text:
After Fires, California Wine Country Wants Tourists Back
By editor • Nov 13, 2017
View Slideshow 1 of 4
Charred hills are visible behind field workers as they pick Syrah grapes during a harvest operation on October 25, 2017 in Kenwood, California.
Justin Sullivan / Getty Images
Tom Blackwood, general manager for Buena Vista, stands in front of the winery's cellar in Sonoma, Calif. on Nov. 7, 2017. Since the winery reopened two weeks ago, the number of visitors has dropped significantly, he said.
Farida Jhabvala Romero / KQED
Charred hills are near vineyards in Sonoma Valley, Calif. on Nov. 7, 2017. Local wineries such as Buena Vista were close to the flames.
Bill and Debbie Hart (front) from Springfield MO visit Buena Vista in Sonoma, Calif. on Nov. 7, 2017. "There's been some devastation but so many of the wineries are still open for business and we wanted to do our part to help support them," said Debbie Hart.
Originally published on November 11, 2017 7:41 pm
Buena Vista winery in Sonoma Valley, founded in 1857, is considered the birthplace of California wine. The cavernous cellar, carved into a hill by Chinese laborers, has survived earthquakes, several owners and last month's fires in Northern California.
Now, the black tree stumps and scorched hills right next to the winery's buildings show just how close the flames came — less than 30 feet, says Tom Blackwood, general manager at Buena Vista.
"The fire could not have come any closer without hitting the buildings. Buena Vista was surrounded by flames," says Blackwood, who credited firefighters with saving the winery, which withstood untouched. "We are so lucky."
But since Buena Vista reopened a couple of weeks ago, Blackwood is facing another problem: a big drop in visitors. During the month before the fires began, Buena Vista saw 6,000 visitors, says Blackwood. But since the winery reopened about two weeks ago, only 500 visitors have shown up.
"If the fires hadn't happened we would probably see about 50 or more people here at the bar," says Blackwood, gazing at the winery's relatively quiet tasting room. "What do we have here, like six people now at the bar?"
Last month's fires in Northern California hit wine country during peak tourist season. While some businesses burned, many others were forced to close temporarily because of lack of road access or bad air quality when the fires raged. Now that the danger has passed, wineries and restaurants across the region are open and want visitors to return.
Most of the cancellations came from tourists who are not local, according to small businesses in Sonoma Valley — a region where burned hills, homes and cars can be seen.
"Once the fires were under control, we found that very few people had decided to return. There was initially a fear of the entire valley being burned," says Hunt Bailie, who owns a small segway and bicycle tour company with his wife in the town of Sonoma. He said about 90 percent of his tours were cancelled.
"We found that most folks are interested in returning, but they think it might be too soon," says Bailie. "Typically October is the time when we can save all the pennies until spring, but that month dried up for us."
While the affected areas were "very limited," news coverage all over the world mostly showed destruction from the fires, says Caroline Beteta, who heads Visit California, the organization tasked with attracting tourists to the state.
"Just the imagery alone I would argue did more damage than the actual damage to the tourism infrastructure," Beteta told a conference of wine marketers in Santa Rosa, the biggest city in Sonoma county. News images of charred houses and red glowing skies flashed behind her.
Tim Zahner, chief operations officer for Sonoma County Tourism, says most hotels and wineries in the county are fine, and are pouring in their tasting rooms today.
"The weather is mild. You know if you're in Chicago and it's November and it's snowing, out here it is not snowing. It's gorgeous," says Zahner, who was also attending the wine marketing conference. "It's a good time to come visit."
His group and Beteta's are trying to convince visitors to return to the region. Visit California launched a $2 million dollar advertising campaign to bring back images of sunny vineyards and happy couples enjoying a glass of cabernet sauvignon — wine country images.
Economist Robert Eyler says it's too early to tell the economic impact of the fires on tourism. But he expects the county to overcome any downturn in visitors.
"The brand of Sonoma and wine country is going to survive because the brand is very very established," says Eyler, a professor at Sonoma State University. "This is something that is a brand challenge in the short term. I would be flabbergasted if it was in the long."
That brand is something local small business owners are counting on. People like Mingma Sherpa, who co-owns a Mexican restaurant about two miles from the fire line.
The immigrant from Nepal estimates half of his customers are gone. Before the fires, at least one tour bus would stop here daily, he said.
"Since that happened, most of them have cancelled," says Sherpa, adding that the sudden loss in revenue forced him to cut shifts for servers and other employees.
"It's definitely tough. But this town is very special. So hopefully they'll come back," he says.
Copyright 2017 KQED. To see more, visit KQED.
The fires that ravaged parts of Northern California came during peak tourist season for the wineries in the area. Now that the fires are out, Sonoma County wineries and restaurants are open but feeling an economic hit. From member station KQED, Farida Jhabvala Romero reports.
FARIDA JHABVALA ROMERO, BYLINE: Buena Vista winery in Sonoma Valley is considered the birthplace of California wine, founded in 1857. Now, the black tree stumps and scorched hills right next to the winery cellar show just how close the flames came - about 30 feet.
TOM BLACKWOOD: The fire could not have come any closer. Buena Vista was surrounded by flames.
ROMERO: Tom Blackwood is general manager here. He thanks firefighters that the winery survived untouched. But now, he's got another problem. He says the month before the fires, they had close to 6,000 visitors, but since they reopened two weeks ago, just 500. He walks to the tasting room and shows me.
BLACKWOOD: You know - what do we have? - six people now at the bar.
ROMERO: Blackwood says it should be like 50 and that the big hit is from tourists who canceled their trips entirely.
BLACKWOOD: The people that called us that saw the destruction, that thought or think that, you know, wine country was destroyed, everything was destroyed.
ROMERO: News coverage all over the world showed destruction from the fires says Caroline Beteta. She heads Visit California, the organization tasked with attracting tourists to the state. Beteta spoke to a conference of wine marketers in Santa Rosa, the biggest city in the county. News images of charred houses and red glowing skies flashed behind her.
CAROLINE BETETA: Just the imagery alone, I would argue, did more damage than the actual damage to the tourism infrastructure.
ROMERO: If you start driving on back roads in Sonoma Valley, you could see some scorched houses and cars. But Tim Zahner with Sonoma County Tourism says most hotels and wineries in the county are fine now and are pouring in their tasting rooms today.
TIM ZAHNER: You know, if you're back in Chicago and it's November and it's snowing - out here, it's not snowing. You know, it's gorgeous. So it's a good time to come visit.
ROMERO: His group and Beteta's are trying to convince people to come back. Visit California launched a $2 million ad campaign to bring back images of sunny vineyards and happy couples enjoying a glass of red - you know, wine country images.
ROBERT EYLER: This is something that is a brand challenge in the short term.
ROMERO: Economist Robert Eyler at Sonoma State University says, for now, that's all he expects it to be.
EYLER: Unless we have, let's say, repeated fires year after year after year, which will unfortunately act as an erosion of brand, but there's no history to expect that to happen.
ROMERO: That brand is something local small business owners like Mingma Sherpa are counting on. He co-owns La Casa, a Mexican restaurant about 2 miles away from the fire line. It's happy hour here, but Sherpa says half of his customers are gone. Before the fires, at least one tour bus would stop here daily.
MINGMA SHERPA: But since that happened, we get like once a week. So all six, seven days, most of them are cancelled.
ROMERO: He says this town is special. And for those tourists that return, he'll be serving them ice-cold margaritas. For NPR News, I'm Farida Jhabvala Romero. Transcript provided by NPR, Copyright NPR.


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text:
\section{1. Introduction}

Ising and Heisenberg models are spin Hamiltonians which have been
originally proposed in the study of magnetism in pure and diluted materials
\cite{kobe,stinch,belan,wolf}. They are widely studied and employed in both
classical
and quantum  contexts. However, a great interest has also been devoted
to the $XY$ model due to the richness of its phase diagram and the character
of its transition \cite{be,kt}. In particular, the XY model in two dimensions
is of prime interest in the field of statistical mechanics
because of its intriguing and unusual phase transition.
Recently, the study of the $XY$ model has
been motivated not only due to its applicability in describing
real magnetic materials (for instance, it has been quite recently shown that
the phase diagram of the compound RbFe(MoO$_4$)$_2$ is in good agreement
with the theoretical predictions for a two-dimensional XY classical
model \cite{svistov}) but as well as in condensed  matter systems,
for example liquid crystals \cite{liu} and
superconductors \cite{pierson,choi,franz}, among others.

The one-dimensional version of the quantum spin-1/2 $XY$ model has been
exactly solved by Lieb, Shultz and Mattis \cite{lms}.
Although the quantum nature of real magnets cannot be forgotten,
the study of classical models continues to be an important subject of
research. The two-dimensional classical version of the $XY$ model
has been treated by Berezinskii and Kosterlitz and Thouless \cite{be,kt} and
they showed that the vortices and anti-vortices play a central role in the
thermodynamic behavior of the model. For higher dimensions
this model (as well as a planar rotator version)
has been studied through approximate analytical techniques
\cite{beth,tonico3,tonico1,tonico2} and Monte Carlo simulations \cite{landau}.
In addition, classical models in general, and in particular the XY model,
have become
very popular recently in the context of quantum phase transitions, where a
d-dimensional quantum model at $T=0$ is transformed into a classical $d+1$
dimensional one \cite{sach,lonz}.

The effort for a better theoretical understanding of the high
temperature superconductors has also lead to an increase in
treating anisotropic $XY$ type models \cite{franz,min,shenoy,eric},
specially its two-dimensional version.
However, despite the layered structure of these systems,
the high temperature superconductors are not strictly two
dimensional. For this reason, inter layer interaction should be important
in describing their thermodynamic properties \cite{franz},
as well as the inclusion of possible crystal field interactions.

In this work we study the classical anisotropic $XY$ model with a crystal
field interaction described by the following Hamiltonian
\begin{eqnarray}
\label{ham} {\cal H}&=&-J\sum_{ \langle \vec{r},
\vec{r}^{'}\rangle}\{S_{\vec{r}}^{x} S_{\vec{r}^{'}}^{x}+
S_{\vec{r}}^{y}S_{\vec{r}^{'}}^{y}\}
\nonumber\\
&-&J_{z}\sum_{ \langle \vec{r},
\vec{r}^{'}\rangle}\{S_{\vec{r}}^{x} S_{\vec{r}^{'}}^{x}+
S_{\vec{r}}^{y}S_{\vec{r}^{'}}^{y}\}+
D\sum_{\vec{r}}(S_{\vec{r}}^{z})^{2}~,
\end{eqnarray}
where $J$ is the exchange interaction between spins in the layers parallel to
the $xy$ plane and $J_z$ the exchange interaction between spins in
different adjacent layers. $D$ is the crystal field and $S_{\vec{r}}^{\alpha}$
are the $\alpha=x,y,z$ components of a classical spin $|\vec{S}_{\vec{r}}|=1$.
The first sum runs on nearest neighbor spins $\langle \vec{r},
\vec{r}^{'}\rangle$ within the layers and the second sum  on
nearest neighbor spins $\langle \vec{r}, \vec{r}^{'}\rangle$ between layers
(in order to avoid confusion here and in the following expressions,
 the subscript of the exchange interaction or the variational parameter
in front of the sums will define whether the spins belong to the same layer
or to adjacent layers). The last sum is made over the entire $N$ spins on
the simple cubic lattice.

