text:
\section{Introduction}
Two-dimensional (2D) electron layers
exist, for example, at the interface between GaAs and
Ga$_{1-x}$Al$_x$ As, or at the interface of a metal oxide and a
semiconductor. Such interfaces are important in field-effect
transistors and other devices.
The state of this 2D electrons system can be fluid or,
 at sufficiently low density, the electrons condense and
 crystallize\cite{ando,krav}.
We define
the 2D-density parameter $r_s$ given by $A/N=\pi{r_s}^2$ where $A$
 is the area
occupied by the $N$ electrons. The Wigner solid appears for $r_s\geq
35 a_0$ \cite{attac} where $a_0=\hbar^2/(m^*e^{*2})$ is the Bohr radius.
Here $m^*,e^*$ are effective parameters for the mass and the charge
of the electron, and absorb the dielectric constant, the band
mass and other material properties of the system. Thus
in GaAs, the effective atomic unit of energy is reduced from 27.21 eV
to the milli-Volt range. These (reduced) atomic units,
such that  $m^*=e^*=\hbar$=1 will be
assumed through out this paper.
There has been many studies of 2D-electron liquids or Wigner crystals
\cite{attac, rapisarda,tanatceper,ceper,bonsall,iyakutti}, especially
 using quantum Monte Carlo (QMC)
simulations and other methods\cite{bonsall,prl2}
assuming that the 2-D layers are infinitely thin.
However, although the 2D electrons reside
in the $(x,y)$-plane, they have a transverse
 density $\eta(z)$
confined to the lowest subband of the hetero-structure \cite{ando}.
While the quasi-2D electron liquid has recently seen much
attention, both experimental\cite{tan, stormer} and
theoretical\cite{ssc,asgari,zhang,morsen}, the Wigner crystal in
thick 2D layers has not been followed up since the work of
Fujiki and Geldart
\cite{fuji2}. Fujiki et al., have
determined the effect of the 2D-layer thickness on the
electrostatic energy and found that the hexagonal lattice
is the most-stable crystal structure, as with the
 $\delta$-thin 2D layer ($\delta$2D).
However, they did not consider the effect of
exchange and correlation which is usually addressed
via Quantum Monte Carlo methods, or via a detailed analysis of
the correlated  phonons in the
electron crystal\cite{bonsall}.
We note that recent Hartree-Fock (HF) calculations of $\delta$2D
 Wigner crystals
using large plane-wave basis sets,
e.g, those of Trail et al\cite{trail}.,
seem to recover a HF energy nearly identical to the single-
Gaussian {\it harmonic} approximation for localized electrons.
Various aspects of such a model have been considered in
a brief but insightful paper by Nagy\cite{nagy,polini}.
In this study we show that the single-Gaussian approximation,
and the local-density approximation (LDA),
can recover the QMC total
energy with surprising accuracy. We also show that a
method based on constructing a constant-density approximation
(CDA) to the inhomogeneous density\cite{ggsavin,ssc}
can be profitably used for calculating the
electrostatic potentials and the exchange-correlation
energies of these systems.

