Sudan1979}.
The two-fluid (Hall MHD) formulation elucidates
a fundamental structure in the coupling of flow and magnetic field in terms of the
\emph{canonical vorticities}\,\cite{bib:MahajanYoshida1998};
the simultaneous ion and electron Beltrami conditions
yields the \emph{double Beltrami fields},
which have various applications in both laboratory and
astrophysical plasmas; e.g. \cite{bib:Ohsaki,bib:Mahajan-Nana,bib:Yoshida2010}.
Another generalization is made by including the coupling of vortex and compressible motions;
by boosting such generalized Beltrami fields, we obtain
modulating nonlinear Alfv\'en waves\,\cite{bib:Yoshida2011}.

\begin{figure}
\begin{center}
\includegraphics[scale=0.7]{streamlines.eps}
\caption{
In a disk-jet system,
the accreting flow and jet align parallel to a \emph{generalized vorticity}.
This figure shows the streamlines of a ``generalized Beltrami flow''
to be constructed in Sec.\,\ref{sec:similarity-solution}
}
\label{fig:streamline}
\end{center}
\end{figure}

This work extends the scope of Beltrami fields to show that
the disk-jet system is a ``generalized'' Beltrami vortex\,\cite{bib:Shatashvili};
the generalization is made by introducing a new \emph{generalized vorticity}
that combines the vorticity of a ``reduced momentum'' ---the reduction is to account for
a viscous dissipation as well as to subtract the centrifugal
force of the Keplerian rotation.

\section{Generalized vorticity and Beltrami condition}
\label{sec:formulation}

To demonstrate how the alignment condition arises and how it
determines the structure of a thin disk and
narrowly-collimated jet, we invoke a simple
model of neutral fluid; for a generalization to magneto-fluid, see
Appendix A.
Let $ \bm{P} = \rho \bm{V}$ denote the mechanical momentum density, where
$\rho$ is the mass density and $\bm{V}$ is the (ion) flow
velocity. The momentum equation read as
\begin{equation}
\partial_t \bm{P} + \nabla\cdot(\bm{V}\bm{P})
= -\rho\nabla\phi - \nabla p -\nabla\cdot\bm{\Pi}
\label{momentum-i-1}
\end{equation}
where $\phi$ is the gravity potential, $p$ is the scalar pressures, and $\bm{\Pi}$
is the (effective) viscosity tensor.
The variables are normalized as follows: We choose a
representative flow velocity $V_0$ and a mass density $\rho_0$ in
the disk, and normalize $\bm{V}$ and $\rho$ by these units. The
energy densities $\rho\phi$
(gravitational) and $p$ (thermal) are normalized by the unit
kinetic energy density ${\cal{E}}_0:=\rho_0 V_0^2/2$.
The independent variables (coordinate $\bm{x}$ and time $t$) are
normalized by the system size $L_0$ and the corresponding transit
time $T_0=L_0/V_0$.

We consider stationary solutions; putting
$\partial_t=0$ in (\ref{momentum-i-1}), we obtain
\begin{equation}
\nabla\cdot(\bm{V}\bm{P}) =
-\rho\nabla\phi - \nabla p - \nabla\cdot\bm{\Pi}.
\label{momentum-i-1-scaled}
\end{equation}
In order to derive a term that balances with the viscosity term, we
decompose the ``inertia term'' [the left-hand side of
(\ref{momentum-i-1-scaled})] as follows: we first write
\begin{equation}
\rho = \rho_1 \rho_2 , \label{decomposition1}
\end{equation}
and denote
\begin{equation}
\bm{P}_1 := \rho_1\bm{V}, \quad \bm{P}_2 := \rho_2 \bm{V}.
\label{decomposition2}
\end{equation}
Using these variables, we may write
\begin{equation}
\nabla\cdot(\bm{V}\bm{P})
=\nabla\cdot(\rho\bm{V}\bm{V})
=(\nabla\cdot\bm{P}_1)\bm{P}_2 + (\bm{P}_1\cdot\nabla)\bm{P}_2.
\label{decomposition3}
\end{equation}
In the conventional formulation of fluid mechanics, we choose
$\rho_2=1$ and $\rho_1=\rho$.  Then,
using the mass conservation law $\partial_t \rho +
\nabla\cdot\bm{P}=0$, we can rewrite the left-hand side of
(\ref{momentum-i-1}) as $\rho[\partial_t\bm{V}+(\bm{V}\cdot\nabla)\bm{V}]$.
In the preset analysis, however, we choose a different separation of the
inertia term in order to match $(\nabla\cdot\bm{P}_1)\bm{P}_2$
with the viscosity term.
By a reduced $\rho_2$ ($<1$), we will define a \emph{generalized vorticity}
of a \emph{reduced momentum}.
Multiplying $(\rho_2/\rho_1)$ on both sides of (\ref{momentum-i-1-scaled}), we obtain
(assuming a barotropic relation, we put $\nabla p=\rho\nabla h$ with an enthalpy $h$)
\begin{equation}
\bm{P}_2\times\bm{\Omega}_2 = \frac{1}{2}\nabla P_2^2 + \rho_2^2
\nabla\,(\phi + h)
+ \frac{\rho_2}{\rho_1}\,[(\nabla\cdot\bm{P}_1)\bm{P}_2 + \nabla\cdot\bm{\Pi}] ,
\label{momentum-2}
\end{equation}
where
\begin{equation}
\bm{\Omega}_2
:= \nabla\times\bm{P}_2
\label{g-vorticity}
\end{equation}
is a \emph{generalized vorticity}.

In the next section, we will show that a generalized Beltrami condition,
demanding that $\bm{\Omega}_2$ parallels $\bm{P}_2$
(thus, (\ref{momentum-2}) holds with both sides being zero),
is a unique recourse to avoid singular energy densities in a disk-jet geometry.

\section{Beltrami Model of Disk-Jet System}
\label{Sec:Disk-Jet}

Now we consider an axisymmetric ($\partial_\theta =0$ in the
$r$-$\theta$-$z$ coordinates) disk-jet system.
A massive central object produces $\phi = -MG/r$
(we neglect the mass in the disk and jet). In the disk,
$\bm{V} \approx V_\theta \bm{e}_\theta$ with
the Keplerian velocity $V_\theta \propto r^{-1/2}$.
Then, $\nabla\times\bm{V} \propto r^{-3/2} \bm{e}_z$.
The momentum is strongly
localized in the thin disk, and the vorticity diverges near the axis.
This particular configuration
poses strong constraints on the force balance equation (\ref{momentum-2}),
allowing only a special class of solutions to exist;
following conclusions are readily deducible.

\subsection{Balance of viscosity force and partial inertia}
\label{subsec:partial_inertia}
In the disk, a radial flow (much smaller than
$V_\theta$) is caused by the viscosity
(a finite dissipation breaks the conservation of the angular momentum and enables
the flow to cause accretion).