The Hamiltonian (\ref{ham}) can be written in a more convenient form by
means of a polar representation for the spins \cite{beth,tonico3}
\begin{eqnarray}
\label{polar}
\vec{S_{\vec{r}}} &=& (S_{\vec{r}}^{x}, S_{\vec{r}}^{y}, S_{\vec{r}}^{z}) =
({\sin \theta_{\vec{r}}} {\cos \phi_{\vec{r}}},
{\sin \theta_{\vec{r}}} {\sin \phi_{\vec{r}}}, S_{\vec{r}}^{z}),
\nonumber\\
\vec{S_{\vec{r}}}&=&({\sqrt{1- {(S_{\vec{r}}^{z}})^2}\cos \phi_{\vec{r}}},
 \sqrt{1- {(S_{\vec{r}}^{z}})^2}{\sin \phi_{\vec{r}}},
S_{\vec{r}}^{z})~,
\end{eqnarray}
where $\theta_{\vec r}$ and $\phi_{\vec r}$ are the spherical angles of the
spin at the site $\vec r$. In this representation
the Hamiltonian given by Eq. (\ref{ham}) takes the form
\begin{eqnarray}
\label{hplanar} {\cal H}&=&-\frac{J}{2}\sum_{  \vec{r}, \vec{a}}
\sqrt{1- {(S_{\vec{r}}^{z}})^{2}} \sqrt{1-
{(S_{\vec{r}+\vec{a}}^{z}})^{2}}\cos
(\phi_{\vec{r}+\vec{a}}-\phi_{\vec{r}})
  \nonumber\\
&-&\frac{J_{z}}{2}\sum_{ \vec{r}, \vec{c}} \sqrt{1-
{(S_{\vec{r}}^{z}})^{2}} \sqrt{1-
{(S_{\vec{r}+\vec{c}}^{z}})^{2}}\cos
(\phi_{\vec{r}+\vec{c}}-\phi_{\vec{r}})
\nonumber\\
&+&D\sum_{\vec{r}}(S_{\vec{r}}^{z})^{2},
\end{eqnarray}
where  $\vec a$ labels the four nearest-neighbor sites of $\vec r$
in the $xy$ plane and $\vec c$ the two nearest-neighbor sites of
$\vec r$ along the $z$ direction.

The above model has been treated according to the self-consistent harmonic
approximation (SCHA) in the case $D=0$ for the three-dimensional model
\cite{tonico2} as well as the planar rotator model \cite{tonico1}
(in this case there is no $z$ spin components). The approach
in \cite{tonico2}, however, only
considers the cases $J_z\approx J$ and $J_z<<J$, that is, quasi-isotropic
case or weak layer coupling and no general treatment has been done for any
value of $0\le J_z\le J$.

In what concerns the theoretical approach, it is well known that
the SCHA has been extensively used in the literature
\cite{franz,tonico1,tonico2,eric,ari1,ari2,spis,wood,lozo,fish1,
fish2,ari3,darcy}.
It consists of replacing the original Hamiltonian (\ref{hplanar}) by
a harmonic one by expanding the corresponding cosines to the second order
with effective exchange constants that take into account the nonlinearities
of the interactions. The effective couplings are then chosen to minimize the
corresponding free energy of the system.
In the present work we use a variational method based on Bogoliubov inequality
for the free energy to study the model Hamiltonian (\ref{ham})
in order to obtain its low temperature thermodynamic properties.
This procedure is the same as the SCHA employed in previous works.
Some simplifications are also suggested  in order to
easier handle the awkward self-consistent implicit equations.

The plan of the paper is as follows. In the next section, we present the
analytical procedure according to the variational approach for the free
energy in order to obtain the thermodynamic properties of the model.
In section 3, the
numerical results are presented, where the role played by the anisotropy in
the presence of a crystal field is shown to be for itself  relevant (for
instance, in the context of high temperature superconductors). Additional
assumptions are also suggested which can make the
implicit self-consistent equations easier to be handled. Some concluding
remarks are discussed in section 4.

\section{2. Variational Approach for the free energy}

The present variational approach is based on the Bogoliubov inequality for
the free energy
\begin{equation} \label{bi}
F\leq F_{0}+\langle {\cal H}-{\cal H}_0(\gamma)
\rangle_{0}\equiv \Phi(\gamma) ,
\end{equation}
where ${\cal H}$ is the Hamiltonian in study given by Eq. (\ref{ham})
or (\ref{hplanar}), ${\cal H}_0(\gamma)$ is a trial Hamiltonian which can be
exactly solved and depends on variational parameters $\gamma$. $F$ is the free
energy of the system described by $\cal H$, $F_o$ is the free energy of the
trial Hamiltonian ${\cal H}_o$, and the thermal average $<... >_0$ is taken
over the ensemble defined by ${\cal H}_0$. The
approximate free energy is given by the minimum of $\Phi(\gamma)$ with
relation to $\gamma$, that is, $F\equiv \Phi_{min}(\gamma)$.

In general, the trial Hamiltonian should resemble, in some aspects, the
one under study. In this case, ${\cal H}_0$ can be chosen  as a sum of two
parts
\begin{eqnarray}
\label{Ho} {\cal H}_{o}= {\cal H}_{o}^\phi + {\cal H}_{o}^z,
\end{eqnarray}
in such a way that the first part is a kind of a planar Hamiltonian
\begin{eqnarray}
\label{Hopb} {\cal H}_{o}^\phi=\frac{\gamma}{4}\sum_{
\vec{r}, \vec{a}}(\phi_{\vec{r}+\vec{a}}-\phi_{\vec{r}})^{2}
+\frac{\gamma_{z}}{4}\sum_{ \vec{r},
\vec{c}}(\phi_{\vec{r}+\vec{c}}-\phi_{\vec{r}})^{2}
\end{eqnarray}
and the second term is an axial Hamiltonian
\begin{eqnarray}
\label{Hoab}
{\cal H}_{o}^z=
(D+2J+J_{z})\sum_{
\vec{r}}(S_{\vec{r}}^{z})^{2} ,
\end{eqnarray}
where $\gamma$ and $\gamma_z$ stand for the variational parameters.
This harmonic choice for ${\cal H}_0$
is also motivated by the fact that at low temperatures the
angle differences $|\phi_{\vec{r}+\vec{a}}-\phi_{\vec{r}}|<<1$ and
$|\phi_{\vec{r}+\vec{c}}-\phi_{\vec{r}}|<<1$ so the cosines in Eq.
(\ref{hplanar}) can be expanded up to second order to give the terms
$(\phi_{\vec{r}+\vec{a}}-\phi_{\vec{r}})^2$ and
$(\phi_{\vec{r}+\vec{c}}-\phi_{\vec{r}})^2$ in ${\cal H}_0^\phi$.
Since in this case there is
a negligible variation in the $z$ components of the spins, we can further
assume that $S_{\vec r}^z\approx S_{\vec r + \vec a}^z$ and
$S_{\vec r}^z\approx S_{\vec r + \vec c}^z$,  so the square roots in Eq.
(\ref{hplanar}) are eliminated and we end up to a term $D+2J+J_z$ in
the corresponding axial term. Thus, it turns out that this approach will
be valid only in the low temperature region.

Obtaining the averages regarding the trial Hamiltonian requires
diagonalizing (\ref{Ho}).
The planar Hamiltonian ${\cal H}_0^\phi$ can be diagonalized in the reciprocal
space through the Fourier transform of $\phi_{\vec{r}}$
\begin{equation}
\label{ft}
\begin{array}{ccc}
\phi_{\vec{r}}=\frac{1}{\sqrt{N}}\sum_{\vec{q}}e^{-i\vec{q}\cdot\vec{r}}
\phi_{\vec{q}} ,
\end{array}
\end{equation}
with the inverse transform $\phi_{\vec{q}}$ given by
\begin{equation}
\label{ift} \phi_{\vec{q}}=\frac{1}{\sqrt{N}}\sum_{
\vec{r}}e^{i\vec{q}\cdot\vec{r}} \phi_{\vec{r}}.
\end{equation}
Using the transformations (\ref{ft}) in Eq. (\ref{Hopb}) and the fact that
the system is translationally invariant we get
\begin{eqnarray}
\label{Hopfp} {\cal H}_{o}^{\phi}&=&
\frac{1}{2}\sum_{\vec{q}}\{\gamma\sum_{\vec{a}}
(1-e^{-i\vec{q}\vec{a}})
\phi_{\vec{q}}\phi_{\vec{-q}}\nonumber \\
&+&\gamma_z\sum_{\vec{c}}
(1-e^{-i\vec{q}\vec{c}})\phi_{\vec{q}}\phi_{\vec{-q}}\}.
\end{eqnarray}
Summing now over the vectors ${\vec a}$ in the $xy$ plane and $\vec c$
along the $z$ direction and rearranging terms
we obtain the diagonal form of the planar trial Hamiltonian
\begin{equation}
\label{Hopf} {\cal
H}_{o}^{\phi}=\sum_{\vec{q}}(\gamma_{q}+\gamma_{qz})\vert \phi_{q}
\vert^{2},
\end{equation}
where $\gamma_{q}=\gamma(2-\cos q_{x}a -\cos q_{y}a)$,
$\gamma_{qz}=\gamma_{z}(1-\cos q_{z}c)$, $a=|\vec a|$,
 $c=|\vec c|$ and $\vert \phi_{q}
\vert^{2}= \phi_{\vec{q}}\phi_{-\vec{q}}$.

The diagonalizing of the axial term of the harmonic Hamiltonian (\ref{Hoab})
is obtained by introducing the corresponding Fourier transform of the $z$
component of the spins $S_{\vec{r}}^{z}$
\begin{eqnarray} \label{fts}
S_{\vec{r}}^{z}=\frac{1}{\sqrt{N}}\displaystyle\sum_{\vec{q}}e^{-i\vec{q}
\cdot\vec{r}}S_{\vec{q}}^{z} ,
\end{eqnarray}
and the inverse transform $S_{\vec{q}}^{z}$ given by
\begin{eqnarray}
\label{ifts}
S_{\vec{q}}^{z}=\frac{1}{\sqrt{N}}\sum_{  \vec{q}}e^{i\vec{q}\cdot\vec{r}}
S_{\vec{r}}^{z}.
\end{eqnarray}
Applying (\ref{fts}) to Eq. (\ref{Hoab}) one gets
\begin{eqnarray}
\label{Hoaq}
{{\cal H}_{o}^{z}}=
(D+2J+J_{z})\sum_{  \vec{q}}
|S_{\vec{q}}^{z}|^2,
\end{eqnarray}
where  $\vert S_{\vec{q}}^{z}\vert^{2}=S_{\vec{q}}^{z}S_{-\vec{q}}^{z}$.