The plan of the paper is as follows. In section~\ref{coul-sec} we
introduce the Hamiltonian, the effective Coulomb interaction
in quasi-2D layers, and calculate the electrostatic energy
of the lattice for several 2D-crystal structures. Here we use the CDA
to replace Fang-Howard type densities in the $z$-direction\cite{ando,ssc},
thus simplifying the analytical work.
The details of lattice-sum evaluations
are relegated to an appendix.
In section~\ref{perfect} we consider the
$\delta$-thin 2D layer and present results for the
gaussian-localized model.
we also present the
exchange-correlation energy $E_{xc}$ calculation using the CDA and the
LDA.
The resulting total energy is very
close to that of QMC and recovers a liquid$\to$solid
Wigner transition (WT) at
$r_s\sim$32 to 38, while the current QMC estimate is $r_s=35\pm5$.
In section~\ref{gau-thick} we consider Gaussian-localized
2D systems with finite
thickness, for 2D layers found in HIGFETS.
That is, in systems where the layer thickness is
also defined by the sheet density, as in Tan et al\cite{tan,stormer}.
 Here we have no QMC results for comparison. The total
energy of the quasi-2D Wigner crystal is compared with the
total energy of the quasi-2D liquid\cite{ssc}.
Here the WT is  found to occur at $r_s\sim$15 to 21
 in quasi-2D layers realized in clean HIGFETS,
\section{The Coulomb energies of 2D lattices}
\label{coul-sec}
The Hamiltonian of our system is, in atomic units,
\begin{equation}
H=H_{ke}+H_{ee}+H_{eb}+H_{bb}
\end{equation}
where the first term is the kinetic energy of the electrons.
The three remaining terms are the electron-electron interaction and
the interactions involving the uniform, static neutralizing background,
indicated by the subscript $b$.
This neutralizing background arises from a homogeneous
layer of donor ions which have acquired a positive charge after
donating their valence electrons in forming the 2D-electron layer.
We assume that the electron layer is confined
 near the plane $z=0$ and extends into
the region of $z>0$ due to the finite width of the envelope function.
 The donor ions are modeled by a homogeneous layer of
  positive charge of areal density $\rho_d=N/A$, situated at $z=-b_d$,
  where $b_d=|b_d|$ is a positive quantity.
The $z$-direction density is $\eta(z)$, and
 in the plane, an areal density $\rho_e(\mathbf{r})$ with $\mathbf{r}=(x,y)$.
 The subband distribution $\eta(z)$ is usually modeled by a
 Fang-Howard distribution $\eta_{fh}(z)=(1/2 b^3)z^2 e^{-\frac{z}{b}}$
 (n.b., our $b=1/b$ used in  Ref.~\cite{ando}),
 or various other forms, e.g, that of a quantum well.
 The form of the density is obtained by fitting to a self-consistent
calculation of the Schrodinger equation for the electron motion in the
$z$-direction. In our work, we do not repeat this calculation, but simply
take the value of the parameter $b$, or other parameters
needed to define the self-consistent solution for the subband.
Moreover, as discussed below, such inhomogeneous
densities can be replaced by a constant-density slab
having an {\it equivalent electrostatic potential},
using the CDA discussed by Dharma-wardana\cite{ssc}.
The CDA method \cite{ssc} involves
replacing an inhomogeneous density $\eta(z)$ by
a slab of constant-density
$\bar{\eta}$ of width $a$ linked to $\eta(z)$ by
\begin{equation}
\label{cda-eqn}
\bar{\eta}=\frac{1}{a}=\int {\eta(z)}^2 \,dz
\end{equation}
This equation has also been proposed by Gori-Giorgi
et al\cite{ggsavin}., in a method for
calculating system-adapted correlation
energies.
Using Eq.~\ref{cda-eqn} a Fang-Howard (FH)
 density of length scale $b$ can
 be replace by a homogeneous
density of width $a=(16b)/3$.
\begin{figure}[t]
\includegraphics*[width=8cm,height=6cm]{density.eps}
\caption{(Color online) Profiles of the Fang-Howard density (solid curve)
 for $b=4$ and its
  equivalent constant density approximation(CDA, dashed curve).
  Inset: the bare Coulomb potential $1/r$ and the Coulomb
  potential $F(r)/r$ modifed by the Fang-Howard profile. The
  triangles are calculated using the CDA. The CDA width
  a=21.33 for $b$=4 corresponds to a HIGFET at $r_s=32.496$.
}\label{fang}
\end{figure}

Consider two electrons in a quasi-2D
layer separated by a distance $r$ in the 2D plane,
and located at $z_1$ and $z_2$,
with a FH distribution $\eta(z)$ in the $z$ direction.
Then the Coulomb interaction is of the form
\begin{equation}
W(r)=\int d z_1\, d z_2
\frac{\eta(z_1)\eta(z_2)}{|r^2+(z_1-z_2)^2|^{1/2}}
\end{equation}