Since the flow $\bm{V}$ is primarily in the azimuthal ($\theta$) direction,
the viscosity force can be approximated as
(under assumption of the azimuthal symmetry, $\nabla\cdot\bm{V}\approx0$)
\begin{equation}
-\nabla\cdot\bm{\Pi} \approx -\nabla\times (\rho\eta\nabla\times\bm{V}),
\label{viscosity_term}
\end{equation}
where $\eta$ is the shear viscosity coefficient.
In a Keplerian thin disk, where $\bm{V}\approx V_0 r^{-1/2}\bm{e}_\theta$, and
$\nabla(\rho\eta)$ is approximately vertical,
we may estimate
\begin{equation}
-\nabla\cdot\bm{\Pi} \approx
-\rho \eta \nabla\times(\nabla\times\bm{V}) =
- \rho \eta V_0 \frac{3}{4} r^{-5/2} \bm{e}_\theta.
\label{viscosity_term-2}
\end{equation}
Hence, we may write $-\nabla\cdot\bm{\Pi}= -\nu \bm{P}$ with a positive coefficient $\nu(r)$,
i.e., the viscosity force is primarily in the azimuthal (toroidal)
direction, which can be balanced by the term
$(\rho_2/\rho_1)\,(\nabla\cdot\bm{P}_1)\bm{P}_2$ that has been
extracted from the inertia term;
see (\ref{decomposition3}). Using the steady-state mass
conservation law $\nabla\cdot\bm{P}=0$, we observe
\[
\rho_1^{-1} \nabla\cdot\bm{P}_1
=  \rho_2 \bm{V}\cdot\nabla\rho_2^{-1} = -
\bm{V}\cdot\nabla\log\rho_2 .
\]
Hence, the  balance of the viscosity and the partial inertia term
demands
\begin{equation}
\bm{V}\cdot\nabla\log\rho_2 = \nu,
\label{friction-balance}
\end{equation}
which determines the parameter $\rho_2$.
(Since $\partial_\theta=0$, we can integrate (\ref{friction-balance}) for
$\rho_2$ along the streamline of $\bm{V}$ on the poloidal $r$-$z$ plane.)

The remaining part $\rho_1$ of the density is determined by the mass
conservation law:
By $\nabla\cdot\bm{P} =\nabla\cdot(\rho\bm{V})
= \rho_2\bm{V}\cdot\nabla\rho_1 + \rho_1\bm{V}\cdot\nabla\rho_2
+ \rho_1\rho_2\nabla\cdot\bm{V}
= 0$
and (\ref{friction-balance}), we obtain a relation
\begin{equation}
\bm{V}\cdot\nabla\log\rho_1 = -\nabla\cdot\bm{V}-\nu.
\label{friction-balance'}
\end{equation}

\subsection{Beltrami condition}
\label{subsec:Beltrami}
Near the axis, the poloidal component of the flow
begins to have an appreciable vertical ($z$) component
---this is the place where the jet is created;
we are going to unearth the mechanism that collimates the flow.

After balancing the third and fourth terms in
(\ref{momentum-2}), the remaining terms do not have a
toroidal (azimuthal) component.
In fact, the right-hand-side
gradient terms have only poloidal components, and
hence, the left-hand-side $\bm{P}_2\times\bm{\Omega}_2$ must not have a toroidal component
(to put it in another way, we have extracted the partial inertia term
$-(\rho_2/\rho_1)(\nabla\cdot\bm{P}_1)\bm{P}_2$ from the total
inertia to separate the toroidal component).
The vorticity $\bm{\Omega}_2$ includes a singular factor
$\nabla\times\bm{V} \propto r^{-3/2}\bm{e}_z$.
To eliminate the divergence of $\bm{P}_2\times\bm{\Omega}_2$ near the axis,
$\bm{P}_2$ must \emph{align} to $\bm{\Omega}_2$,
i.e., the \emph{Beltrami condition}
\begin{equation}
\bm{\Omega}_2 = \lambda \bm{P}_2
\label{Beltrami1}
\end{equation}
must be satisfied, where $\lambda$ is a certain scalar function.
The flow $\bm{V}=\bm{P}_2/\rho_2$ is, therefore, collimated by the
\emph{generalized vorticity} $\bm{\Omega}_2$ creating a jet.

\begin{remark}
\label{remark:Keplerian-velocity}
Here the essential part of the Beltrami condition is its poloidal component,
which dictates the poloidal flow so as to eliminate the toroidal component of the inertia term $\bm{P}_2\times\bm{\Omega}_2$.
As for the toroidal flow $V_\theta\bm{e}_\theta$,
which yields primarily a radial (centrifugal) inertia force, the ``Beltrami condition''
brings about an extra constraint.
In fact, if we were to use the conventional vorticity
$\bm{\Omega}=\nabla\times\bm{V}$ (i.e., if $\rho_2=1$) and estimate the
centrifugal force of the Keplerian flow $\bm{V}=V_0r^{-1/2}\bm{e}_\theta$,
the term $\bm{P}\times\bm{\Omega}$ contributes a half of
the total centrifugal force $(\bm{V}\cdot\nabla)\bm{P} = \rho V_0^2/r$,
while the term $\nabla V^2/2$ on the right-hand side of (\ref{momentum-2})
contributes the remaining half; combining these two terms, we obtain
the right balance with the gravity $-\rho MG/r^2$.
Hence, the conventional Beltrami condition $\bm{P}\times\bm{\Omega}=0$
would lead to an inadequate estimate of the toroidal flow.
However, our \emph{generalized Beltrami condition},
based on the generalized vorticity $\bm{\Omega}_2$ (including $\rho_2\neq1$),
can be made consistent with the Keplerian velocity;
see Sec.\,\ref{sec:similarity-solution}.
\end{remark}

\subsection{Bernoulli condition}
\label{subsec:Bernoulli}
When the Beltrami condition eliminates the left-hand side of
(\ref{momentum-2}), the remaining potential forces must
balance to achieve the \emph{Bernoulli
condition}\,\cite{bib:MahajanYoshida1998} that reads as
\begin{equation}
\frac{1}{2\rho_2^2}\nabla P_2^2 + \nabla( \phi + h)
=\nabla \left( \frac{1}{2}V^2 + \phi + h \right) + V^2 \nabla
\log\rho_2
= 0. \label{Bernoulli-1}
\end{equation}

The system of determining equations is summarized as follows: By
(\ref{friction-balance}), we determine $\rho_2$
for a given $\nu$. This equation involves $\bm{V}=\bm{P}/\rho$
that is governed by the Beltrami equation (\ref{Beltrami1}).
After determining $\bm{V}$ and $\rho_2$, we can solve the
Bernoulli equation (\ref{Bernoulli-1}) to determine $h$
(the gravitational potential is approximated by $\phi=-MG/r$).

\section{Parameterization by Clebsch potential}
\label{Sec:2D-formulation}

We may rewrite the determining equations
(\ref{friction-balance})-(\ref{Bernoulli-1})
in a succinct form by invoking the Clebsch parameterization.
In an axisymmetric geometry, the divergence-free vector $\bm{P}$
may be parameterized as
\begin{equation}
\bm{P} = \nabla\psi\times\nabla\theta + I \nabla \theta,
\label{Grad-form-1}
\end{equation}
where $I = \rho r V_\theta$.  Both $\psi$ and $I$ do not depend on
$\theta$. Since $\bm{P}\cdot\nabla\psi=0$, the level sets
(contours) of $\psi$ are the streamlines of $\bm{P}$ (or those of
$\bm{V}=\bm{P}/\rho$).
In a disk region, $rV_\theta \propto r^{1/2}$,
while $\rho$ is a strongly localized function with respect to $z$.

Substituting (\ref{Grad-form-1}) into
(\ref{friction-balance}) yields
\begin{equation}
\nu = \frac{1}{\rho} \bm{P}\cdot\nabla \log \rho_2
= \frac{1}{r\rho}\{\log\rho_2,\psi\},
\label{friction-balance-2}
\end{equation}
where $\{a,b\} := (\partial_r b) (\partial_z a) - (\partial_r
a)(\partial_z b)$. For a given set of $\bm{P}$, $\rho$ and $\nu$,
we can solve (\ref{friction-balance-2}) to determine
$\rho_2$, as well as $\rho_1=\rho/\rho_2$ that is consistent to
(\ref{friction-balance'}).

Substituting (\ref{Grad-form-1}) into the Beltrami condition (\ref{Beltrami1}),
we obtain,
from the toroidal component,
\begin{equation}
\lambda\rho_1^{-1} \nabla\psi= \nabla \left(\rho_1^{-1}I \right) ,
\label{Beltrami-I-unmag}
\end{equation}
implying that $\rho_1^{-1}I =: I_2 = I_2(\psi)$ and
$\lambda\rho_1^{-1} = I_2'(\psi) $ (we denote
$f'(\psi)=\rmd f(\psi)/\rmd\psi$),
and, from the poloidal component,
\begin{equation}
{\cal L} \psi - \nabla\psi\cdot\nabla\log\rho_1 = - \rho_1^2 I_2'(\psi) I_2(\psi) ,
\label{Beltrami3'}
\end{equation}
where ${\cal L}\psi := r \partial_r(r^{-1}\partial_r \psi) +
\partial_z^2 \psi$.  This elliptic partial differential equation determines
the poloidal-momentum Clebsch potential $\psi$.