The partition function ${\cal Z}_0$ can be computed by first noting that
the planar and the axial parts of the harmonic
Hamiltonian are independent so
\begin{equation}
{\cal Z}_0=Tre^{-\beta{\cal H}_0}=Tre^{
-\beta({\cal H}_{o}^\phi + {\cal H}_{o}^z)}={\cal Z}_0^\phi{\cal Z}_0^z.
\end{equation}
Since both ${\cal H}_0^\phi$ and ${\cal H}_0^z$ are quadratic in their
variables one has
\begin{equation}
\label{Zop} {\cal Z}_{o}^{\phi}=Tre^{-\beta {\cal H}_{o}^\phi}=
\prod_{\vec{q}}\left[\frac{\pi}{\beta (
\gamma_{q}+\gamma_{qz})}\right]^{\frac{1}{2}}
\end{equation}
and
\begin{equation}
\label{Zoa} {\cal Z}_{o}^{z}=Tre^{-\beta {\cal H}_{o}^z}=
\prod_{\vec{q}}\left[\frac{\pi}{\beta \Omega}\right]^{\frac{1}{2}},
\end{equation}
where $\Omega=D+2J+J_{z}$.
The free energy $F_0$ is then given by
\begin{eqnarray}
\label{F0} F_0=-
\frac{k_{B}T}{2}\sum_{\vec{q}}\ln{\frac{\pi}{\beta (
\gamma_{q}+\gamma_{qz})}}-\frac{k_{B}T}{2}N\ln{\frac{\pi}{\beta
\Omega}}
\end{eqnarray}

The mean value $<{\cal H}_0>_0$ can be evaluated by using the equipartition
theorem resulting in
\begin{equation}
\label{NKT} \langle {\cal
H}_{0}\rangle_{0}=\frac{Nk_{B}T}{2}+\frac{Nk_{B}T}{2}=Nk_{B}T.
\end{equation}

On the other hand, the mean value of $<{\cal H}>_0$ is not so straightforward
computed. It can be written as
\begin{eqnarray}
\label{Hm1}
\langle{\cal H}\rangle_{0}= \hspace{7cm} \nonumber \\
- \frac{J}{2}\sum_{ \vec{r},
\vec{a}}\langle \sqrt{1- (S_{\vec{r}}^{z})^{2}} \sqrt{1-
(S_{\vec{r}+\vec{a}}^{z}})^{2}\rangle_{0}\langle
\cos (\phi_{\vec{r}+\vec{a}}-\phi_{\vec{r}})\rangle_{0}\nonumber\\
- \frac{J_{z}}{2}\sum_{  \vec{r}, \vec{c}}\langle
\sqrt{1- (S_{\vec{r}}^{z}})^{2} \sqrt{1-
(S_{\vec{r}+\vec{c}}^{z}})^{2}\rangle_{0}\langle
\cos (\phi_{\vec{r}+\vec{c}}-\phi_{\vec{r}})\rangle_{0}
\nonumber \\
+D\sum_{\vec{r}}\langle(S_{\vec{r}}^{z})^{2}\rangle_{0},\hspace{5.5cm}
\end{eqnarray}
where in the  first two sums the mean value of the product of the planar and
axial terms regarding the trial Hamiltonian has been factorized and
\begin{equation}
\label{sm2}
\langle(S_{\vec{r}}^{z})^{2}\rangle_{0}=\frac{k_{B}T}{
2(D+2J+J_z)}
\end{equation}
is the out-of-plane spin fluctuation.

For the
Gaussian variables $(\phi_{\vec{r}+\vec{a}}-\phi_{\vec{r}})$ we can write
\begin{equation}
\label{gauss}
 \langle \cos
(\phi_{\vec{r}+\vec{a}}-\phi_{\vec{r}}) \rangle_{0}
=e^{-\frac{1}{2}\langle (\phi_{\vec{r}+\vec{a}}-\phi_{\vec{r}})^2
\rangle_{0}},
\end{equation}
where the mean value appearing in the exponential is given by
\begin{eqnarray}
\label{difangaf}  \langle (\phi_{\vec{r}+\vec{a}}-\phi_{\vec{r}})^2 \rangle_0
=\frac{2}{N}
\sum_{  \vec{q}}(1-\lambda_{\vec{q}})
\langle |\phi_{\vec{q}}|^2\rangle_0,
\end{eqnarray}
where $\lambda_{{q}}=\frac{1}{2}(\cos q_{x}a +\cos q_{y}a)$
and
\begin{equation}
\label{phiq2}
\langle\vert \phi_{q}\vert^{2}\rangle_{0}=\frac{k_{B}T}{
2(\gamma_{q}+\gamma_{qz})}.
\end{equation}
Similarly, for the Gaussian variable $(\phi_{\vec{r}+\vec{c}}-\phi_{\vec{r}})$
we have
\[
 \langle \cos
(\phi_{\vec{r}+\vec{c}}-\phi_{\vec{r}}) \rangle_{0}
=e^{-\frac{1}{2}\langle (\phi_{\vec{r}+\vec{c}}-\phi_{\vec{r}})^2
\rangle_{0}},
\]
and
\begin{equation}
\label{difangcf}
\langle(\phi_{\vec{r}+\vec{c}}-\phi_{\vec{r}})^2\rangle_0 =\frac{2}{N}
\sum_{  \vec{q}}(1-\lambda_{\vec{q}}^{z})
\langle |\phi_{\vec{q}}|^2 \rangle_0,
\end{equation}
where $\lambda_{{qz}}=\cos q_{z}c$. In this way, Eq. (\ref{Hm1})
assumes the form
\begin{eqnarray}
\label{origmed2} \langle {\cal H}\rangle_{0}= -
\frac{J}{2}\sum_{ \vec{r}, \vec{a}} (1- \langle
(S_{\vec{r}}^{z})^{2}\rangle_{0}) e^{-\frac{1}{N}
\sum_{\vec{q}}(1-\lambda_{q})\langle\vert \phi_{q}
\vert^{2}\rangle_{0}} \nonumber\\
- \frac{J_{z}}{2}\sum_{  \vec{r}, \vec{c}}(1- \langle
(S_{\vec{r}}^{z})^{2}\rangle_{0})e^{-\frac{1}{N}\sum_{\vec{q}}(1-\lambda_{qz})
\langle\vert\phi_{q}\vert^{2}\rangle_{0}}\nonumber\\
+\sum_{\vec{q}}D\langle \vert
S_{\vec{q}}^{z}\vert^{2}\rangle_{0},\hspace{4cm}
\end{eqnarray}
where we have used an additional assumption that
$S_{\vec r}^z\approx S_{\vec r + \vec a}^z$ and
$S_{\vec r}^z\approx S_{\vec r + \vec c}^z$.
The last term can again
be computed from the equipartition theorem and as the terms in the
sums do not depend on the respective indexes we have
\begin{eqnarray}
\label{H0f}
{\langle {\cal H}\rangle_{0}}= \hspace{7cm} \nonumber \\
- 2JN(1- \langle
(S_{\vec{r}}^{z})^{2}\rangle_{0})
e^{-\frac{1}{2N}\sum_{\vec{q}}(2-(\cos{q_{x}a} +
\cos{q_{y}a}))\langle\vert \phi_{q}
\vert^{2}\rangle_{0}} \nonumber\\
-J_{z}N(1- \langle
(S_{\vec{r}}^{z})^{2}\rangle_{0})e^{-\frac{1}{N}\sum_{\vec{q}}
(1-\cos{q_{z}c})\langle\vert
\phi_{q}\vert^{2}\rangle_{0}}+\frac{NDk_BT}{2\Omega}.
\end{eqnarray}
The right hand side of Eq. (\ref{bi}) is then written as
\begin{eqnarray}
\Phi(\gamma ,\gamma_{z})= -
\frac{k_{B}T}{2}\sum_{\vec{q}}\ln{\frac{\pi}{\beta (
\gamma_{q}+\gamma_{qz})}}-\frac{k_{B}T}{2}\sum_{\vec{q}}\ln{\frac{\pi}{\beta
\Omega}}\nonumber\\
- 2JN(1- \langle
(S_{\vec{r}}^{z})^{2}\rangle_{0})
e^{-\frac{1}{2N}\sum_{\vec{q}}(2-(\cos{q_{x}a} +
\cos{q_{y}a}))\langle\vert \phi_{q}
\vert^{2}\rangle_{0}}\nonumber\\
-\mbox{} J_{z}N(1- \langle
(S_{\vec{r}}^{z})^{2}\rangle_{0})e^{-\frac{1}{N}\sum_{\vec{q}}(1-
\cos{q_{z}c})\langle\vert
\phi_{q}\vert^{2}\rangle_{0}}
\nonumber\\
-(2-\frac{D}{\Omega})\frac{NK_BT}{2}.
\label{phi}
\end{eqnarray}