$W(r)$ may be written as $F(r)/r$ where
$F(r)$ is the form factor. No analytic form exists if
$\eta(z)$ is the FH form, while the $q$-space form,
$F(q)2\pi/q$
is analytically available.
For GaAs/AlAs based HIGFET-like systems, it takes the form,
\begin{equation}F(q)=[1+\frac{9q}{8b'}+
\frac{3q^2}{8b'^2}][1+\frac{q}{b'}]^{-2}
\end{equation}
where $b'=1/b$ and follows the definition in
Ref.~\cite{ando}.
 However, if the FH distribution is
replaced by the CDA, then $F(r)$ and $F(q)$ are given by
\begin{eqnarray}
\label{cdmeqn}
W(r)&=&V(r)F(s),\;\; s=r/a, \;\; t=\surd{(1+s^2)} \\
F(s)&=&2s\left[\log\frac{1-t}{s}
\,\,+1-t\right]
\end{eqnarray}
and
\begin{eqnarray}
W(q)&=&V(q)F(p),\,\,\, p=qa, \,V(k)=2\pi/q\\
F(p)&=&(2/p)\{(e^{-p}-1)/p+1\}
\end{eqnarray}
The form factors $F(r)$, $F(q)$ are a
measure of the reduction of the strength of
the 2D interaction due to the thickness effect.
These results provide equivalent analytical
formulae for the FH-density,
and tend to the ideal 2D Coulomb
potential when the width $a$ tends to zero.
Also, for HIGFETS, it is known that the
FH-parameter $b$ is linked to the 2D density parameter
$r_s$. Hence it can be shown\cite{ssc} that
\begin{eqnarray}
\label{fh2w}
b&=&(2r_s^2/33)^{1/3}\\
a&=&16b/3\\
\beta&=&b/r_s=[2/(33r_s)]^{1/3}
\end{eqnarray}
Hence $\beta$, the FH parameter $b$
in units of $r_s$, and also the ratio $a/r_s$,
 i.e., ($z$-width)/(2D-disk radius)
decrease as $r_s^{1/3}$ with increasing $r_s$.
\subsection{Coulomb energy}
In the following we do not at first specify the form
of the transverse density $\eta(z)$.
In calculating the Coulomb energy $E_{Cou}$, i.e, the
electrostatic energy, we
isolate the long-range contributions which cancel in the $q=0$
limit, since we are dealing with a homogeneous, neutralizing, static
background.  The total Coulomb energy
 is the sum,
\begin{equation}\label{ecoul}
E_{Cou}=\lim_{q \rightarrow 0} [E_{dd}(q)+E_{ee}(q)+2E_{ed}(q)]
\end{equation}
where
\begin{equation}
E_{dd}(q) =\frac{1}{2}\int d^2r \int
d^2r'{\rho_d}^2\,\frac{e^{i\mathbf{q}\cdot(\mathbf{r-r'})}}{|\mathbf{r-r'}|}
\end{equation}

\begin{widetext}
{\setlength\arraycolsep{2pt}
\begin{eqnarray}
E_{ee}(q) & = & \frac{1}{2} \int d^2r \int
d^2r'\rho_e(\mathbf{r})\rho_e(\mathbf{r'})e^{i\mathbf{q}
\cdot(\mathbf{r-r'})}\int_{0}^{\infty} dz \int_{0}^{\infty}
 dz' \frac{\eta(z)\eta(z')}{[(\mathbf{r-r'})^2+(z-z')^2]^{1/2}}\\
E_{ed}(q) & = & -\frac{1}{2}\int d^2r \int d^2r'\rho_d
\rho_e(\mathbf{r'})e^{i\mathbf{q}\cdot(\mathbf{r-r'})}
\int_{0}^{\infty} dz'\frac{\eta(z')}{[(\mathbf{r-r'})^2+(b_d+z')^2]^{1/2}}
\end{eqnarray}}
\end{widetext}
$E_{dd}$ is the interaction energy of the ions, $E_{ee}$ is
the interaction of the electron layer and $E_{ed}$ is the
energy due to interaction between the ions and the electrons.
To calculate these terms, we proceed as in Fujiki
 and Geldart \cite{fuji2,fuji1}.