The Beltrami condition has decoupled the gradient forces from the momentum
equation, which must balance separately ---the Bernoulli
condition (\ref{Bernoulli-1}) which now reads as
the determining equation of the enthalpy:
\begin{equation}
\nabla h =
-\nabla \left[ \frac{1}{2r^2\rho^2}\left(|\psi|^2+ I^2 \right) + \phi \right]
-  \frac{1}{r^2\rho^2}\left(|\psi|^2+ I^2 \right) \nabla \log\rho_2.
\label{Bernoulli-2}
\end{equation}

\section{Analytic Similarity Solution}
\label{sec:similarity-solution}

\subsection{A similarity solution modeling disk-jet structure}

In this section, we construct a \emph{similarity solution} of the
model (\ref{Beltrami3'}), which describes a
fundamental disk-jet structure.
We define
\begin{equation}
\tau := \frac{z}{r}
\quad (r>0),
\label{similarity-0}
\end{equation}
and an orthogonal variable ($\nabla\tau\cdot\nabla\sigma=0$)
\begin{equation}
\sigma := \sqrt{r^2 + z^2} \ . \label{similarity-0'}
\end{equation}
In the thin disk region, we may approximate $\sigma\sim r$, while in the
narrow jet region, $\sigma\sim z$.
The system is mirror symmetry with respect to the $z=0$ plane, and
the axes $r=0$ and $z=0$ are left as singularities.
We consider $\psi$ such that
\begin{equation}
\psi = \psi(\tau) = -J \tau^p  -D \tau^{-q},
\label{similarity-1}
\end{equation}
where $J$ and $p$ ($D$ and $q$) are positive constants, which
control the strength of the jet (disk) flow.

\begin{figure}
\begin{center}
\includegraphics[scale=0.7]{psi_similarity.eps}
\caption{ The momentum field (contours of $\psi$ that describe the
streamlines of the poloidal component of $\bm{P}$) of the
similarity solution (with $D=1$, $p=1$, $J=0.1$ and $q=1$). }
\label{fig:flow}
\end{center}
\end{figure}

As shown in Fig.\,\ref{fig:flow}, this $\psi$ models a disk-jet flow.
The level sets of $\psi$ (hence, those of $\tau$) are the
streamlines of $\bm{P}$. On the other hand, $\sigma$ serves as the
coordinate directed parallel to the streamlines. We assume that
$\rho_1$ is written as
\begin{equation}
\rho_1(\tau,\sigma) = \rho_\perp(\tau) \rho_\parallel(\sigma),
\label{similarity-1'}
\end{equation}
and, then, $\log\rho_1= \log\rho_\perp(\tau)+\log\rho_\parallel(\sigma)$.

Let us see how the stream function $\psi$ defined by (\ref{similarity-1})
satisfies the determining equations (\ref{friction-balance-2}), (\ref{Beltrami3'}), and
(\ref{Bernoulli-2}), i.e., we determine all other
fields $I_2(\psi)$, $\rho_1$, $\rho_2$, $\nu$ and $h$ that allow
this $\psi$ to be the solution. For arbitrary $f(\tau)$ and
$g(\tau)$, we observe
\[
{\cal L} f =
\frac{1}{r^2} \left[ (\tau^2+1) f'' + 3\tau f' \right] ,
\]
\[
\nabla f \cdot \nabla g
= \frac{1}{r^2} (\tau^2+1)f' g' .
\]
Hence, the left-had side of (\ref{Beltrami3'}) is (denoting
$g(\tau):=\log\rho_\perp(\tau)$)
\begin{equation}
{\cal L} \psi - \nabla \psi \cdot \nabla \log \rho_1
= \frac{1}{r^2} \left[ (\tau^2+1) \psi'' + 3\tau \psi' - (\tau^2+1)g'\psi' \right].
\label{similarity-2}
\end{equation}
For this quantity to balance with the right-hand side of
(\ref{Beltrami3'}),
$r^{-2}\rho_1$ must be a function of $\tau$ if $I_2'(\psi) \neq 0$.
Instead of demanding this relation for $\rho_1$ (cf. Remark\,\ref{remark:generalization}),
we recourse to an assumption $I_2'(\psi) =0$
(the implication of this simple condition will be
discussed later).
Then, (\ref{Beltrami3'}) reduces to
\begin{equation}
(\tau^2+1) \psi'' + 3\tau \psi' - (\tau^2+1)g'\psi' = 0.
\label{Beltrami3''}
\end{equation}
We note that the Beltrami condition (\ref{Beltrami3''}) is freed
from $\rho_\parallel(\sigma)$. This fact merits in solving
(\ref{friction-balance-2}); see (\ref{friction-balance-3}).

\begin{figure}
\begin{center}
\includegraphics[scale=0.7]{rho_perp.eps}
\caption{ The distribution of $\rho_{\perp}$ of the similarity
solution (with $D=1$, $p=1$, $J=0.1$ and $q=1$). Contour levels
are given in the log scale of $\rho_{\perp}$.
}
\label{fig:density_1}
\end{center}
\end{figure}

For the specific form (\ref{similarity-1}) of $\psi$, we have to
determine an appropriate $g=\log \rho_\perp$ to satisfy
(\ref{Beltrami3''}), i.e.,
\begin{eqnarray}
g' &=&
\frac{\psi''}{\psi'} + \frac{3\tau}{\tau^2 + 1}
\nonumber
\\
&=&  \frac{J\,p\,(p-1)\tau^{p+q} +
D\,q\,(q+1)}{J\,p\,\tau^{p+q+1}-D\,q\,\tau}
+\frac{3\tau}{\tau^2+1} .
\label{similarity-3}
\end{eqnarray}
Solving (\ref{similarity-3}), we obtain
\[
g := \log\rho_\perp =
\log\frac{|Jp\tau^{p+q}-Dq|}{\tau^{q+1}}
+\frac{3}{2}\log(\tau^2+1) ,
\]
and, thus,
\begin{equation}
\rho_\perp = \frac{(\tau^2+1)^{3/2}|Jp\tau^{p+q}-Dq|}{\tau^{q+1}} .
\label{similarity-4}
\end{equation}
In Fig.\,\ref{fig:density_1}, we show the profile of $\rho_\perp(\tau)$.

\begin{remark}
\label{remark:generalization}
Here we considered the case of $I_2'(\psi) =0$, but a more
general solution can be obtained by demanding
$r^{-2}\rho_1$ to be a function of $\tau$.
For example, we may put $\rho_1=\rho_\perp(\tau)\rho_\parallel(\sigma)$
with $\rho_\parallel(\sigma)=\sigma^2=r^2+z^2$.  Then, $r^{-2}\rho_1=
(1+\tau^2)\rho_\perp(\tau)$.
\end{remark}

\subsection{Bernoulli relation in the disk region}
\label{subsec:disk_Bernoulli}

As mentioned above, this solution assumes $I_2'(\psi)
~(=\lambda)=0$, and hence, $I_2 = \rho_2 r V_\theta$ must
uniformly distribute. In the disk region (the vicinity of $z=0$),
we may approximate $V_\theta \approx \sqrt{MG/r}$ (Keplerian
velocity). Hence,  $\rho_2 \propto r^{-1/2}$.
In Fig.\,\ref{fig:density}, we show the profile of $\rho=\rho_1\rho_2$
for the case of $\rho_1\propto\rho_\perp$ (i.e., $\rho_\parallel=$constant).