Minimizing the above equation with respect to the variational parameters gives
an upper bound limit for the free energy. The variational parameters are
determined from the conditions
\begin{equation}
\label{dg}
\frac{\partial \Phi(\gamma ,\gamma_{z})}{\partial
\gamma}=0~ (a)\mbox{~~~~~and~~~~~} \frac{\partial \Phi(\gamma ,\gamma_{z})}
{\partial
\gamma_z}=0.~(b)
\end{equation}
The mathematical expressions for Eqs. (\ref{dg}) are rather lengthy to be
reproduced here. However, factorizing terms that can be canceled out and
defining
\begin{equation}
\label{exy}
\eta_{xy}=\frac{1}{2N}\displaystyle\sum_{\vec{q}}\left[2-\left(\cos{q_{x}a}
+ \cos{q_{y}a}\right)\right]\langle\vert \phi_{q} \vert^{2}\rangle_{0},
\end{equation}
\begin{equation}
\label{ez}
\eta_{z}=\frac{1}{N}\displaystyle\sum_{\vec{q}}(1-\cos{q_{z}c})\langle\vert
\phi_{q}\vert^{2}\rangle_{0},
\end{equation}
we arrive at the following expression
\begin{equation}
\label{minenerg2}\left[ 1- \langle(S_{\vec{r}}^{z})^{2}\rangle_{0}\right]
\left(2J\eta_{xy}e^{-\eta_{xy}}+J_{z}\eta_{z}e^{-\eta_{z}}\right)
=\frac{k_{B}T}{2}.
\end{equation}
It is interesting to notice that  this very same equation is obtained
either from condition (\ref{dg}a) or (\ref{dg}b), meaning that both variational
parameters cannot be obtained from this equation alone. However, from the
Gaussian variable definitions (\ref{gauss})-(\ref{difangcf}) one can deduce
the following additional relation for the fluctuations $\eta_{xy}$ and $\eta_z$
\begin{equation}
\label{extraeq}
2\gamma\eta_{xy}+\gamma_z\eta_z=\frac{k_BT}{2}.
\end{equation}
Comparing now Eqs. (\ref{minenerg2}) and (\ref{extraeq}) we end at the
following identifications
\begin{equation}
\label{noacople1b}\gamma=J
\left[ 1- \langle(S_{\vec{r}}^{z})^{2}\rangle_{0}\right]e^{-\eta_{xy}},
\end{equation}
\begin{equation}
\label{noacople2b}\gamma_z=J_z
\left[ 1- \langle(S_{\vec{r}}^{z})^{2}\rangle_{0}\right]e^{-\eta_{z}},
\end{equation}
which are now two parametric equations from which the two variational
parameters can be obtained. These equations can be put in a more convenient
form by noting that
\begin{eqnarray}
\label{soma1} e^{-\eta_{xy}}=
\exp{\left\{-\frac{1}{N}\sum_{  \vec{q}}
\frac{k_{B}T(1-\lambda_{{q}})}{2\left[2{\gamma}(1-\lambda_{{q}})
+{\gamma_{z}}(1-\lambda_{{qz}})\right]}\right\}}.
\end{eqnarray}
Taking the continuum limit of the above equation in cylindrical coordinates
$\frac{1}{N}\displaystyle\sum_{\vec{q}}\to
\frac{a^{2}c}{2\pi^{4}}\int_{0}^{2\pi}d\theta
\int_{0}^{\frac{\pi}{a}}qdq\int_{-\frac{\pi}{c}}^{\frac{\pi}{c}}dq_{z}$
and the long wave length limit $\vec{q}\approx0$  we find
\begin{eqnarray}
\label{resut1}
e^{-\eta_{xy}}=\hskip3.5cm
\nonumber\\ \exp{\left\{-\frac{k_{B}T}{2{\gamma}}
\left[\frac{\arctan{g^{\frac{1}{2}}}}{3g^{\frac{1}{2}}}+
\frac{1}{6}-\frac{g}{6}\ln{(1+\frac{1}{g})}\right]\right\}},
\end{eqnarray}
where $g=\frac{{\gamma_{z}}}{{\gamma}}$. Analogously we find
\begin{eqnarray}
\label{resut2}
e^{-\eta_{z}}=
\exp\{-\frac{k_{B}T}{2\gamma}\hskip2cm \nonumber\\
\times \left[\frac{1}{g}-\frac{1}{3g^{\frac{3}{2}}}\left(
2\arctan{g^{\frac{1}{2}}}
+g^{\frac{1}{2}}-g^{\frac{3}{2}}\ln(1+\frac{1}{g})\right)\right]\},
\end{eqnarray}
so that the variational parameters are finally obtained from
\begin{eqnarray}
\label{noacople3} \gamma&=& J(1- \langle
(S_{\vec{r}}^{z})^{2}\rangle_{o})\exp\{-\frac{k_BT}{2\gamma}
[\frac{\arctan{g^{\frac{1}{2}}}}
      {3g^{\frac{1}{2}}}         \nonumber \\
&+&\frac{1}{6}
-\frac{g}{6}\ln{(1+\frac{1}{g})]\}},
\end{eqnarray}
\begin{eqnarray}
\label{noacople4} \gamma_z&=& J_{z}(1- \langle
(S_{\vec{r}}^{z})^{2}\rangle_{o})\exp\{-\frac{k_{B}T}{2{\gamma}}
[\frac{1}{g}- \nonumber \\
&-&\frac{1}{3g^{\frac{3}{2}}}(2\arctan{g^{\frac{1}{2}}}
+ g^{\frac{1}{2}}-g^{\frac{3}{2}}\ln{(1+\frac{1}{g})})]\}.
\end{eqnarray}
The two equations above can also be obtained by employing the usual SCHA.
Thus, for a given value of $t=k_BT/J$, $D/J$ and $J_z/J$ one can solve the
non-linear system (\ref{noacople3}) and (\ref{noacople4}) to get
$\gamma/J$ and $\gamma_z/J$, and from them the desired thermodynamics of
the model.
For example, by taking the continuum limit in the long wave length regime
the $x$ component of the magnetization is given by
\begin{eqnarray}
\label{magh} m&=&(1-\frac{1}{2}\langle(S_{\vec{r}}^{z})^{2}
\rangle_{0})\exp\{-\frac{k_{B}T}{2\pi^{2}{\gamma}}
[\frac{\arctan{(g^{\frac{1}{2}})}}
{g^{\frac{1}{2}}} \nonumber \\
&+&\frac{1}{2}\ln{(1+\frac{1}{g}})]\}.
\end{eqnarray}
The transition temperature is obtained when the only solution of Eqs.
(\ref{noacople3}) and (\ref{noacople4}) is $\gamma=\gamma_z=0$.

Before exploring possible simpler solutions of Eqs. (\ref{noacople3})
and (\ref{noacople4}) and presenting the numerical results, it is worthwhile
now to discuss and compare some limiting cases.

Let us consider first $D=0$.
In this case we have the anisotropic $XY$ model. The
out-of-plane spin fluctuation takes the form
\begin{equation}
\label{sm2D0}
\langle(S_{\vec{r}}^{z})^{2}\rangle_{0}=\frac{k_{B}T}{4J+2J_z},
\end{equation}
which is the same as that obtained by Costa et al. \cite{tonico2}.
The transition temperature for
the two-dimensional model $J_z=0$, as well as the isotropic three-dimensional
model $J_z=J$, are also identical to those from reference \cite{tonico2},
respectively, $t_c=1.076$ and $t_c=1.605$. However, it is worth to stress here
that the present approach not only is a generalization over the model treated
by Costa et al. \cite{tonico2} to other values of
the axial interaction $J_z$, but also includes, as it will be seen below,
the important contribution of the crystal field interaction $D$.

In the limit $D\to\infty$, as it will be discussed below,
we have the planar rotator model. Again, we find the same
transition temperature for the two-dimensional model $t_c=1.472$ and,
for the three-dimensional model, $t_c=2.190$ \cite{tonico2}.
The transition temperatures for $D=0$ and $D\to\infty$ are given in Table
\ref{tab1} for the isotropic two- and three-dimensional models together with
those coming from other approaches.

\begin{table}
\caption{\it Reduced transition temperatures $t_c$ for the anisotropic $XY$
model in some isotropic limiting cases according to Monte Carlo (MC),
series, present approach, and Assumption 1 and Assumption 2
(Ass. 1-2).}
\label{tab1}
\vskip0.1in
\begin{tabular}{|c|c|c|c|} \hline
  & MC or series & present & Ass. 1-2 \\ \hline
 \hline
$D\to\infty$, $J_{z}=0$  &  $0.90$\cite{chakra}
           &  1.472     &  1.472  \\ \hline
$D\to\infty$, $J_{z}=J$  &  $2.17$\cite{kohr}
           &  2.190     &  2.207  \\ \hline
$D=0$, $J_{z}=0$          &  $0.78(2)$\cite{kawa}
      &  1.076     &  1.076\\ \hline
$D=0$, $J_{z}=J$  &  $1.54(1)$\cite{tonico2},  $1.55$\cite{ferer}   &  1.605

&  1.613 \\ \hline
\end{tabular}
\end{table}

In addition, the present approximation can also be used to evaluate the
behavior of the $x$ component of the magnetization for small axial
interaction   $J_{z}\ll J$ and any value of $D$. In this limit, we also have
$g\rightarrow 0$ so  Eq. (\ref{magh}) gives
\begin{equation}
\label{mag6} m\approx \left[1-\frac{1}{2}\langle(S_{\vec{r}}^{z})^{2}
\rangle_{0}\right]\left(\frac{{\gamma}_{z}}{{\gamma}}\right)^{\frac{k_{B}T}
{4\pi^{2}{K}}}.
\end{equation}
For the planar rotator model we have $\langle(S_{\vec{r}}^{z})^{2}
\rangle_{0}=0$ and the above equation should be compared to
\begin{equation}
\label{mag5} m\approx
\left(\frac{{\gamma}_{z}}{{\gamma}}\right)^{\frac{k_{B}T}{8\pi {K}}},
\end{equation}
obtained from a SCHA where $\gamma_z/\gamma$ plays the role of
$K_z/K$ of Ref. \cite{tonico1} and
\begin{equation}
\label{mag4} m=\left(\frac{\gamma_{z}}{\gamma}\right)^{\frac{k_{B}T}{8\pi J}},
\end{equation}
obtained from spin wave theory where now $\gamma_z/\gamma$ plays the role of
$J_z/J$ of Ref. \cite{hika}. The exponent here is not the same,
although numerically comparable to other approaches.

\subsection{3. Numerical Results, Parametric Procedure and Simple Assumptions}

\subsection{ Numerical Results}

In Figure \ref{dfD0}
we have the reduced transition temperature as a function of the anisotropy
$\eta=J_z/J$ for $D=0$. From hereon the present approach means the results
obtained by solving the non-linear system of equations (\ref{noacople3}) and
(\ref{noacople4}) numerically (by using standard iterative procedures)
for the variational parameters.
As can be seen from this figure the results are quite
similar to those from reference \cite{tonico2} in the region close to the
isotropic three-dimensional case $J_z\sim J$.
On the other hand, the slope of the phase boundary close to isotropic
two-dimensional case $J_z=0$ is zero according to the
present approach while the procedure from reference \cite{tonico2} for the
$XY$ model  (and also for the planar rotator model \cite{tonico1}) furnishes a
positive slope.
\begin{figure}[ht]
\includegraphics[clip,angle=0,width=8.5cm]{TcxetaD0-sc.eps}
\caption{\label{dfD0}Reduced transition temperature $t=k_BT/J$ as a
function of $\eta=J_z/J$ for $D=0$.
The solid line represents the present approach and
the dot-dashed line the results from Ref. \cite{tonico2}.
}
\end{figure}

Figure \ref{dfD} shows the phase diagram in the reduced temperature $t=k_BT/J$
and $\eta=J_z/J$ plane for several values of $D/J$.
One can clearly note that the crystalline anisotropy $D$ plays an
important role in the critical behavior of the model.

For positive values of the crystal field $D>0$ the
transition temperature increases as $D$ increases, since in this case
the out-of-plane fluctuations are reduced implying a greater tendency
of the spin components to lie in the $xy$ plane. For $D\to\infty$ we
recover the planar rotator model because there will be no $z$ component
of any spin. As shown in Table \ref{tab1},
in this limit, the result $t_c=1.472$ for $J_z=0$ are quite different
from that obtained by Monte Carlo simulations $t_c=0.90$, reflecting the
fact that the present variational approach does not take into account
vortices effects,
which are relevant for such two-dimensional model. On the other hand,
for $J_z=J$ the result $t_c=2.190$ for the isotropic three-dimensional planar
rotator model are quite comparable to the Monte Carlo simulations $t_c=2.17$.
Moreover, in the
two-dimensional limit ($J_z=0)$,  Eqs. (\ref{noacople3})
and (\ref{noacople4})  can be written as
\begin{equation}
\label{tcJz0}
\frac{k_BT_c}{J}=t_c=\frac{8+4\frac{D}{J}}{2+e(2+\frac{D}{J})},
\end{equation}
which gives the transition temperature of Fig. \ref{dfD} for $\eta=0$
down to the value $\frac{D}{J}=-2$.
\begin{figure}[ht]
\includegraphics[clip,angle=0,width=8.5cm]{TcxetaD50-27-bscreferee.eps}
\caption{\label{dfD}
Reduced transition temperature $t=k_BT/J$ as a function of
$\eta=J_z/J$ for several values of $D/J$ (indicated by the numbers)
according to the present approach (full lines), and Assumption 1
(dashed lines) and Assumption 2 (dot-dashed lines).
}
\end{figure}

For negative values of the crystal field $D<0$ we have an inverse situation.
We note
that as $D$ decreases the transition temperature also decreases. This can be
understood because the out-of-plane fluctuations are now enhanced
implying in a tendency for the spins to lie out of the $xy$ plane and to
become more Ising like. For a given value of $D$ there is a critical
value of the ratio $\eta_c=J_z/J$ at which the temperature goes to zero.
This value is given by
\begin{equation}
\label{etac}
\eta_c=-D/J-2
\end{equation}
at which the out-of-plane
fluctuation (\ref{sm2}) diverges.