\begin{equation}\label{edd}
E_{dd}(q)=\frac{\pi A{\rho_d}^2}{q}=\frac{N}{q{r_s}^2}
\end{equation}
We introduce the integral transformation
\begin{equation}\label{trans}
\frac{1}{|\mathbf{v}|}=\int_{0}^{\infty} \frac{dy}{\sqrt{\pi}}
 y^{-1/2}e^{-y|\mathbf{v}|^2}
\end{equation}
and note that
{\setlength\arraycolsep{2pt}
\begin{eqnarray}\label{eed}
E_{ed}(q) & = & -\frac{1}{2}\int d^2r\int d^2r'\rho_d
 \rho_e(\mathbf{r'})e^{i\mathbf{q}\cdot(\mathbf{r-r'})}
\int_{0}^{\infty} dz' \eta(z')\nonumber\\
& & \int_{0}^{\infty}\frac{dy}{\sqrt{\pi}}
 y^{-1/2}e^{-y|\mathbf{r-r'}|^2-y|b_d+z'|^2} \nonumber\\
& = &  -\frac{N}{2\sqrt{\pi}{r_s}^2}\int_{0}^{\infty}dy\, y^{-3/2}
e^{-\frac{q^2}{4y}}\nonumber\\
& &  \int_{0}^{\infty} dz'\eta(z')e^{-y|z'+b_d|^2}
\end{eqnarray}}
For $E_{ee}$, we use a lattice sum technique based on the
 $\theta$ Jacobi function, Eq.(\ref{theta1}),
  and its imaginary transform, Eq.(\ref{theta2}), given below:
\begin{equation}\label{theta1}
\theta(z,X)\equiv \sum_{l=-\infty}^{\infty} e^{2\pi lz}e^{-\pi l^2 X}
\end{equation}
\begin{equation}\label{theta2}
\theta(z,X)=\frac{e^{\pi z^2/X}}{\sqrt{X}}\theta(\frac{z}{iX},\frac{1}{X})
\end{equation}
We decompose the lattice into rectangular sublattices
 indicated with sublattice vectors $\mathbf{\rho_j}$.
 So, the position vectors of the electrons on
  nodes $I$ and $J$ are given by
\begin{center}
$\mathbf{r_I}=m a_1 \hat{x} + n a_2 \hat{y},
 \quad \mathbf{r_J}=(m'a_1+\rho_{j}^{x})
 \hat{x}+(n'a_2+\rho_{j}^{y})\hat{y}$
\end{center}
where $m,m',n,n'$ are integers,
 $a_1,a_2$ are lattice constants of sublattices.
For example, in a square lattice $a_1=a_2$ and
 $\{ \mathbf{\rho_j} \}=\{(0;0)\}$,
 in a hexagonal lattice $a_2=\sqrt{3}a_1$ and $ \{ \mathbf{\rho_j}
 \}=\left\{(0;0),\left ( \frac{a_1}{2};\frac{a_1\sqrt{3}}{2} \right)\right\}$.
 %
To proceed further, we need to specify the form of the density.
 If the electrons are assumed to be
exactly localized on the nodes of the crystal, then
\begin{equation}\label{rhoefg}\rho_{e\delta}(\mathbf{r})=\sum_{I}
  \delta(\mathbf{r-r_I}).\end{equation}
Such exact localization of the electrons provides the model for
the classical electrostatic energy, i.e, {\it the
Madelung energy}.
In the quantum calculation
 we suppose that each electron is localized around a node $I$ of the
lattice and the wavefunction  is
taken to be a gaussian normalized over the 2D plane,
\begin{equation}\label{phi} \phi_I(\mathbf{r})=\sqrt{\frac{2\alpha}{\pi}}e^{-\alpha
    (\mathbf{r-r_I})^2}\end{equation}
The parameter $\alpha$ is chosen to
minimize the total energy. Hence the localized density is
\begin{equation}\label{rhoegauss}
  \rho_{eG}(\mathbf{r})=\frac{2\alpha}{\pi}\sum_{I} e^{-2\alpha
    (\mathbf{r-r_I})^2}
\end{equation}
The gaussian-width parameter $\alpha$ is of the form
$a/r_s^{3/2}$, with $a$ taking a lower-bound value of 0.5 (see
Ref~\cite{nagy}).
These two forms of the density will be studied below, and the Gaussian
approximation will be justified by comparison with
results from detailed plane-wave calculations.
\subsection{Calculation with the $\delta$-distribution}
\label{gau-thin}
Using Eq.(\ref{trans}) and (\ref{rhoefg}) we have
\begin{eqnarray}
\label{delta-ee}
E_{ee}(q)&=&\int_{0}^{\infty} \frac{dy}{2\sqrt{\pi y}}f(y)
 \sum_{I\ne J}e^{i\mathbf{q\cdot(r_I-r_J)}}e^{-y|\mathbf{r_I-r_J}|^2} \\
f(y)&=&\int_{0}^{\infty} dz \int_{0}^{\infty} dz'\eta(z)\eta(z')e^{-y(z-z')^2}
\nonumber
\end{eqnarray}
The details of the evaluation are given in the Appendix.

\begin{table}
\caption{The
Madelung energy, $E_{Cou}$ per electron are given for
  different values of the Fang-Howard
   parameter $\beta=b/r_s$ for hexagonal(hex), square(sq),
  rectangular(rec), centered rectangular(cr) lattices defined by
  their unit vectors $a_1$:$a_2$. The $r_s$ parameter
  in the corresponding HIGFET, Eq.~\ref{fh2w},
  is also given.
 The energies are in
   units of $1/r_s$. Thus the Madelung energy in Hartrees
    for a $\delta$-thin
   hexagonal lattice is $-1.106103/r_s$}
\label{tabecoul}
\begin{ruledtabular}
\begin{tabular}{lccccc}
HIGFET $r_s$                         &$\infty$ & 60606      & 60.606      & 0.06060\\
$\;\;\;(a1:a2)$ $\beta\to$\rule{0pt}{2.6ex} & $0$     &  $10^{-2}$ & $10^{-1}$ & $1$ \\