For $\rho=\rho_1\rho_2=\rho_\parallel \rho_\perp r^{-1/2}$,
(\ref{friction-balance-2}) reads as
\begin{equation}
\nu = \frac{-\rmd\psi/\rmd z}{2 \rho_\parallel \rho_\perp} r^{-3/2}
\propto \frac{r^{-5/2}}{\rho_\parallel(r)}
\label{friction-balance-3}
\end{equation}
along each streamline in the disk region. For a given $\nu$, we
can solve (\ref{friction-balance-3}) for $\rho_\parallel$ to
determine the density profile.

In the disk region the Bernoulli relation (\ref{Bernoulli-1})
accounts as follows: by $\nabla\cdot\bm{P}=0$, we have $P_r =
\rho V_r \propto r^{-1}$.
If $\rho_\parallel(\sigma) =$ constant, for example,
$\rho\propto r^{-1/2}$ (evaluated along a streamline in the disk region).
Then, we have $V_r = V_{r0} r^{-1/2}$ with a (negative) constant $V_{r0}$.  Combining
the azimuthal velocity $V_\theta = V_{\theta 0} r^{-1/2}$ (which
must be slightly smaller than the Keplerian velocity
$\sqrt{MG/r}$), we obtain
\[
V^2 = (V_{r0}^2 + V_{\theta0}^2) r^{-1} = V_0^2 r^{-1}.
\]
By $\rho_2 \propto r^{-1/2}$, we obtain $ \partial_r (\log \rho_2)
= -(1/2) r^{-1}$. Hence, the Bernoulli relation
(\ref{Bernoulli-1}) demands
\[
\partial_r h = (V_{0}^2-MG) r^{-2},
\]
which yields $h = (MG -V_{0}^2) r^{-1}$. In this estimate, all
components of the energy density (gravitational potential $\phi$,
kinetic energy $V^2/2$ and enthalpy $h$) have a similar profile
($\propto r^{-1}$).

\subsection{Bernoulli relation in the jet region}
\label{subsec:jet_Bernoulli}
In the jet region (vicinity of $r=0$),
the streamlines (contours of $\tau=z/r$) are almost vertical, and
we may approximate $\sigma \approx z$.

Let us first estimate $\rho_2$ using
(\ref{friction-balance-2}), which is approximated, in the jet
region, by
\begin{eqnarray}
r \rho \nu = \{\log\rho_2,\psi\}
&\approx& (\partial_r\psi)\,(\partial_z\log\rho_2)
\nonumber \\
&=& J\,p\,\tau^{p+1}\frac{1}{z}\,
\partial_z(\log\rho_2), \label{jet-Bernoulli-1}
\end{eqnarray}
which shows that $\rho_2$ is an increasing function of $|z|$.
Using $\rho = \rho_\parallel(\sigma)\rho_\perp(\tau)\rho_2$, we
integrate (\ref{jet-Bernoulli-1}) along the streamline
($\tau=$constant, $\sigma \approx z$):
\begin{equation}
\frac{\rmd\rho_2}{\rho_2^2} = - \rmd\left(\frac{1}{\rho_2}\right)
=\frac{\nu}{Jp}\ \tau^{p+2}\,\rho_\perp(\tau) \rho_\parallel(z) z^2
\rmd z . \label{jet-Bernoulli-2}
\end{equation}
With this $\rho_2(z)$, we may estimate the toroidal (azimuthal)
component of the velocity: $V_\theta = I_2/(r\rho_2) =
(I_2\tau)/(z\rho_2)$, where $I_2$ and $\tau$ are constant (the
latter is constant along each streamline). We find that the
kinetic energy $V_\theta^2/2$ of the azimuthal velocity decreases
as a function of $|z|$ (both by the geometric expansion factor
$z^{-2}$ and the viscosity effect $\rho_2^{-2}$). The steep
gradient of the corresponding hydrodynamic pressure yields a
strong boost near the foot point ($z\approx 0$).

The poloidal component of the kinetic energy is estimated as follows:
We may approximate
\begin{eqnarray}
\frac{1}{2}(V_r^2 + V_z^2) = \frac{1}{2\rho^2 r^2}\,|\nabla\psi|^2
&\approx& \frac{1}{2\rho^2 r^2} \left(
Jp\frac{z^p}{r^{p+1}}\right)^2
\nonumber \\
&=&
\frac{(Jp)^2\tau^{2p+4}}{2\rho^2z^4} . \label{jet-Bernoulli-2'}
\end{eqnarray}
Here, the vertical distribution of the density $\rho =
\rho_\perp(\tau) \rho_\parallel(\sigma) \rho_2$ is primarily
dominated by $\rho_\parallel(\sigma)\approx\rho_\parallel(z)$.

At long distance from the origin, the jet has a natural similarity
property. For simplicity, let us ignore the effect of viscosity
($\nu=0$), and assume $\rho_2=1$. Then, $\rho_\parallel \propto
|z|^{-3/2}$ yields $(V_r^2 + V_z^2)/2 \propto z^{-1}$, which may
balance with the gravitational potential energy $\phi = -MG
|z|^{-1}$. Note, that the azimuthal component of the kinetic
energy disappears at large scale ($V_\theta^2 \propto z^{-2}$).
The Bernoulli condition (\ref{Bernoulli-1}) gives $h$ that also
has a similar distribution of $\propto |z|^{-1}$.

Figure\,\ref{fig:density} shows the profile of $\rho =
\rho_\perp\rho_\parallel\rho_2$ with $\rho_\parallel \propto
|z|^{-3/2}$ (jet region) and $\rho_2 \propto r^{-1/2}$ (disk
region).
Dividing $\bm{P}$ by the density $\rho$,
we obtain the velocity field $\bm{V}$;  Fig.\,\ref{fig:streamline}
shows the streamlines of $\bm{V}$ corresponding to Figs.\,\ref{fig:flow}
and \ref{fig:density}.

\begin{figure}
\begin{center}
\includegraphics[scale=0.8]{fig-disk-jet.eps}
\caption{
The contours (in log scale) of the density $\rho$
in the similarity solution (\ref{similarity-1})
of the Beltrami model (with parameters
$D=1$, $p=1$, $J=0.1$, and $q=1$).
}
\label{fig:density}
\end{center}
\end{figure}

\section{Summary and Concluding Remarks}

We have shown that the combination of a thin disk and
narrowly-collimated jet is the unique structure that is
amenable to the singularity of the Keplerian vorticity; the
Beltrami condition ---the alignment of flow
and \emph{generalized vorticity}--- characterizes the geometry.
Here the conventional vorticity is generalized as (\ref{g-vorticity}) to
subtract the viscosity force causing the accretion
and the centrifugal force of the Keplerian velocity.
Identifying the disk-jet structure as a generalized Beltrami vortex, we will be
able to understand the self-organization process in terms of the
``generalized helicity.''
As we have learned in the present practice,
the helicity of the generalized vorticity is the key parameter
that characterizes the self-organizing of a disk-jet system.

We end this paper with a short comment on the singularity of the Keplerian velocity.
The similarity solution has a singularity at the origin (where
$\phi=-MGr^{-1}$ diverges), which disconnects the
disk and jet parts of our solution.
To ``connect'' both subsystems, we need a \emph{singular
perturbation} that avoids the divergence of physical quantities
dictating the small-scale hierarchy on which the disk and jet regions
are connected smoothly;
Shiraishi {\it et al.}\,\cite{bib:Shiraishi} describes how the different topologies of magnetic
field-lines in the disk and jet regions can be connected in a
``boundary layer'' determined by the the Hall effect in
a weakly ionized plasma.