Figures \ref{mD01} and \ref{mDinf} show the temperature
dependence of the magnetization obtained from Eq. (\ref{magh}) where one can
see a discontinuous behavior.
This discontinuity  in the magnetization
is an artifact of the present method. The transition temperature is
given when the non-linear system of equations
(\ref{noacople3}) and (\ref{noacople4}) admit only the trivial solution.
In all cases they do not go smoothly to the trivial solution presenting
thus a discontinuity. This is a general feature of such methods.
For instance, the temperature behavior for $D\to\infty$ and $J_z/J=0.1$ and
$J_z/J=1$ shown in Figure \ref{mDinf} is quite similar to
those given in Figure 3 of reference \cite{tonico1}.
\begin{figure}[ht]
\includegraphics[clip,angle=0,width=8.5cm]{mbscrefJz01D0-1.eps}
\caption{\label{mD01}
Magnetization $m$ as a function of the reduced temperature $k_BT/J$
for $\eta=J_z/J=0.1$ and
two different values of the crystal field, $D/J=0$ and $D/J=1$, according to
the present approach (full lines), and Assumption 1 (dashed lines) and
Assumption 2 (dot-dashed lines).
}
\end{figure}
\begin{figure}[ht]
\includegraphics[clip,angle=0,width=8.5cm]{mbscrefJz01-1Dinfty.eps}
\caption{\label{mDinf}
Magnetization $m$ as a function of the reduced temperature $k_BT/J$
for $D\to\infty$ and
two different values of $\eta=J_z/J$, $\eta=0.1$ and $\eta=1$, according to
the present approach (full lines), and Assumption 1 (dashed lines) and
Assumption 2 (dot-dashed lines).
}
\end{figure}

\subsection{Parametric Procedure and Simple Assumptions}

If we take the ratio between the variational stiffness
$g=\frac{\gamma_z}{\gamma}$,
we can compute the quadratic fluctuations given by Eqs. (\ref{exy}) and
(\ref{ez}) by taking the continuum limit in the long wavelength regime
\begin{equation}
\label{exyzF}
\eta_{xy}=\frac{k_BT}{2\gamma}F(g),~~~~~~\eta_{z}=\frac{k_BT}{2\gamma}
\left[\frac{1-2F(g)}{g}\right],
\end{equation}
where
\begin{equation}
\label{Fg}
F(g)=\frac{1}{3}\left[\frac{\arctan{(g^{\frac{1}{2}})}}
{g^{\frac{1}{2}}}+ \frac{1}{2}
-\frac{1}{2}g\ln{(1+\frac{1}{g}})\right].
\end{equation}
On the other hand, Eq. (\ref{minenerg2}) can be written as
\begin{equation}
\label{QG}G(Q)=Q\ln{Q}\left[2+\eta\alpha Q^{\alpha-1}\right]=
\frac{-t}{2\left[1-
\langle (S_{\vec{r}}^{z})^{2}\rangle_{0}\right]},
\end{equation}
where $Q=e^{-\eta_{xy}}$, $\alpha=\frac{\eta_z}{\eta_{xy}}$ and
$\eta=\frac{J_z}{J}$.
From Eqs. (\ref{exyzF}) the parameter $\alpha$ and, in the same way from
Eqs. (\ref{noacople1b}) and (\ref{noacople2b}) the quantity $Q$, can be written
in terms of the ratio $g$ as
\begin{equation}
\label{alpha}\alpha=\left[\frac{1-2F(g)}{2F(g)}\right],~~~~
\label{Q}Q=\left(\frac{g}{\eta}\right)^{\frac{1}{\alpha-1}}.
\end{equation}
Finally, the temperature can be expressed in terms of $G(Q)$ as
\begin{equation}
\label{t}t=\frac{-2G(Q)}{1-\frac{J}{\Omega}G(Q)}.
\end{equation}
So, knowing a priori the Hamiltonian parameters $\eta$ and $D/J$ and for a
given value
of $g$ one gets
\begin{equation}
\label{flux}
g \rightarrow F(g) \rightarrow \alpha  \rightarrow Q \rightarrow G(Q)
\rightarrow t.
\end{equation}
This is indeed what really happens when we use the numerical solution
of the implicit self-consistent equations  (\ref{noacople3}) and
(\ref{noacople4}).
However, it would be quite nice if one could track the inverse path of Eq.
(\ref{flux}). Unfortunately, as one can see, this is in fact not possible
since for a given
$t$ (the usual parametric procedure to get the different thermal dependences)
we cannot solve Eq. (\ref{QG}) because $\alpha$ is unknown. It is at this point
where some additional assumptions could be made in order to explore simpler
solutions of Eq. (\ref{QG}).

\vskip0.5cm
{\bf Assumption 1.} ~~~ $\alpha=\eta$
\vskip0.5cm
In this case Eq. (\ref{QG}) reduces to
\begin{equation}
\label{Qa1}Q\ln{Q}\left[2+\eta^2 Q^{\eta-1}\right]=
\frac{-t}{2\left[1-
\langle (S_{\vec{r}}^{z})^{2}\rangle_{0}\right]}.
\end{equation}
In Figure \ref{dfD} it is shown, by the dashed lines, the corresponding
critical
temperatures according to this assumption. It can be seen that, within that
scale, Assumption 1 and the present variational approach are almost
indistinguishable. For $D=0$
the transition temperature obtained from Eq. (\ref{Qa1}) for
the two-dimensional model $J_z=0$ is identical to that from the present one
$t_c=1.076$. However, for the isotropic three-dimensional model $J_z=J$
one has $t_c=1.613$, which is slightly different from
the value $t_c=1.605$ according to reference \cite{tonico2}.
On the other hand, in the limit $D\to\infty$ we find the same transition
temperature for the two-dimensional planar rotator model $t_c=1.472$ and,
for the three-dimensional case,
$t_c=2.207$  is comparable to
$t_c=2.190$ obtained from Ref. \cite{tonico2}. These values are
depicted in Table \ref{tab1} together with those coming from other
approaches. The  magnetization as a function of the temperature
is presented in Figures
\ref{mD01} and \ref{mDinf}. A different behavior is observed, except for the
planar rotator model.

The quite good agreement of the present approach and Assumption 1 reflects
the fact that
the term $\eta\alpha Q^{\alpha-1}$ in Eq. (\ref{QG})
varies very weakly with $g$ and thus with
temperature. Reproducing the correct limits at $\eta=0$ and $1$ the phase
boundaries are then a sort of smooth interpolation for different values of the
anisotropy, explaining the accidental good agreement. With this in mind other
simplifications can also be done.
\vskip0.5cm
{\bf Assumption 2.}~~~$F(g)=\frac{1}{2+g}$
\vskip0.5cm
In the interval $[0,1]$, the function $F(g)$ given by Eq. (\ref{Fg}) can be
approximated by (with an error of order less than $10\%$)
\begin{equation}
\label{modF}F(g)=\frac{1}{2+g}.
\end{equation}
This implies that $\alpha=1$ and $\eta_z=\eta_{xy}$, meaning that the quadratic
fluctuations are not very different in vertical or in-plane bonds. The
self-consistent Eq. (\ref{QG}) adopts now a very simple form
\begin{equation}
\label{Qa2}Q\ln{Q}\left[2+\eta\right]=
\frac{-t}{2\left[1-
\langle (S_{\vec{r}}^{z})^{2}\rangle_{0}\right]}.
\end{equation}
Unlike Eq. (\ref{Qa1}) the above equation permits obtaining an analytical
expression for the critical
temperature. Since $\frac{dQ}{dt}=0$ at $t_c$ one gets $Q_c=e^{-1}$ and
\begin{equation}
\label{tca2}t_c=\frac{2(2+\eta)}{\frac{J}{\Omega}(2+\eta)+e}.
\end{equation}
The above equation also yields  exactly the same limiting results as in the
last column of Table \ref{tab1}. The boundaries as a function of $D$ are given
in Figure \ref{dfD} by the dot-dashed lines. In this case, for positive values
of the crystal anisotropy the agreement is not as good as for negative values.
The  corresponding magnetizations as a function of the temperature
are also shown in Figures \ref{mD01} and \ref{mDinf}.

\section{ 4. concluding remarks}

The anisotropic $XY$ model in a crystalline field has been studied according
to a variational approach for the free energy.
This system is a generalization of the planar rotator model and the
anisotropic $XY$ model previously treated in the literature
\cite{tonico1,tonico2}. We believe we have obtained a satisfactory
picture of the thermodynamic behavior of the model as a function of its
parameters. Not only is the phase diagram in the anisotropic case
$J_z\ne J$ different from the previous one
obtained for $D=0$, but the crystal field has been show to play an important
role in the critical behavior of the system.

Regarding Assumptions 1 and 2, one could see that the former one
($\alpha=\eta$) would imply that the mean quadratic fluctuation on a given
bond scales with the coupling constant of the bond,  while the latter one
($\alpha=1,~\eta=1$) means
that the quadratic fluctuations are not very different in vertical or in-plane
bonds. So, according to Assumption 2, the average contribution to
the internal energy from each bond scales approximately with the coupling
constant of the considered bond. This seems more acceptable than the
conceptually wrong assumption $\alpha=\eta$, since one expects that softer
bonds should develop stronger fluctuations. Thus, at first sight, from the
numerical point of view, the better agreement of Assumption 1 with
the complete approach can be ascribed to an artifact of the method.

It is clear from the approximation employed in this work that it
should be valid only at low temperatures. It is also rather surprising
that the values for the transition temperatures shown in Table \ref{tab1} for
the three-dimensional model are quite comparable to those coming from more
reliable methods (for the two dimensional model one would not expect such
agreement due to the vortices effects). It would then be quite nice to have
a clearer picture of the range of the temperature validity of the present
procedure. In Figure \ref{val} we show the out-of-plane spin fluctuations given
by Eq.(\ref{sm2}) for several values of the Hamiltonian parameters compared
to Monte Carlo simulations. We have chosen this quantity because it is easily
obtained from the present approximation, Eq.(\ref{sm2}).
The simulations have been done in
the three-dimensional model described by Hamiltonian (\ref{ham})
and employing the single spin-flip Metropolis algorithm. A finite
lattice of $L\times L\times L$ ($L=14$)
has been used with periodic boundary conditions. The averages have been taken
by considering $10^5$ Monte Carlo steps (MCS) per spin after equilibration.
For the  first temperature, $100L^2$ MCS have been discarded and,
with the previous configuration being the initial configuration for the next
temperature, additional $3\times 10^3$ have been discarded.
It is evident from this figure that the
transition temperatures are not far from the temperature range where
the corresponding results are comparable to the Monte Carlo simulations.
\begin{figure}[ht]
\includegraphics[clip,angle=-90,width=9.3cm]{limSCHA.ps}
\caption{\label{val}
Out-of-plane spin fluctuation as a function of the temperature for
several values
of the Hamiltonian parameters. The full lines are the results from Eq.
(\ref{sm2}) and the different symbols are Monte Carlo simulations \cite{rod}.
The arrows indicate the transition temperatures obtained from the
present approximation. The MC results saturates at $1/3$ as
$T\to\infty$.
}
\end{figure}

{\bf Acknowledgments - }The authors would like to thank CNPq, FAPEMIG and
CAPES (Brazilian agencies) for financial support. Special thanks for the
nicely and extensively written referee comments and suggestions are also
addressed.

redpajama_set_name: RedPajamaArXiv


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Open nightly until 11pm Sunday through Thursday and 12am Fridays and Saturdays, we offer a wide selection of beers, wines and spirits, plus a tasty lounge menu for a light snack or enjoy a meal from our full menu. Add in some flat screen TVs and service with a smile, and you have the perfect mix for a great night.