\hline
hex($\sqrt{3}:1$) \rule{0pt}{2.6ex} & $-1.106103$ &  $-1.052959$ & $-0.591433$
& $3.144793$ \\

cr($\sqrt{2}:1$) \rule{0pt}{2.6ex} & $-1.104080$ &  $-1.050937$ & $-0.589507$ &
$3.145401$ \\

sq(1:1) \rule{0pt}{2.6ex} & $ -1.100244$ &  $-1.047103$ & $-0.585854$ & $3.146555$ \\

rec($\sqrt{2}$:1) \rule{0pt}{2.6ex} & $-1.078201$ &  $-1.025072$ & $-0.564890$ &
$3.153217$\\

rec($\sqrt{3}:1$) \rule{0pt}{2.6ex} & $-1.042843$ &  $-0.989733$ & $-0.531301$ &
$3.163948$ \\

\end{tabular}
\end{ruledtabular}
\end{table}

 We have evaluated $E_{Cou}$, Eq.~\ref{ecoul} for
 different lattices:
  square, rectangular, hexagonal and
  centered-rectangular. The Coulomb energy depends
  only on $\beta=(b/r_s)=(3a)/(16 r_s)$, $r=(a_2/a_1)$
   and $\{\mathbf{\rho_j}\}$.
Our numerical calculations of $E_{Cou}$ are summarized in
  Table \ref{tabecoul}. Results for $\beta=10^{-2}$ are at
 unrealistically low HIGFET densities, but are of formal
 interest. Results for even smaller values
 of $\beta$ may be found in Fujiki et al\cite{fuji1,fuji2}.
 A comparison with the results of Ref.~\cite{fuji2}
  shows that our results are in
  agreement when a geometrical term arising from the slight
  difference in the models is taken into account.
   (As seen from the details given in the appendix,
    we have an additive term
  $N(2a/3)/{r_s}^2=N(32b/9)/{r_s}^2$ in our calculation while Fujiki
  and Geldart have $N(33b/8)/{r_s}^2$. Agreement is obtained if
  we replace our term by theirs).

   It is seen that the total Coulomb energy increases as
  $\beta=b/r_s$ increases for all cases studied. The hexagonal lattice
  has the lowest energy for all $\beta$. Moreover, there is
  no crossing between the different energy curves for any of the
  lattice structures.

The dependence of the total Coulomb energy of the
 centered-rectangular lattice
and rectangular lattice as a function of the
 ratio $r=a_1/a_2$ for the quasi-2D system
remains similar to the $\delta$-thin case. Two equivalent minima
at $r=\sqrt{3}$ and $1/\sqrt{3}$ correspond to
 the hexagonal structure. For the
rectangular lattice, the minimum corresponds to $r=1$, i.e., to the
square structure.  We choose the range $\beta$=0.05 to 0.5, which
corresponds to $r_s\sim$ 0.5 to $\sim$500
and fit the Madelung energy of the stable hexagonal
lattice (see Table \ref{tabecoul}) to the analytic form
\begin{equation}
\label{thick-madelung}
E_{Cou}(r_s,\beta)=\sum_{i=0}^{i=4}c_i\beta^i/r_s
\end{equation}
where $c_0=-1.106103$, $c_1$=5.34722, $c_2=-2.15257$, $c_3$=1.48663, and
$c_4=-0.430473$.