\section*{Acknowledgments}

The authors are grateful to Professor S. M. Mahajan,
Professor R. Matsumoto, Professor G. Bodo,
and Professor V. I. Berezhiani for
their suggestions and comments.
The work of ZY was supported by
Grant-in-Aid for Scientific Research (23224014) from MEXT, Japan,
and that of NLS was partially supported by the Rustaveli NSF Grant
project 1-4/16 (GNSF/ST09-305-4-140).

redpajama_set_name: RedPajamaArXiv


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Home » FLC community participation in the DOD's Peer Reviewed Cancer Research Program
FLC community participation in the DOD's Peer Reviewed Cancer Research Program
FCF would like to extend a special thank you to Jenny Carroll who participated in the 2021 grant review process this fall as a consumer advocate for the Congressionally Directed Medical Research Programs' (CDMRP) Peer Reviewed Cancer Research Program (PRCRP) in the Department of Defense (DOD). Jenny was nominated for participation in the program by the Fibrolamellar Cancer Foundation. As a consumer reviewer, she was a full voting member, (along with prominent scientists) at meetings to help determine how the $115 million appropriated by Congress for Fiscal Year 2021 will be spent on cancer research.
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Home » Business Management Courses, Skills, Subjects, Certificate & Scope
Business Management Courses, Skills, Subjects, Certificate & Scope
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Benefits of Business Management Degrees
With various benefits associated with the business management degrees, you can choose the usable carrier path as per your interest. Once you have business management degrees, you will be in demand because businesses need the people capable of managing business & organization with confidence.
The skill sets you will get by business management programs are extremely beneficial and transferable. You can give various benefits to the business in different ways.
You have the flexibility to decide and jump in any industry you wish as per your business management programs.
Benefits of business management programs/degree, you can earn a six-figure salary working in the finance field if you have a degree from top schools.
Future of Business Management
Technology is growing rapidly and no field left to affecting by technological advancement. With the big data and artificial intelligence the business management field changing its nature day by day.
It could be possible that there will not be a big change for everyone in the business management field but it will be positive according to experts.
People with a business management degree will be in demand and keep the average growth in the filed as other job industries.
What to Look for in a Business Management Courses?
Accounting (Accounting for Decision-Making)
Marketing (Marketing Management)
Business Strategy (Strategic Management)
What are Business Management Career Options?
If you want to prepare your carrier in business management, you should be aware of the role and responsibility you could responsible for the below-mentioned roles.
Chartered management accountant
Corporate investment banker
Forensic accountant
Some of the Career Options where Business Management Degree can be Beneficial.
Costs lawyer
Human resources officer
Logistics & distribution manager
Urban designer
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Recently renovated, third floor, one bedroom apartment located one block from the Old Harbor! Hardwood floors throughout, central air, and in-unit laundry. This apartment has a bus stop directly outside the building as well as a twelve minute walk to either of the MBTA's Red Lines, Broadway Station and Andrew Square. This apartment is available on April 1st with the an August 31, 2019 or 2020 termination. First, security and broker due at lease signing. Pet friendly!
Listing courtesy of Tana Bramley of Boston Realty Advisors.
Listing provided courtesy of Tana Bramley of Boston Realty Advisors.