Spring fever's on hold as the region experiences three days of expected rain. Photo by Keegan Barber.
What a beautiful week! Five days of straight sun, Monday through Friday. It looked marvelous from my seat in Psych.
Of course, it didn't last long.
The night before the SAT, a torrential downpour woke me up and knocked out the power. If the pounding of watery pellets hadn't interrupted my parents' sleep, I would have missed the Saturday SAT essay and maybe some critical reading.
In my urgency to get out of the rain and into my testing room, I forgot to turn my car lights off. Standing outside, waiting for a jump after four hours of testing was quite pleasant.
There is one thing about a rainy weekend, though: it provides plenty of time for chatting with friends on Facebook and watching videos. That is, it would have, if my internet wasn't down. I guess I got to finish my World History homework for once instead.
Outside, everything is wet. The pavement is stained, the ground is muddy and the roofs drip at every unguttered edge. The gloom is complete in front of Whitman: stains on the wall, bricks a dampened red and light poles pointing skyward under a uniform grey overcast.
The smell reminds me of play dough, potty language and boys-versus-girls soccer games on Wood Acre's muddy fields. It reminds me of walking in line (1, 2, 3, eyes on me!) to the portables on a rainy day, or sour water colors in art class. The smell is nostalgia, a smell of being innocently dirty.
Appropriately, the smell is actually of worms emerging from the soggy ground outside of Whitman. Gross, you say? That's exactly what you used to say, along with a funny first-grade giggle.
Outside of our high school, it smells like elementary school.


The case relates to action taken by University of Queensland against Prof. Paul Frijters because of his alleged conduct of a project without appropriate ethical clearance. The project related to the deception of participants (Brisbane bus drivers) and the dissemination of findings that reflected on them poorly as a cohort. The Bissert determination overturned UQ's actions on procedural grounds without comment on the underlying ethical issue of the conduct of the project without the appropriate ethical clearance.
It is understood (see http://www.brisbanetimes.com.au/queensland/uq-suppressed-bus-racism-study-academics-20150226-13q5lu.html) that Prof. Frijters disputes that university ethical clearance was required. The determination does reflect to some degree on the process followed to determine whether research ethics review and ethical clearance was required (e.g. provisions 286, 291 and 322-336). However it does not proffer a view as to whether prior research ethics review was required.
The substance of the Fair Work Act determination is that UQ failed to adhere to the misconduct provisions of its enterprise bargaining agreement, the framing its own research misconduct processes and denied Prof. Frijters procedural fairness.
The determination (pp21-22) rejects UQ's assertion that the research misconduct procedure is exempt from the requirements/rights/redress articulated by the relevant enterprise bargaining agreement (EBA).
The case highlights the importance of carefully describing the interface between research misconduct procedures vis-à-vis the Australian Code and misconduct procedures as described in the Academic EBA (and indeed the general staff EBA for research assistants and student misconduct policies). This is perhaps most acute when the research misconduct process will be making the substantive determination that there is 'a case to answer' and the EBA process will largely be an operational application of punitive consequences of the finding of a case to answer.
The case also highlights that correspondence from a respondent (such as disputing the process or the findings of the reviewing officer) should be considered both in terms of its research integrity and its human resources (i.e. EBA process) implications. Another matter Bissert found troubling was the replacement and appointment of supervisors to Prof. Frijters, especially given the important role of supervisors described by the misconduct procedures.
correspondence from a complainant expressing dispute with proceedings should always be considered by a Human Resources Department staff member (to determine the EBA implications of the matters raised).
This may necessitate a complete rethinking of the approach many universities take to 'Part B' proceedings and allegations. The matters to consider include research integrity (e.g. adherence to the Australian Code), human resources (e.g. with regard to misconduct proceedings articulated by the relevant EBAs), and institutional compliance (e.g. as per the ARC/MHMRC deeds of agreement and annual compliance reporting).
Largely lost (except for provisions 286, 291 and 322-336) throughout the discussion about correct procedures and the EBA is the degree to which failure to seek ethical clearance is a serious matter especially as the project involved overt deception and risk. It also involved 'agents acting on behalf of the researchers' unlawfully seeking to evade paying for travel. The assessment of these matters requires a sophisticated understanding of the National Statement on Ethical Conduct in Human Research and Australian Code for the Responsible Conduct of Research. Arguably it appears the University did not adequately consider whether social science research (at least from one academic area) is being correctly submitted for prior research ethics review.
(*) It is not entirely clear why the Head of School, as Prof Frijters' line supervisor was not an appropriate person to conduct the investigation. At various points in the process, different reasons were offered.


Frequent flyers on Alaska Airlines have been talking about it for months, but a press release finally went out today that announces the planned opening of a second Board Room location at Sea-Tac's North Satellite. On first glance I'd say it looks similar to the new Centurion Studio but much, much bigger.
Demand for this lounge has been obvious for some time. First, the current Board Room in the main terminal is often overcrowded. It's rarely so bad I won't go in, but it's unlikely you'll find dozens of open seats. Second, Alaska has shifted many of its operations to the North Satellite, making it inconvenient to visit the main terminal Board Room before taking the underground transport to the North Satellite.
Video and still image renderings of the new lounge were provided by Alaska Airlines.
Alaska Airlines used to share the North Satellite with United, which moved its operations to the A Concourse a few years ago. That left the old United Club empty. It's right across from the inter-terminal station, behind the escalators, and I understand that Alaska took over this space to create its second Board Room. I've been lucky enough not to pass through the North Satellite in months, so I don't have visual confirmation. If this is actually located somewhere else, please tell me!
Update: Martin provides information in the comments that the new lounge is actually located upstairs on the main concourse. This makes a lot more sense. I guess the old United Club will remain empty for now.
The new lounge appears to have a much cleaner, brighter look than the current lounge, which has a lot of dark surfaces. I'm also excited about the windows. The old United Club was nice enough, but it was a series of windowless rooms that felt a bit claustrophobic as a result. Alaska's lounge will actually be upstairs between gates N1 and N2 so you'll be able to look out at ground operations while you wait.
Remember that Board Room access is complementary when you fly first class on Alaska Airlines, whether on a paid or award ticket (upgraded fares are not eligible). Travelers with an Admirals Club membership can also gain access when flying on Alaska or American Airlines.
And guess what? It's technically a temporary facility — if you can call several years "temporary." My understanding is that Alaska still plans to eventually move this lounge upstairs, above the departure gates, after it completes a thorough renovation of the North Satellite in 2018.
New Hours — Open Late!
Some Board Room Locations will be also be open later as of November 7. In Seattle, both lounges will be open from 5 AM to midnight. This is common sense given all the new routes Alaska has initiated in recent years, as well as the large amount of connecting traffic it handles. Previously the one lounge would close at 10:30 PM. Lounges in Los Angeles and Portland will also be open later (Anchorage is already open until 1:30 AM).
Is Partner Lounge Access Increasing or Decreasing?
Travelers with an Alaska Airlines Board Room membership or American Airlines Admirals Club membership can always get access to each others' lounges when traveling on these two airlines. Board Room members get access to many other lounges, too, since the Board Room network only includes a few locations.
Part of this morning's announcement includes the addition of new United Club locations in Philadelphia, Minneapolis, and Phoenix. Sounds good, except it comes at a big cost. Not mentioned in the press release is that Alaska will be ending its access agreement with Delta Sky Clubs. The new United locations appear to be a replacement for the gap this change will create. As Board Room members previously had access to the entire Sky Club network — even Narita — when traveling on Delta or Alaska, it's a big negative.


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On the Saturday night back at Newtonmore Hostel, my friend Ali and I checked out the forecast for the next day. Sadly it was even worse than the constant heavy rain formerly predicted. Winds of up to 55mph, severe wind chill, persistent snow, possibly thunder and lightening.
After last weekend's failed trip, we had managed to order the new part for Bertha (the Bongo) and book her in to a friend's garage near Forres to get fixed. On Friday night we dropped her off up in Forres and headed down the road towards Newtonmore. We had been invited to Glen Etive by the 45 Degree Mountaineering Club for the weekend, but due to the journey, we planned to break it up by stopping in Newtonmore for the night (at the excellent Newtonmore Hostel) and going to Glen Etive the following night.
The following morning turned out quite a stunner – I was very surprised because it was way better than what was forecast. Our plan was to walk up the two Glen Spean Munros, Beinn a'Chaorainn and Beinn Teallach, before heading to Glen Etive.


Diese Veranstaltung ist als Bildungsurlaub nach dem Arbeitnehmerweiterbildungsgesetz (AWbG) NRW anerkannt, kann aber von allen Interessierten gebucht werden.
You feel that your language skills have gotten a little rusty? You're not alone! This course helps you to get back into the swing of things. Moving and interacting, talking and discussing, you will learn to express yourself more fluently and interact spontaneously in everyday conversations: negotiations, discussions, small talk, socializing and a bit of talking grammar (e.g. simple vs continuous, past tense vs present perfect, future tenses and conditional sentences). Come in and find out how much fun it can be to brush up your English!


0. Create a method that takes a value and indicate whether it is positive or negative by a return to boolean.
1. Create a method that takes a value and tell whether it is null or not.
For it exists, the coefficient 'a' must be nonzero.
4. Create a method that takes two numbers and returns the largest value.
5. Create a method that takes two numbers and returns the lowest value.
6. Create a method that takes three numbers and returns the largest value, use the Math.max().
7. Create a method that takes 3 numbers and return the lowest value, use the Math.min ().
8. As a method called rollDice() which returns through draw a number from 1 to 6.
9. Use the method of question and toss the dice past 1 million times. Count how many times each number came out.
The probability worked? That is, the percentage of numbers was about the same?
10. Create an application for conversion between Fahrenheit and Celsius temperatures.
First the user must choose whether to enter the temperature in Celsius or Fahrenheit, chosen after the conversion is performed through a command switch.
11. A teacher, very cool, did 3 tests during a semester but will only take into account the two highest grades to average.
Write a Java application that asks the value of 3 notes, show how it would mean to these 3 tests, average with the 2 highest grades, as well as his highest score and your lowest note. These averages must be calculated using the same method, because you're a Java programmer and will not stand idly creating methods.
Create a method that receives all 3 grades and returns the largest. And another that returns the smallest.
Prime number is one that is divisible only by 1 and itself.
Challenge: Write a Java program that takes two integers and returns the GCD, greatest common divisor.
Challenge: Find all perfect numbers up to 1000.
Perfect number is one that is the sum of its factors. For example, 6 is divisible by 1, 2 and 3 while 6 = 1 + 2 + 3.
Challenge: Create a Java program that receives a number and print it in reverse order.
That is, if the whole received 123, should print the integer 321.