In Figure \ref{bfh}, we have plotted the Coulomb
energy as a function of $r_s$
using Eq.(\ref{fh2w}) to relate the thickness to the $r_s$ value.
We observe that the thickness of the system
has a significant effect on the energy.
\begin{figure}
\includegraphics*[width=8cm,height=6cm]{bfh.eps}
\caption{(Color online) (Coulomb energy per electron in atomic units for a perfectly 2D
system  and for 2D layers in a HIGFET, using
Eq.(\ref{fh2w}) to define the thickness.}\label{bfh}
\end{figure}
\subsection{Classical calculation with the gaussian distribution.}
If the electron distribution at each site were
a gaussian, the classical {\it electrostatic}
energy, $E_{ee}$, can be calculated using the same
techniques as before (Appendix).
{\setlength\arraycolsep{2pt}
\begin{eqnarray}
E_{ee}(q,\alpha) & = & \frac{1}{2\sqrt{\pi}}\int_{0}^{\infty}
dy\,y^{-1/2}\left(\frac{\alpha}{y+\alpha}\right)e^{-\frac{q^2}{4(y+\alpha)}}\nonumber\\
& & \sum_{I\ne
  J}
e^{-\frac{y\alpha}{y+\alpha}(\mathbf{r_I-r_J})^2}
e^{-i\frac{\alpha}{y+\alpha}\mathbf{q\cdot(r_I-r_J)}}
\end{eqnarray}}
We use the same integral separation with $E_{ee}^{<}$ and $E_{ee}^{>}$,
the Jacobi function $\theta$ and its transformation.
We may verify that when $\alpha$ tends to zero, that
is to say the gaussian distribution tends to the $\delta$-distribution,
$E_{ee}$ reduces to the Madelung energy of the
 previous section. Also, if there is no effective
 overlap among the gaussian distributions,
 the distributions can be replaced by equivalent
 point charges at the lattice sites and the Coulomb
 energy should reduce to the Madelung
 energy. However, as already remarked by
 previous authors\cite{nagy,polini}, the charge
 is not perfectly contained within the Wigner-Seitz
 disk in the 2D problem.
  The variations of the thickness and of the lattice type give results
 similar to the $\delta$-thin case.
 We consider the variation of $\alpha$ to minimize the
 total energy within a quantum calculation, and hence do not develop this
 classical calculation any further.
\section{Perfectly two-dimensional systems}\label{perfect}
 In this section we consider a perfect,
  i.e., $\delta$-thin 2D layer within a
  Kohn-Sham density-functional approach\cite{kohn}
  to the quantum mechanics of the problem. Since the
  $\delta$-thin 2D system has been studied extensively, we use it
  as a reference system to examine the LDA and the CDA as
  useful tools for calculations of $E_{xc}$ of Wigner
  crystals. The Hohenberg-Kohn theorem
  asserts that the total energy is a functional
   of the one-electron density,
  and that it is a minimum for the true density distribution. We model the
  one-electron density as a sum of gaussians centered on each lattice
  site, and hence the variational problem reduces to a determination
  of the width parameter $\alpha$ of the Gaussian that minimize the
  total energy.
  The total energy of the system at a given $r_s$ can be written as:
  \begin{equation}
  \label{dft-etot}
  E_T= E_{HF}(\alpha,r_s) +E_{xc}(\alpha,r_s)
  \end{equation}
  where $E_{HF}(\alpha,r_s)$ is the Hartree-Fock energy of an electron.
  It will be seen that this is effectively
  the energy of an electron on a single site,
   and moving in
  the potential well created by the gaussian
  distributions on other sites. If the gaussians were
  perfectly localized, the Coulomb energy would not
  depend on $\alpha$.  The effect of the overlap
  can be easily included in the variational problem,
  with the energy given by $<\psi|H|\psi>/<\psi|\psi>$, and
  this has an effect for small $r_s$. Here $\psi$ is
  a Slater determinant of gaussians. For the hexagonal lattice,
  the
  overlap contribution from two nearest-neighbour gaussians is
  $$s_{ij}(r_s)=\exp[-(\alpha/2)(1.09r_s)^2]$$
  where $1.09r_s$ is the nearest-neighbour distance.
  Unless  the contrary is stated, the results reported here
  will include the overlap correction.
  The $\alpha$ which minimizes
  the Hartree-Fock problem is not the same as that which minimized
  the total energy inclusive of $E_{xc}$. In the next section we
  look at the problem without $E_{xc}$

\subsection{The Hartree-Fock energy $E_{HF}$}
\label{hf-sec}
The Hartree-Fock energy is composed of the classical Madelung energy
which defines a constant energy term, plus the quantum mechanical
energy associated with the motion of the electron in the field of the
other electrons. Since the electrons are strongly
localized, especially for large $r_s$,
a Slater determinant made up of one gaussian function
at each lattice site is commonly assumed.
The total energy consists of a
kinetic energy  term and a potential energy term. These two
terms are equal by the virial theorem and hence we only
need to evaluate the kinetic energy.
Usually, Hartree-Fock energies contain a sizable exchange
contribution. However, the localized-gaussian exchange energy is
easily shown to be negligible,
 and we called it the Wigner-exchange
energy, $E_{Xwc}$.