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Chase Sapphire Preferred vs. Citi Premier: Which Card Is Better?
by Ethan Steinberg
While we generally think of Chase and American Express as the leaders in the world of transferable points cards, the truth is Amex doesn't have a card that can rival the Chase Sapphire Preferred Card. In fact, only one card can compete with the Sapphire's entry-level annual fee, strong bonus categories, flexible redemption options and travel perks. The card that checks all these boxes is the Citi Premier Card.
Now that a 60,000 point sign-up offer has returned on the Citi Premier, let's take a look at how these two cards stack up against each other and which card and welcome bonus is best for you.
Current Welcome Bonus Offers
Chase and Citi have both recently tweaked the offers on these popular cards to provide a higher sign-up bonus, but not waive the annual fee the first year.
New applicants for the Chase Sapphire Preferred can earn 60,000 Ultimate Rewards points after spending $4,000 in the first three months. TPG values Ultimate Rewards points at 2 cents each, making this offer worth $1,200. After subtracting the $95 annual fee, you'll walk away with a first year value of $1,105.
The Citi Premier also requires $4,000 of spending in the first three months to earn its welcome bonus of 60,000 ThankYou points. Although the offers are identical in terms of points and spend, there's one important difference: TPG only values ThankYou points at 1.7 cents each, making this bonus worth $1,020. After accounting for the $95 annual fee, your first year value is $925.
Winner: The Chase Sapphire Preferred wins in the very important welcome bonus category, besting the Citi Premier by $180.
Use the Sapphire Preferred's sign-up bonus to take a trip! (Photo by Isabelle Raphael / The Points Guy)
Sign-up bonuses come and go, but it's important to pick a card with strong bonus categories that will help you continue to earn points year after year. Let's take a look at how the bonus categories differ for these two cards:
Bonus Multiplier Chase Sapphire Preferred Citi Premier
3x N/A Travel (including many gas stations)
2x Travel and dining Dining and entertainment
1x All other purchases All other purchases
While the Sapphire Preferred has fewer bonus categories and tops out at 2x, you should keep in mind that a single Ultimate Rewards point is worth more than a single ThankYou point. The Premier clearly wins on travel purchases, with a 3x (5.1%) return compared to the Sapphire's 2x (4%), and on entertainment purchases like concerts, plays and amusement parks which don't earn any bonus points on the Sapphire. Still, if you're looking at a category like dining (2x on both cards) or everyday spend, the Sapphire wins by a small margin.
Winner: The Citi Premier wins because it offers more bonus categories and higher multipliers than the Sapphire Preferred.
The Citi Premier offers 3x on travel, plus 2x on dining and entertainment. (Photo by Isabelle Raphael/The Points Guy)
Redeeming
While the Chase Ultimate Rewards program doesn't have the most transfer partners, it stacks its roster deep with a number of high value options. Points transfer 1:1 (and in most cases, instantly) to all of Chase's hotel and airline partners. Familiar programs like United MileagePlus and British Airways Executive Club can be great options for redeeming award flights both domestically and internationally, but Chase is also the only program that lets you transfer points for hotel redemptions at a reasonable rate.
The transfer ratio of 1:1 to all partners sounds nice, but this doesn't account for the fact that every point or mile is worth a different amount in different programs. Thankfully one of Chase's best partners is Hyatt, where free nights start at just 5,000 points and top out at 40,000 points for luxury hotels in the new partnership with Small Luxury Hotels of the World.
Transferable points are valued for their flexibility, and while you'll usually get the best value by transferring to one of the aforementioned partners, sometimes you need to be on a specific flight and there's no award availability. In this case — or if you find a cheap cash fare — you can consider booking directly through the Chase portal. Sapphire Preferred card holders get a 25% bonus when booking airfare, hotels, car rentals and cruises through the Chase Ultimate Rewards travel portal, giving your points a value of 1.25 cents each. Better yet, these redemptions code as cash tickets, so you'll continue to earn elite miles on your flights (though not on most hotels).
Citi ThankYou Rewards offers 15 transfer partners, but JetBlue is the only American carrier on the list and you generally won't get outsized value from JetBlue TrueBlue points. Still, there are plenty of ways to find value here, especially with programs like Avianca LifeMiles, Virgin Atlantic, Singapore KrisFlyer and Etihad Guest. The other consideration is that none of these valuable partners are unique to Citi (in the way that Hyatt is to Chase). All of the programs I mentioned are also transfer partners of other major programs like American Express Membership Rewards or Capital One. The Citi Premier also offers a 25% bonus on airfare bookings made through the Citi portal.
Winner: This is a close call, but Ultimate Rewards rank higher in TPG's valuation series for a reason. While Citi has valuable transfer partners, it offers no unique value that can't be replicated in another program.
One of Chase's best transfer partners is Hyatt. (Photo of the Park Hyatt New York by Mitch Berman/The Points Guy.)
You're not going to get as many perks on a $95 a year card as you will with a premium card that costs $450 or more, but both of these cards offer a number of great travel benefits that are worth keeping in mind.
Let's start with just some of the benefits offered by the Chase Sapphire Preferred:
Primary rental car insurance: may provide reimbursement up to the actual cash value of the vehicle
Trip delay protection: may reimburse up to $500 per ticket for delays of 12 hours or more, or overnight
Baggage delay protection: may reimburse up to $100 per day for up to five days when baggage is delayed more than six hours
Purchase protection: covers your purchases for 120 days against damage or theft, up to $500 per claim and $50,000 per account
Extended warranty protection: may extend the manufacturer's warranty by an additional year on warranties of three years or less
For more information on these benefits, check out our review of the Chase Sapphire Preferred.
The Citi Premier offers additional purchase protections, though its travel benefits are weaker:
Rental car insurance: may provide reimbursement up to $50,000, secondary in the US and primary abroad
Trip delay protection: may reimburse up to $500 per ticket for delays of 12 hours or more, doesn't cover missed connections where a delay of less than 12 hours caused the missed connection
Baggage delay protection: may reimburse up to $100 per traveler when baggage is delayed by more than six hours
Citi Price Rewind: may reimburse you when the price drops on an item you purchased within the last 60 days, up to $200 per item and $1,000 per year
Purchase protection: covers your purchases for 90 days against theft or damage, up to $10,000 per incident and $50,000 per year
Return protection: may reimburse you when a merchant won't accept a return within 90 days of purchase, up to $300 per item and $1,000 per year
Extended warranty protection: may extend the manufacturer's warranty by two additional years on warranties, total coverage can't exceed seven years
Again, for more information on these benefits, take a look at our review of the Citi Premier.
Winner: The Citi Premier offers additional purchase protection features with its Price Rewind program and return protection, but the Chase Sapphire Preferred offers better travel protections. The winner will depend on what protections you value most, but we'll give the Citi Premier the win for offering additional purchase protections.
The Citi Premier offers four types of purchase protections. (Photo by Isabelle Raphael/The Points Guy)
Should I Get Both Cards?
After reading about the sign-up offers, earning, redemption options and benefits offered by the Citi Premier and the Chase Sapphire Preferred, you may be wondering whether you should simply get both cards. If you're considering signing up for both, here are some questions to consider:
Can I meet the minimum spending requirements? Each card requires you to spend $4,000 within the first three months in order to earn the sign-up bonus, and you don't want to miss out on earning the sign-up bonus. So, if you'll have trouble spending $8,000 within three months, you may want to space out your applications so you can tackle the spending requirements separately.
Can I be approved for the Chase Sapphire Preferred? Due to Chase's unstated 5/24 rule, you can only be approved for the Sapphire Preferred if you've opened four or fewer personal credit cards across all banks in the last 24 months. If you've opened more personal credit cards in the last 24 months, then you have to decide whether to wait to apply for the Sapphire Preferred once you're under 5/24 or forgo the Sapphire Preferred.
Am I eligible for the Chase Sapphire Preferred sign-up bonus? Two types of people aren't eligible for the sign-up bonus. First, current card members of any Sapphire credit card aren't eligible. Second, previous card members of any Sapphire credit card who received a new cardmember bonus within the last 48 months also aren't eligible.
Am I eligible for the Citi Premier sign-up bonus? You aren't eligible for the sign-up bonus if you've received a new card member bonus for Citi Rewards+, Citi ThankYou Preferred, Citi Premier or Citi Prestige, or if you have closed any of these accounts, in the past 24 months.
Does my spending align well with having both cards? If you decide to get both cards, you'll want to use the Citi Premier for travel (5.1% return), gas purchases (5.1%) and entertainment (3.4%) and the Chase Sapphire Preferred for dining (4%) and general spending (2%). Assuming you agree with TPG's valuations, you'd need to spend $1,868 per year — just $156 per month — on travel and gas with the Citi Premier to earn enough points to offset the annual fee, and you'd need to spend $1,584 per year — $132 per month — on dining with the Sapphire Preferred to earn enough points to offset the annual fee.
If your answer to the above questions is "yes," then you could definitely benefit from applying for both cards. You'll want to apply for the Sapphire Preferred first due to Chase's 5/24 rules, but once you're approved, you can apply for the Citi Premier the same day. And if your only hang-up is spending $8,000 within three months, you may want to apply for the Sapphire Preferred and reach the minimum spending requirement first before applying for the Citi Premier, although there are techniques for reaching minimum spending requirements when your spending falls short.
The Citi Premier and Chase Sapphire Preferred are the clear leaders when it comes to affordable, entry-level cards that earn valuable transferable bank points. Each card wins two categories in our analysis, so the best card for you will depend on (1) the other cards currently in your wallet and (2) which benefits you value most.
Many travelers could certainly get value from having and using both cards. However, if we're forced to select a winner, the Chase Sapphire Preferred comes out on top for one main reason: it's not just about how many points you earn, it's about how valuable and flexible those points are. Chase Ultimate Rewards points are just about as good as it gets in this category, good enough that it might be worth sacrificing the 3x travel bonus on the Citi Premier in order to stay within the Chase ecosystem.
Here are the official sign-up links for the Chase Sapphire Preferred Card and the Citi Premier Card, both of which currently offer 60,000 points after spending $4,000 in the first three months.
Ethan Steinberg joined TPG as a points and miles contributor in early 2017 and loves sharing his high-value redemption strategies with readers. If you asked him where he wants to travel next he'd quote Anthony Bourdain and tell you "anytime I'm eating spicy noodles in a bowl, I'm happy.
Experiencing Taipei's Night Markets With Kids


Eva Peron in Rome during her European tour.
World War II had benefitted the Argentine coffers. Argentina emerged as one of the world's wealthiest countries due to its robust beef and wheat industries that exported to severely weakened countries, such as Great Britain [source: Barnes]. Capitalizing on the handicapped European economies, Argentina inflated its export prices, and the other countries had no choice but to pay up. But the Peron administration didn't take advantage of the healthy economy only to help the poor. It also financed a lavish lifestyle that included Eva's penchant for couture clothing and jewelry. In 1947, Eva set off without her husband for a publicity tour of Europe, including visits to meet fascist Gen. Francisco Franco in Spain and the Pope in Italy. During that "rainbow tour," as she referred to it, Evita from the pampas made her global debut.
Back home, Argentina under Juan Peron was anything but a democratic nation. Peron was heavily influenced by the fascist and nationalist political parties that dominated the Axis powers during the war. However, the dictatorship that he built -- with Eva's help -- didn't act as a vise grip, clamping down on people's daily lives. Citizens were allowed to do as they pleased, but the social and cultural establishments were tightly controlled. For instance, the government outlawed student political activism on campuses. Some opposition parties were dissolved, and anti-Peronists were silenced. The state controlled the major newspapers and radio stations, while closely monitoring the others.
Eva also manipulated this authoritarian rule for her own purposes. She ensured that enormous, smiling portraits of her face were plastered in prominent public spaces. On outings, a photographer rarely left her side, ready to capture the attractive first lady kissing babies or cutting ribbons. One of Eva's most successful ventures that won her even more recognition was the creation of the Eva Peron Foundation. Before that, the Sociedad de Beneficia was the leading charity in the country. But the upper-class women who ran the organization bristled at Eva's humble background and denied her the ceremonial director position. In response, Eva crippled the charity by eliminating its government funding and replacing it with her own foundation that financed the construction of schools, orphanages, hospitals and other social services.
By 1951, Eva's hectic pace drove her to the sickbed. After becoming first lady at 27, she had suffered from occasional fainting spells and stomach pains. But after doctors diagnosed her with uterine cancer, Eva's health quickly deteriorated. Her public appearances became scarce, and she became drastically thin and bedridden at barely 33 years of age.