text:
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Personal Guarantee Lawyers
At MBM Commercial we are the industry leading experts at advising clients on all aspects of Scottish Personal Guarantees and have a strong track record in helping clients navigate their way out of them.
We have successfully helped our clients avoid paying over £2million of personal debt due under personal guarantees.
This page will help you understand what a personal guarantee is and how we might be able to help you avoid your liability under them.
What is a Personal Guarantee?
A personal guarantee is an agreement that means an individual takes personal liability for his or her company's debts in the event that they cannot be paid back by the company itself.
Lenders often use them as an added level of security to make sure that they will get their money back if the business can't pay and are commonly included in or alongside any loan documentation.
Personal guarantees can be called on as soon as the business is unable to pay and lenders do not need to wait until any administration or liquidation is completed before asking a guarantor to pay up.
If a lender calls in a personal guarantee and you can't pay, then this could lead to you being made personally bankrupt.
Ways Out
There are a range of grounds that we at MBM have used to help people out of a personal guarantee.
Misrepresentation - Before signing the bank's personal guarantee, the bank said or wrote something false which you relied upon and that induced you to sign the guarantee. In other words, but for the bank's false assurance about something, you would not have signed the guarantee.
Economic Duress - If the bank put extreme pressure on you to sign the personal guarantee, then a judge may decide that by the bank's actions, you did not consent (despite signing the guarantee), and the personal guarantee is void and cannot be enforced against you. If you were left with no practical choice but to submit to the economic pressure from the bank, then this remedy may be of assistance to you.
Duty of Good Faith – in some banking relationships it may be possible to argue that a duty of good faith exists. This is an argument that can be advanced where there has been a long standing and close relationship between the business and the bank, and where the bank in reality provided advice to the business. In these circumstances it can be argued that a duty to act in good faith has been created, and if the bank, in its actings towards the business, has breached that duty, then the duty to act in good faith may render the personal guarantee unenforceable. The duty is quite broad and may cover any acts of bad faith by a bank towards the business. For example, if your bank is the main instigator of the collapse of the company or person that borrowed the money, then by acting in an unfair manner, the personal guarantee may be held to be unenforceable by a court.
Promise - If the bank used clear words either in writing or verbally that it will unequivocally not enforce the personal guarantee for a certain period of time or until something is done then a legally binding promise may have been created which could be relied upon to defend enforcement proceedings brought by the bank. A unique feature of the law of promise in Scotland in contrast to England is that a promise is legally binding even when the person making the promise receives nothing in return from the other person. So while in England a bare promise from a bank not to enforce the personal guarantee would not be binding, the promise would be binding if made north of the border.
Error - If the personal guarantee was signed on terms which, by mistake, do not reflect the agreement between you and the bank, then it can be argued that there is no agreement due to error. However, it seems that the current law in Scotland is that for the personal guarantee to be rendered void and unenforceable, there must not only be error but also some other factor such as the bank acting in bad faith.
Force and Fear – if the individual was induced to sign a personal guarantee in circumstances where he or she is placed under "force and fear", whether by the bank or by a third party, it can be argued that the guarantee is void. Examples include the situation in which a husband owns and runs a business, but through threats, intimidation or abuse, persuades the wife to guarantee the debts of the company. In these circumstances the wife has not freely and voluntarily given her consent to the personal guarantee, and it matters not that the bank may have been unaware of the circumstances in which the wife came to sign the guarantee document: the abusive conduct of the husband was such, it can be argued, to overpower the wife's will.
Prescription -The personal guarantee expires 5 years from becoming enforceable at which time it can no longer be enforced by the bank. This is not 5 years from signing the personal guarantee but from when the bank calls in the debt. The exact time when the guarantee became enforceable is open to dispute.
Contact our Financial Disputes Team Edinburgh, Scotland
If you think that you may be subject to a personal guarantee or would like some advice regarding navigating your way out of one, then please do not hesitate to contact a member of the Financial Disputes Team on 01312268200 or fill out our online enquiry form.
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redpajama_set_name: RedPajamaCommonCrawl


If you come to see the emblem of the police department of your small town on the large door of an armored truck, you'll have seen the end of a long story — the story of America's lurch into and out of what's sometimes called, in Pentagon jargon, the battlespace.
One Navistar MaxxPro now belongs to the police department of Madison, Wisconsin; there's another in Watertown, New York. The Georgia communities of Waycross, Cartersville, Doraville, and Newnan each have their own large armored vehicles. In fact MRAPs and machines like them now appear in semi-official photographic tableaux on law-enforcement homepages across the country. Ohio State University has an MRAP; Virginia Tech has one that appears during athletic events, with the Nike "swoosh" logo and the words, "PREPARE FOR COMBAT" across the back. These vehicles look like bigger versions of the ones that gathered redundantly around the Arsenal Mall during Boston's post-Marathon manhunt last April, and that roll back and forth down Storrow Drive on the Fourth of July.
We may forget that many of these vehicles were built for a military purpose: to endure the kind of explosive that is never detonated in the United States, to win the sort of war that we are supposed to have left behind.
The U.S. Department of Defense called a new wave of MRAPs into being in 2007 in an attempt to counter the improvised explosive device, or IED, which was still wreaking havoc on American forces in Iraq. This was fully two years after a frustrated army specialist—one of thousands who had been asked to prepare for IED attack by, at worst, affixing plywood and sandbags to his Humvee—confronted Secretary of Defense Donald Rumsfeld during a town-hall meeting in Kuwait. His question: "Now why do we soldiers have to dig through local landfills for pieces of scrap metal and compromised ballistic glass to up armor our vehicles, and why don't we have those resources readily available to us?" Rumsfeld's reply may serve as the epitaph of the entire war.
Memos from the weeks following show Rumsfeld worrying aloud about armored trucks to Pentagon brass, but quickly he was reassured. No one, he was told, was going to be asked to travel around Iraq without sufficient armor: "They are simply going to change the tactics… That issue ought to be eliminated, one would think." Two days later, Gen. Peter Schoomaker, the Army Chief of Staff, followed up: the Army would stick with the (supremely vulnerable) Humvee, while it considered whether to buy MRAPs and which ones. Over the next two years, IEDs would continue to kill and maim soldiers — 993 dead, more than 11,000 wounded — unless they were riding in MRAPs. According to one manufacturer, Force Protection, Inc., its model, the Cougar, was hit 3,200 times over five years, but only five of its passengers were killed. It is unclear who to blame for the slow trickle of these vehicles into the warzones through the end of 2006, but it is clear by now that many parties — Secretary Rumsfeld's office, the contracted manufacturers, and military leadership — share responsibility for the protracted vulnerability of Americans at war.
It was Rumsfeld's replacement, Robert Gates, who openly embraced the MRAP, ordering more than 15,000 vehicles by the end of 2007 and jumpstarting production. $44 billion was earmarked for the vehicle program in total. This allotment was for the most part separate from the more than $20 billion spent on the Joint IED Defeat Organization, the search for a durable high-tech solution to the roadside-bomb problem which is considered one of the wars' great sources of waste. Together, the initiatives amounted to at least $64 billion spent in response to a weapon, the IED, that costs around $30 to make.
Across 2007 and 2008, IED and other violence dropped across the board in Iraq, following the surge in troop levels. It is not clear to what extent the late-coming MRAPs played a role, or what good effect they might have had on veterans' lives or on the course of the American adventure in Iraq if they had been available in sufficient numbers from day one. There are now 10,000 and more of the vehicles in Afghanistan, the graveyard of Soviet tanks.
The acquisition program has alarmed both the ACLU, which began a "Towns Don't Need Tanks" campaign last year, and a more extreme libertarian set online. When the website Infowars reported (erroneously) last year that the Department for Homeland Security was going to acquire 2,700 MRAPs for itself, some posted strategies for disabling the vehicles if they were ever put to use on American citizens in what's called the "S.H.T.F." contingency. Recommendations include tipping them over (they have a high center of gravity), leading them into holes hidden under leaves, and blowing them up using homemade IEDs.
As soldiers waited in Iraq and Afghanistan, now we wait here — not for the armor-plated rescue vehicle, but for the emergency that could warrant its place in our lives.


Michael D. Falater is an associate of the Firm, practicing primarily in the areas of insurance defense, construction law, appellate litigation, personal injury, family law, products liability, medical malpractice, and healthcare professionals advocacy.
Raised in Phoenix, Arizona, Mike graduated from Brigham Young University with a degree in Urban, Rural, and Environmental Planning and a minor in Communications. Mike earned his Juris Doctorate from the S.J. Quinney College of Law at the University of Utah in 2011. During law school, Mike was a Legal Extern for Justice Ronald Nehring of the Utah Supreme Court, a William H. Leary Scholar and a Lionel Frankel Fellow. He was also an articles editor for the Utah Law Review. Prior to joining Hutchison & Ste en, Mike worked at a litigation rm in Las Vegas, Nevada, where he defended employers, hospitals, and transportation companies. He has also defended individual insureds in simple to complex motor vehicle accidents. Mike is admitted to practice in both federal and state courts in Nevada.
In his spare time, Mike enjoys reading comic books and spending time with his wife and four daughters. He also is a volunteer scoutmaster for a local Boy Scout troop and a youth soccer coach.


What is a CNC Plasma Cutter? - Machinery Resources International Inc.
A plasma cutting torch is a tool most commonly used for cutting metals. While purposes vary, the hand-held plasma torch is ideal for cutting quickly through metal plates, bolts, pipes, sheet metal, or straps. They are also perfect for gouging, whether back-gouging or the ability to remove poor yields. You can also use a hand torch for cutting small shapes from a larger piece of steel. However, accuracy is lacking, and it is virtually impossible to achieve a quality edge in most cases.
Accuracy is improved with the update to a CNC plasma cutter. This system consists of a machine that includes a plasma torch. The plasma torch can move by a computer's directions. CNC stands for computer numerical control, so a computer controls a CNC machine. These mechanized plasma cutters are made to operate as an electric torch and plasma system. While some CNC plasma cutters include hand-held torches, those more properly made for mainstream manufacturing will be primarily mechanized.
CNC plasma and flame cutting systems consist of several important parts. The controller has an interface panel and a console specifically designed for the CNC machine. It could also be as simple as a laptop used to run a software program designed to communicate with the device. Entry level machines typically use this simpler method.
The torch moves on directions set forward by the CNC to cut the parts from a steel plate. Generally known as m-codes and g-codes, this text describes the part's dimensions, and when the torch will turn off or on. Post processors are programs that help translate codes into the codes read and implemented by a CNC machine.
A mechanized plasma cutter requires a drive system as well. This system consists of encoders, cables, amplifiers, and motors. At least two engines are included, depending on the needs of the machine. Each motor has a drive amplifier that takes a lower power signal from the controls, and this turns into a high-powered signal to move the engine. Each axis needs a feedback mechanism – an encoder – that indicates how far the axis moves. Feedback is retaken to the CNC via signals to the drive system and actions are measured and corrected every few milliseconds.
The last part is a type of electrical system that regulates inputs and outputs. It allows the CNC to turn on the plasma appropriately.
Finding quality machinery for your company is important. When it comes to finding the best CNC plasma cutter for sale, choose a company with a combined 60 years of experience in the industry: Machine Resources International.
As an experienced dealer offering high-quality pre-owned machinery to the worldwide manufacturing industry; from simple to more complex, MRI's expert team will help you find the machine that works best for your business' needs.