In Table~\ref{hf-tab} we compare our localized-gaussian
(harmonic) calculation with the results of the extensive
plane-wave HF calculation by Trail et al\cite{thank-trail}.
\begin{table}
\caption{Comparison of the plane-wave calculation\cite{trail}
 of the HF energies $E_{HF}$ of the $\delta$-thin 2D hexagonal Wigner
lattice with the single-Gaussian harmonic lattice energies.
$E^*_{har}$ and $E_{har}$ are energies without and
with the overlap corrections.
}
\begin{ruledtabular}
\begin{tabular}{ccccccc}
$r_s\to$ & 20& 30&40 & 60 \\
\hline
-$E_{HF}\times10 $   &0.447270 & 0.311642 &0.239528 &0.164036\\
-$E^*_{har}\times10$ & 0.447155 & 0.311786 &0.239822 & 0.164530\\
-$E_{har}\times10$   & 0.437058 & 0.308344 &0.238326 & 0.164113\\
\end{tabular}
\end{ruledtabular}
\label{hf-tab}
\end{table}
The results shown in Table~\ref{hf-tab}
show that the localized single-gaussian model  is adequate to
describe the Hartree-Fock approximation
for this system\cite{trail2}.

Note that our calculation is effectively an ``Einstein model'' of
oscillators, and the kinetic energy is
given by,
\begin{equation}
E_K(\alpha)= -\frac{N}{2}<\phi_I|\nabla_I^2|\phi_I>=N\alpha
\end{equation}
The
gaussian width which minimizes the energy
may be fitted by the form  $\alpha=0.6263/r_s^{1.57}$.

Since the exchange of electrons actually involves a delocalization
process, we believe that the exchange integral evaluated with fixed
gaussians does not lead to a true evaluation of the exchange in
these systems.
The Wigner-exchange energy between
 two electrons of spin $s_i,\,s_j$, is by definition
{\setlength\arraycolsep{2pt}
\begin{eqnarray}\label{excdef}
E^{ij}_{Xwc}& = & -\int d^2 r_i\,d^2 r_j
\phi_I(\mathbf{r_i})\phi_J(\mathbf{r_j})\frac{1}{r_{ij}}
\phi_I(\mathbf{r_j})\phi_J(\mathbf{r_i})\nonumber\\
& = & -\sqrt{\alpha\pi}e^{-\alpha(\mathbf{r_I-r_J})^2} \delta_{s_i,s_j}
\end{eqnarray}}
We can define a polarization parameter
$\zeta=(N_{\uparrow}-N_{\downarrow})/N$, therefore
\begin{equation}
\label{wigner-X}
E_{Xwc}(\alpha,\zeta)=-\frac{1}{2}\sum_{i\ne j} E^{ij}_{Xwc}
\end{equation}
This
$E_{Xwc}$, may be safely neglected for the values of $\alpha$
occurring in this problem.
\subsection{The CDA exchange and correlation energies}
\label{correlperf}
The correlation energy is the most difficult
object to calculate, and QMC has been the
preferred approach, even though this requires a
 a major numerical effort.
However, for an uniform density profile,
 the
correlation energy is well known \cite{attac}. Hence, as in
Eq.i~\ref{cda-eqn}, we map the inhomogeneous density in the
$(x,y)$ plane, $\rho(\mathbf{r})$, to a
homogeneous form via the $<\rho(\mathbf{r})^2>$ average of the CDA method.
Given a gaussian distribution,
{\setlength\arraycolsep{2pt}
\begin{eqnarray}
\bar{\rho} & = & \frac{1}{\pi {r_s}^2}\int d^2 r\, |\phi(\mathbf{r})|^2
|\phi(\mathbf{r})|^2 \nonumber \\
& = & \frac{\alpha}{\pi^2 {r_s}^2}
\end{eqnarray}}
We define the effective $r_s$ parameter  $\bar{r_s}$
corresponding to the CDA density by $\bar{\rho}=1/(\pi{\bar{r}_s}^2)$,
\begin{equation}
\label{rsCDA}
\bar{r}_s=r_s\sqrt{\frac{\pi}{\alpha}}
\end{equation}
The correlation energy in the CDA, $E_{c}^{cda}$ for the
inhomogeneous distribution, inclusive of spin-polarization effects,
is now evaluated using $\bar{r}_s$ in any of the
well-known 2D-functionals\cite{attac}.
Note that for typical values of $\alpha$ at $r_s=20$, the
CDA density parameter is $\sim 400$, while at $r_s$=100,
it becomes $\sim$7000. Thus
we see that the CDA replaces the inhomogeneous fluid with
sharp Gaussian peaks by a uniform, {\it ultra-low-density}
 2D fluid.
In calculating $E_c(\bar{r}_s)$ using, say, the formula
due to Attaccalite et al., a difficulty arises since it is
fitted to a maximum $r_s$ of 40, together with
asymptotic forms, while
the CDA calls for $r_s$ values which are one or two orders
bigger. Nevertheless, we find
surprisingly good results (see below).