Spotify's Genius-powered "Behind the Lyrics" integration, which flashes lyric snippets and behind-the-scenes tidbits during users' listening experience, has become one of the music-streaming service's most viral, beloved features. Not to be outdone, rival service Apple Music is now also partnering with Genius — and in classic one-up fashion for the company, it's gone for bigger scale.
Apple Music recently finalized its year-in-the-making purchase of music-identification company Shazam, after the deal passed a European Union investigation, and added lyrics to a small portion of its catalog in iOS 12. By the latest count, the service has a U.S. user base the same size as Spotify's — though the former still lags behind the Swedish company in global user numbers — and the two closely competing services together account for 80 percent of the U.S. streaming market.


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Look out, little fish, a great white shark is passing above! Ferocious hunters, great whites have rows of razor-sharp teeth. Make your child's day with a coloring page featuring this mighty shark.
Give him a fun and informational coloring page, all about the great white shark!
Starring in this ocean coloring page is the glaring great white shark and he's on the search for prey! Use caution when coloring in his razor sharp teeth.
Let your child color one mean shark, the great white.
Meet one of nature's best fishermen, the America White Pelican! Share a beautiful coloring page with your child.
This coloring page features the building that's housed America's presidents for over 200 years.
This coloring page tells the story of the wolf-dog White Fang.
Color in this cool scene at the White House, and learn a few White House facts too!
Here's a great coloring page to celebrate April Fools' Day!


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Active learning is the key to the Freddy Fit science workshop it engages children in fast paced fitness activities built around four main themes.
Large color backdrops set the scene.
Bones – View the skeleton name the bones and check out some amazing facts, fun fit activities will showcase how regular exercise strengthens bones.
Muscles – Using Freddy Fit grip and arm strength gauges children will see and compare their results and view the various muscles in the body. Activities will demonstrate how muscles work, grow and repair.
Food – The Freddy Fit eat well plate visual breaks food into different sections, the plate will show children how to make good food choices when leading an active lifestyle. How food can repair, energize and protect the body.
Heart – How the heart functions and changes during exercise and rest. Fascinating facts about the veins and arteries, the heart is one of the most important organs children will see how daily exercise will keep the heart strong.
Classroom Worksheets – Follow up worksheets for both key stages will uncover more amazing facts and set various tasks for the children to complete.


The ability to perform the simple activities of daily living–dressing, bathing, toileting, preparing simple meals, and doing light housekeeping, for example–is crucial to an older adult's independence and quality of life.
When older adults begin having trouble managing these activities by themselves, their risks for falls, hospitalization, and even death can increase.
Recently, a group of researchers from the Nara Medical University in Japan examined whether or not participation in social activities could affect an older adult's ability to function. Their study is published in the Journal of the American Geriatrics Society.


text:
Bryan Robinson, Ph.D.
I am the author of 40 nonfiction books, including #CHILL: TURN OFF YOUR JOB AND TURN ON YOUR LIFE (William Morrow) and the long-selling CHAINED TO THE DESK: A GUIDEBOOK FOR WORKAHOLICS, THEIR PARTNERS AND CHILDREN, AND THE CLINICIANS
I am the author of 40 nonfiction books, including #CHILL: TURN OFF YOUR JOB AND TURN ON YOUR LIFE (William Morrow) and the long-selling CHAINED TO THE DESK: A GUIDEBOOK FOR WORKAHOLICS, THEIR PARTNERS AND CHILDREN, AND THE CLINICIANS WHO TREAT THEM (New York University Press). My books have been translated into fifteen languages. I am Professor Emeritus at the University of North Carolina at Charlotte, where I conducted the first studies on children of workaholics and the effects of workaholism on marriage. I built my career on the themes of resilience and work/life balance and have lectured throughout the world on work addiction and workplace issues. My research was featured on 20/20, Good Morning America, ABC's World News Tonight, NBC Nightly News, NBC Universal, The CBS Early Show, CNBC's The Big Idea and NPR's Marketplace. I hosted the PBS documentary, Overdoing It: How to Slow Down and Take Care of Yourself. I maintain a private psychotherapy practice in Asheville, NC and reside in the Blue Ridge Mountains with my spouse, three dogs, one cat, several tropical birds, and occasional bears at night.
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text:
The SCGA offers to its members Publications from external sources that can assist members in their Damage Prevention efforts and keep them current with events of interest.
SCGA 2017 DIRT Report
The CGA releases the annual DIRT report. See the detailed report for a full analysis
The SCGA releases the 2016 Saskatchewan DIRT Report. See the detailed report for a full analysis
CCGA 2015 DIRT Report
The CGA releases a report highlighting for 2015 including Canadian information. See the detailed report for a full analysis
The CCGA released it 2015 DIRT Report for Canada at the fourth annual Damage Prevention Symposium that was held in Banff this October
Western Canada 2015 DIRT Report
The SCGA has joined forces with BC and Alberta to produce the first ever DIRT Report providing detailed analyses and recommendations with respect to the asset incident report data gathered by each province.
CCGA Underground Infrastructure Damage Prevention Best Practice Version 2.0
The SCGA and CCGA are proud to announce the latest release of vision 2.0 of the Harmonized Best Practices.
The CCGA released it 2014 DIRT Report for Canada at the third annual Damage Prevention Symposium that was held in Montreal this October
2014 CGA DIRT Report
The CGA releases a report highlighting for 2014 including Canadian information. See the detailed report for a full analysis.
Digging Safely: One-call Notification Systems
The Standing Senate Committee on Energy, the Envirtonment and Natural Resources releases a report recommending owners of federally regulated infrastructure to join one-call services.
CCGA Best Practices for Damage Prevention (Version 1)
The CCGA is pleased to announce that harmonization of the Best Practices for Underground Infrastructure Damage Prevention is completed. The SCGA Committee will work closely with Saskatchewan members and the national group to ensure an up to date and sustainable document
2013 CCGA National Report on Damage
The CCGA releases a report highlighting 2012 and 2013 damages and an analysis of the data for 4 Canadian Provinces.
The CGA releases a report highlighting a decrease in incidents in 2013. See the detailed report for a full analysis.
SCGA Releases White Paper recommending Mandatory One Call Legislation
The SCGA has recommended that the Saskatchewan government initiate a process to investigate development of a Mandatory One Call Service for Saskatchewan.
CSAA 2014 Information Card
The attached data highlights safety messages and information. If more cards are required please contact the SCGA at info@scga.ca
CCGA Damage to Underground Infrastructure
The attached report compiles and analyses incident data from 3 Canadian Provinces over 2011 and 2012.
Safe Ground Disturbance Checklist
National Click Before You Dig Portal
A Socio-Economic Cost Assessment Regarding Damages to Underground Infrastructures
The Quebec Common Ground Alliance (APISQ) has received a report completed by Ecole Polytechnique de Montreal identifying indirect costs of at least $75 million per year resulting from excavation incidents with underground infrastructure in Quebec in 2012
Move Energy Safely
(Standing Senate Committee on Energy, the Environment and Natural Resources — August 2013)
This report recommends that the federal government facilitate efforts to establish a national access point for information on the location of buried infrastructure, as well as the promotion of one-call centres and call-before-you-dig initiatives. Information on the coordinates of underground infrastructure should be consulted prior to any excavation activities by a third party.
The Damage Information Reporting Tool (DIRT) is the result of the efforts of the Common Ground Alliance (CGA). Data is gathered for 2012 regarding the occurrence of underground facility events. An event is defined as "the occurrence of downtime, damages, and near misses." DIRT provides industry stakeholders with a way to anonymously submit data into a comprehensive database for analysis of the factors that lead to events.
CSA S250 Mapping of Underground Utilities
This attachment introduces CSA S250 Mapping of Underground Utility Infrastructure which is derived from mapping best practices and internal utility company mapping standards. It encourages a management systems approach to mapping and record keeping. ________________________________________________________________________
CRTC Denies CCGA Application for Shared Use of 811
CRTC Denies CCGA Application for Shared Use of 811 22 Mar 2012. It is with disappointment that the CCGA, its Regional Partners across Canada and its National Stakeholders The Canadian Energy Pipeline Association and the Canadian Gas Association, announce the CRTC decision to deny the CCGA application for shared use of the 811 dialling code. For a Telecom proceeding, the CCGA application generated an unprecedented level of positive response from coast to coast. With that in mind, the CCGA remains confident there is a strong public desire to simplify access to One Call systems in Canada enhancing the integrity of our buried critical infrastructure and above all, better protecting public, worker and Community Safety. To that end, the CCGA and its partners are reviewing the CRTC's decision and considering next steps. ________________________________________________________________________
CCGA White Paper "Damage Prevention Legislation Elements Required for Canada"
This white paper, developed by the Canadian Common Ground Alliance articulates a series of principles and specific elements for effective legislation that, along with other key elements like improved communication and the development of safe excavation best practices, would result in safer digging practices, greater protection of underground infrastructure, and community safety.