text:
Judge Identifies CIA-Related Man Who Led the Raid on North Korea's Embassy in Spain
Leader of a would-be regime-change outfit for North Korea from Washington
Ron Paul Institute 29 Mar 19 406 1
The Spanish judge is seeking his extradition from the US to Spain where he will face up to 28 years in prison
A Spanish judge released new information about a raid on the embassy of North Korea in Spain. The leader of the raid was a shady US 'activist' who earlier reports from Spain associated with the CIA.
On March 13 the Spanish newspaper El Pais Spain reported that Spanish authorities identified two CIA related persons who took part in a raid of the North Korean embassy in Madrid. The raid happened on February 22, a few days before the Trump-Kim summit in Hanoi, and seemed designed to influence that event. We asked Who Ordered The CIA To Assault North Korea's Embassy In Spain?
The embassy raid was no normal thievery. There were eight people in the embassy when it was raided at 3:00 PM local time. They were bound, bags were put over their heads and some were interrogated. The thieves left with computer hardware and the cellphones of the personnel.
The Spanish version of the El Pais piece included this detail (machine translated):
After analyzing the recordings of the security cameras in the area, questioning the hostages and analyzing the diplomatic vehicles used in the flight, it has been possible to identify some of the assailants. Although the majority were Koreans, at least two of them have been recognized by the Spanish information services for their links with the American CIA.
The indications that point to the US espionage service, in probable cooperation with that of South Korea, are so strong that Spanish interlocutors have contacted the CIA to ask for explanations. The response was negative, but "unconvincing", according to Government sources.
Two days after the El Pais report the Washington Post national security reporter claimed that the raid was done by a shady group of allegedly North Korean revolutionaries. The report was based on anonymous sources and a 'former' CIA analyst. The group was identified as Cheollima Civil Defense or Free Jaseon.
As the group and its website had all the signs of a CIA regime change front Moon of Alabama headlined:
CIA Blames Its Proxy For Its Raid On North Korea's Embassy In Spain
We also noted that the British Sun related the group to the South Korean spy service which is essentially a subsidiary of the CIA.
Yesterday a Spanish judge lifted the seal of the case and issued arrest warrants against two of the people involved in the raid:
De la Mata identified citizens of Mexico, the United States and South Korea as the main suspects being investigated on charges that include of causing injuries, making threats and burglary. He named Adrian Hong Chang, a Mexican citizen living in the United States, as the break-in's leader.
Hong Chang flew to the US on Feb. 23, got in touch with the FBI and offered to share material and videos with federal investigators, according to the court report.
While in Madrid, Hong Chang also applied for a new passport at the Mexican Embassy, the investigation found, and used the name "Oswaldo Trump" to register in the Uber ride-hailing app.
Others identified as part of the assailants' group were Sam Ryu, from the US, and Woo Ran Lee, a South Korean citizen. Their whereabouts and their hometowns weren't immediately known. None of the suspects were thought to be still in Spain, the judge wrote.
The New York Times adds:
Mr. Hong Chang left for Lisbon and then boarded a plane to Newark Liberty International Airport, where he landed on Feb. 23, according to Judge de la Mata. He said that Mr. Hong Chang got in touch with the F.B.I. and offered to share "audiovisual material" obtained during the embassy attack.
On March 20 the Cheollima Civil Defense group uploaded a new short video to its Youtube channel. It says "Recently, on our homeland's soil .." and then shows a man, face hidden, taking pictures of the deceased North Korean rulers Kim Il-sung and Kim Jong-il off a wall and smashing them on the floor.
Embassy grounds are considered to be territory of the country they represent. It is likely that the video "on our homeland's soil" was made during the raid on the North Korean embassy in Spain.
After the Spanish judge's report appeared, the Cheollima entity published a Facts about Madrid pamphlet that confirmed its role and its contact with the FBI. It claims to feel betrayed:
No information about Madrid was shared with any parties with the expectation of any benefit or money in exchange. The organization shared certain information of enormous potential value with the FBI in the United States, under mutually agreed terms of confidentiality. This information was shared voluntarily and on their request, not our own. Those terms appear to have been broken.
Some time later, some journalists began writing speculative stories about the incident in Madrid, and the identities or affiliations of those involved, citing US government sources. That information was leaked to the media was a profound betrayal of trust. We ourselves never spoke to the media or shared any information with them.
We did not begin this work without full knowledge of the risks we bear. Freedom has already been paid with the blood of families and colleagues. Some of us will be imprisoned, tortured or killed in the course of this fight. But to share information that may help identify any of us who take risks to protect others is to aid and abet the regime in Pyongyang. The leaks and breaches of trust were abhorrent acts pursued in the name of political expediency, in service to a regime who has tortured and killed millions.
The person identified as leader of the raiding party, Adrian Hong Chang, is a know anti-North Korea activist. He usually goes under the name Adrian Hong, not Hong Chang as the AP and NYT reports claim:
Hong was the co-founder and Executive Director of Liberty in North Korea (LiNK), an international NGO devoted to human rights in North Korea. In May 2006, LINK helped arrange the first asylum to be given to North Korean refugees by the US.
Hong was arrested and deported from China for his efforts to help North Korean refugees living in the country illegally.
In 2009, Hong was selected as a TED fellow and an Arnold Wolfers Fellow at Yale University.
A 2007 UN Human Rights Council paper (pdf) list Hong as a member of Freedom House, a neo-conservative infested influence organization largely funded by the US State Department.
Over the years Adrian Hong wrote several op-eds for US outlets. A 2011 piece in Foreign Policy calls for violent regime change:
The time to topple the criminal government in Pyongyang is now. Here's how to do it.
The very progress of our global civilization is for naught if we continue to let the very idea of North Korea exist. North Korea is not a failed state, with warlords fighting for land and treasure. Its atrocities do not stem from factional fighting, crimes of passion, or mob violence. It is on another level entirely — a staggering system entirely built and mastered for the express purpose of propagating human suffering and ensuring the continued exploitation of the people so that the very few can benefit.
It is a moral obligation of the highest order that the international community intervene. What can be done, we must do — and now is the time.
Foreign Policy and other outlets introduce Adrian Hong as "Managing Director of Pegasus Strategies LLC". There are several companies under that name but none that seems to be related to Adrian Hong.
Cheollima, as the Adrian Hong's related regime change entity calls itself, is a mythical winged horse in Asian folklore. Pegasus is a winged horse in Greek mythology.
A 2016 San Diego Union Tribune piece introduces him as:
Hong, a San Diego native, is president of the Joseon Institute, an independent think tank undertaking policy-relevant research and planning in preparation for dramatic change on the Korean peninsula. He was imprisoned in China in 2006 for helping North Korean refugees escape.
At one point the Cheollima Civil Defense Group renamed itself to "Free Joseon". The Joseon dynasty ruled Korea from 1392 to 1897. It went down when Japan tried to gain control of the country which it achieved a few years later.
The Joseon Institute in New York(?) is preparing for regime change in North Korea:
The Joseon Institute draws on on cutting-edge research from the Korean Peninsula and the region, as well as international best practices and learnings from other sudden transitions in the past century, successful and failed, to best prepare for a new North Korea. A core team of scholars and staff in New York City works with a wide-network of world-class scholars, resident and non-resident fellows, policymakers, practitioners, researchers and volunteer collaborators around the world.
While much of the effort remains highly sensitive, the resulting research, blueprints and action plans will be provided to key government stakeholders invested in the future of the Korean Peninsula. Full cooperation, information sharing and assistance will be offered by the Joseon Institute to whatever entity is presiding over change.
While the Union Tribune introduces Adrian Hong as "president of Joseon Institute", the 'Institute's website says that the 'Leadership' of the group is "To be announced." Its 'Senior Fellows' and 'Fellows' are "Undisclosed."
The site list twelve 'Planning Commissions' and four 'Task Forces' but zero content or persons related to them. It lists more than 23 'currently available positions' but seems to have hired no one. The two 'Events' listed at the site are from 2015.
It says that Facebook hosted an event on April 1 2015 in New York about Education In A New North Korea. The 'Event Overview' lists a "Introduction to the Joseon Institute – Adrian Hong". There is no evidence that the event took place.
The latest 'News' item on the site is an August 10, 2017 Update From The Joseon Institute with lots of claims of work done but zero content or links that provide evidence of such work.
The board of advisors of the Joseon Institute consists of a former prime minister of Libya who was "elected" after the murder of Muhammad Ghaddafi, a former prime minister of Mongolia, and the conservative Member of the British Parliament Fiona Bruce. A 2011 Financial Times piece – Christian Tories rewrite party doctrine – associates Fiona Bruce with evangelical Christians.
Evangelicals are involved in "rescuing" North Korean defectors in China, something that Cheollima entity and Adrian Wong also claim to have done.
One wonders if any of these persons know of the high honor bestowed on them by being named as advisor to the empty hull of a regime change 'Institute'.
The other persons involved in the raid, Woo Ram Lee and Sam Ryu, are unlike Adrian Hong not easily identifiable.
The case of Adrian Hong and the raid on the embassy in Madrid will likely escalate. The Washington Post notes that the Spanish judge seeks their extradition from the United States to Spain where they will face up to 28 years in prison.
The NYT adds that the group has evidently prepared for a legal fight:
Lee Wolosky, a former national security and State Department official in several American administrations, said he had been retained as legal counsel by the group, which he said was called the Provisional Government of Free Joseon, or Cheollima Civil Defense.
Wolosky is a high caliber lawyer who for many years served on the National Security Council. As private lawyer he was involved in several legal cases related to 'national security'. He at least once used a variant of graymailing, 'a defensive tactic in an espionage trial whereby theaccused threatens to reveal secret information unless the charges are dropped':
Wolosky has led or co-led some of the firm's high-profile matters in recent years, including […] Restis v United Against Nuclear Iran (UANI), a precedent-setting private defamation case in which the United States Government asserted the state secrets privilege, resulting in a victory for Wolosky's client UANI.
Should Wolosky defend Adrian Hong in a legal fight against the Spanish extradition request he might threaten to reveal secrets the US would not like to have published. The case would then be put down.
Hiring Wolosky must be expensive.
Adrian Hong and the Cheollima group, if it exists at all, have no apparent sources of income. One wonders through which routes the US and/or South Korean secret services finance this game.
Source: Ron Paul Institute
Aen RaBeon says 2 years ago
It's wise of Hong to trust the USA.


text:
Q: what are the differences between SQL and Hive? What are the main differences b/w SQL and HIve?
Its for the interview purpose

A: SQL and HiveQL are programming language that helps to improve the design of the database. Some people tend to use them alternating but they are quite different.
SQL & HiveQL

*

*Both can be used on structured data

*HiveQL support schema for data insertion while SQL support schema for data storage

*SQL is used when we need frequent modification in records whereas HiveQL to query large data sets and analyze historical data.

*SQL has hundreds of built-in functions while HiveQL has a limited number of built-in functions.

*SQL support updates, delete, and insert while HiveQL does not support any.

A: HIVE
This is a tool by Apache built to query large distributed storages (mostly hadoop distributed file system) by using a SQL like language or statements. Its a tool to facilitate users who are familiar with SQL to work on HDFS. So, like any DB query tool it has few components like - query parser, query executor, coordinator, resource manager etc. to work properly.
You can get more info here
SQL
In comparison to hive, this is an umbrella term for querying information from a structured data. So, this is just a language like C, C++, Python with proper syntax/format/standards etc. and any developer can use this to access/modify any structured data. People can write long paragraph on this but you can read all about from Wiki.

redpajama_set_name: RedPajamaStackExchange