The demand for cloud services has greatly increased within the last years. The acceptance of the cloud is rather high in the business world, which you can see from the massive survey we conducted at the beginning of 2017.
In this survey, we asked more than 2,000 IT decision makers (ITDMs) from nearly 100 countries to assess the state of cloud adoption. The clear majority of 80.1% said that they like cloud computing and already use cloud services: email, web hosting, collaboration/Office applications being the most popular.
Of course, as an IT company we belong to the 80% of cloud supporters. That's why we, the IT department at Paessler AG, decided quite a while ago to move from our Exchange servers to Microsoft Exchange Online and Office 365. How we did it, how long it took, and what we learnt from this migration you can read here.
In August, we started with the planning phase for migrating our company's mail system to Microsoft Exchange Online. The reasons why we planned to move to the cloud?
Our colleagues work all over the globe and therefore it is crucial to have easy access to all our mails anytime.
To make your own consideration whether you prefer Exchange Online or Exchange on-premises, have a look at our comparison chart. There is no "better" or "worse" concerning cloud or on-premises Exchange version. The versions are just different. The following table should help you weighing up.
You want Microsoft to take over the main part of maintaining your Exchange system?
Can your IT department guarantee 24/7 maintenance of your Exchange system?
You always want to be up to date and get releases of new features, fixes, patches automatically to your systems?
You want to roll out patches/updates manually and according to your own schedule?
You want somebody who takes care of all the needed hardware?
You use Office with colleagues for easy modifying, collaborating, and sharing, and you need tools like MS Teams, SharePoint Online, Lync Online?
You need your Exchange system only for mailing and calendaring?
Can you guarantee a 24/7 stable internet and network connection like Microsoft can?
You want independence from internet connection?
You want easy access to calendars, emails, and contacts on mobile phones at any time?
Is integration of third-party applications an important factor?
You want unlimited storage space on cloud servers all over the world?
You need to send large amounts of mails regularly?
You want to be flexible in terms of different license subscription plans matching your requirements?
You want a desktop-based mail and calendar server with several Exchange versions?
Do you only need the latest Exchange version?
Security is an important factor? You want security updates immediately?
You want to pay extra for better security?
You don't mind when patches and updates are installed without prior notification?
You want to know exactly where your data has been saved?
You prefer to troubleshoot a single point of failure (all mails are stored at one location)?
Microsoft offers various checklists for home/business/education users that help preparing for the migration to Office 365.
It's important that you have enough bandwidth for fully deployed Office 365 and have at least 20% capacity to manage very busy days.
For migrating our Exchange system to Exchange Online, we furthermore had our own migration concept with all the steps to be taken into consideration. We were also supported by an external IT provider specialized in cloud-based professional services who helped us determine the roadmap for our Exchange migration.
Before migrating public folders with more than 2 GB, contents should be deleted or stored in several public folders.
For running an Office 365 environment connected to your local Active Directory, a local Exchange server is still needed for maintaining the appropriate objects.
To grant a smooth cloud migration, we first created test mail boxes of different sizes, which were moved to the Microsoft cloud. After the successful tests at the end of October we began the official migration of all Outlook data of our IT department only. So, in case of unusual behavior, error tracking would be easier.
All the mails of the Tech Support Team would follow next to the cloud. We decided to execute the migrations always on weekends to minimize disruptions to company operations as much as possible. Due to the comprehensive preparatory work, the migration to Exchange Online was possible without larger failures and could be completed by mid-November. It was five minutes' maximum that the users could not access their mails, so everything went smoothly.
We learned that there is no better or worse concerning Exchange Online or Exchange Server on-premises. It must fit the company's individual needs, and so you should decide. Spend enough time in a detailed planning and perform a step-by-step migration beginning with the least important section.
If you follow all these steps, you can realize even sophisticated Exchange migrations without major downtime.
What about you? Have you already completed a Microsoft Exchange Migration? We'd love to read your experience in the comments!


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Patients Given Less Blood During Surgery Do Fine, Study Reports
Finding could lead to reduced risks for patients
FRIDAY, Dec. 12, 2014 (HealthDay News) -- Heart disease patients who receive smaller amounts of blood during surgery do as well as those who get more blood, a new study finds.
The research included more than 2,000 heart disease patients who were followed for as long as four years after surgery. Half received larger amounts of blood during surgery and half received up to two-thirds less blood.
Those who received less blood did not have an increased risk of death from heart disease, cancer or severe infection, according to the findings published online Dec. 9 in The Lancet.
AHA News: Pregnancy Complications Could Be Early Sign of Heart Disease Risk in Black Women
Tongue, Lip Snip Surgeries May Be Overused in U.S. Newborns
"There has been a steady decline in the amount of blood in transfusions given to patients in the past three to five years," study leader Dr. Jeffrey Carson, chief of the internal medicine division at Rutgers University Robert Wood Johnson Medical School, said in a university news release.
"I think it is very reassuring that we have found that using less blood is OK not just from a short-term perspective, but also a long-term perspective," he added.
About 5 million people receive blood transfusions each year in the United States, according to the U.S. Centers for Disease Control and Prevention. These include: surgery patients; accident, burn and trauma patients; and mothers and babies during and after birth.
Doctors determine how much blood a patient needs by assessing how much blood has been lost and by close monitoring of vital signs such as blood pressure, Carson explained.
Too much blood can overload a patient's circulatory system and lead to breathing problems, according to Carson. There can also be an increased risk of infection.
"There are definite risks associated with transfusion," Carson said. "The classic ones are hepatitis and HIV. They are as rare as being hit by lightning, but even so -- why give more blood to anyone if you can't show it benefits them?"
In addition, being able to give less blood might help prevent blood shortages, the researchers noted.
The U.S. National Heart, Lung, and Blood Institute has more about blood transfusion.
SOURCE: Rutgers University, news release, Dec. 10, 2014


Since Lynn Anderson's passing in 2015, we have been compiling collections of her stage wardrobe and her Western gear for various displays in her honor around the country. Our first exhibit is currently being held at the Country Music Hall of Fame in Nashville, Tennessee, until June 24, 2018. It's a very appropriate honor for our Rose Garden Queen and they have shared a cross section of her fabulous dresses, like the one from her "Rose Garden" album cover. They have also shared her Cowgirl side with several early Nudie's Western outfits and a full size Quarter Horse with a silver encrusted Parade Saddle. Treasures like these will be in the museum's ward in perpetuity, but there was so much that Lynn enjoyed and collected than just the museum pieces.
By June, we hope to have much of Lynn's collection sectioned off. There are many personal keepsakes that the family will enjoy. And the 100s of museum quality pieces will be archived and protected for future exhibits. So it will be the time to share the rest of Lynn's "stuff" with her fans and friends. There will be lots of 'every day items' and clothing to share. THIS WILL BE A ONE TIME EVENT IN NASHVILLE! More details to come on location and time.
Come prepared to share in the love of Lynn's life and the fabulous treasures she has left behind! Looking forward to seeing you in June.
Personal inquiries regarding the sale, SideStreetSutton@gmail.com, and follow the Facebook Page.