At this point we ask if the exchange energy, evaluated
for this ultra-low density fluid, should also be
included. We believe that this is indeed the case. The fixed-gaussian
Wigner-exchange, Eq.~\ref{wigner-X} simply does not allow
any exchange, and ignores the possibilities of tunneling,
ring-exchange etc., that exist in the system. We consider that the
estimate of exchange obtained from the ultra-low density
fluid of the CDA accounts for such exchange effects. This
point of view is justified {\it post-facto} by the good
agreement of our total energies with the QMC total energies.

\subsection{The LDA exchange and correlation energies}
Another approach to replacing the inhomogeneous electron density
by a homogeneous fluid-density is the
local-density approximation (LDA) \cite{kohn}.
Here a uniform density corresponding to each
local density $n(r)$ is invoked.
 Thus a local-density parameter
$\bar{r}_s(r)$ is defined by
\begin{equation}
\label{rsLDA}
\frac{1}{\pi\bar{r_s}^2}=
\frac{\rho(r)}{\pi{r_s}^2}\quad \Longrightarrow \quad
\bar{r}_s(r)=r_s e^{\alpha r^2} \sqrt{\frac{\pi}{2\alpha}}.
\end{equation}
Hence, knowing the exchange-correlation
energy density $e_{xc}$ for a homogeneous
system, the exchange-correlation energy
 of the inhomogeneous system is
given by
\begin{equation}\label{xclda}
E_{xc}^{LDA}=\int d^2r \, e_{xc}[\bar{r}_s(r)]\,\rho(r)
\end{equation}
Just as in the CDA, the LDA demands the evaluation
of $E_{c}$ at densities which are beyond
the range of the standard fits. Thus LDA needs
$r_s(r)\sim 300$ to 5000 at $r_s=20$, i.e., a
little less extreme than the CDA.
Hence, some of the shortcomings of the LDA may
also be due to poorly known correlation energies at
the exceptionally high $r_s$ values that are
required.
The LDA can be further improved by including
gradient corrections. However, we have not
included them in this study.
\subsection{Minimization of the total energy $E_T$}
\label{perfmin}
We have now all the energy contributions
needed to calculate the ground-state energy of a
perfect two-dimensional
 (i.e., $\delta$-thin) Wigner crystal at a given value of
 the density parameter
$r_s$.
The energy minimum with respect to $\alpha$
 is found to be insensitive to the polarization of
the lattice. This in agreement with previous studies
\cite{attac,rapisarda,tanatceper,zhu}.
\begin{table}
\caption{Results of energy minimization for a hexagonal
lattice. The Madelung energy $E_M=-1.106103/r_s$
has been subtracted out from the total energy.
The CDA and LDA results are compared with the  GFMC
 calculations of Tanatar
 \& Ceperley, T-C \cite{tanatceper}

 The energies are in $10^{-2}$ atomic
units. }
\label{tabpol}
\begin{ruledtabular}
\begin{tabular}{ccccccc}
$\;\;\;r_s\to$  & 20   & 30    & 40   & 50    & 60 \\
\hline
CDA  &0.9247 & 0.4824 &0.3059 & 0.2156 &0.1625 \\

LDA  &0.9404 & 0.4899 &0.3102 & 0.2185 &0.1645 \\

T-C  &0.9167 & 0.4983 &0.3234 & 0.2313 &0.1758 \\

\end{tabular}
\end{ruledtabular}
\end{table}
In Table \ref{tabpol}, we give the energy correction to the
Madelung energy
obtained by the minimization of $E_T$,  using the CDA or the LDA
for evaluating the exchange-correlation effects,
together with the results of previous work \cite{tanatceper}.
QMC results by Rapisarda and Senatore\cite{rapisarda} are
very similar to those of Tanatar et al., and the agreement
is similar.
The optimal $\alpha$ which minimizes the energy
is found to be given by
$\alpha=a/r_s^{3/2}$
with a=0.639 for both CDA and LDA approaches. Here
we note that Nagy's method\cite{nagy} predicts
a value $\alpha_{ng}=0.5/r_s^{3/2}$ as a lower bound.
A crucial test of the accuracy of the CDA and LDA would lie
in their ability to predict the liquid$\to$solid phase transition.
This is addressed in section~\ref{wpt-sec}.
The total energy can be represented by:
\begin{equation}
\label{etot-fit}
E_T(r_s)=\frac{a_1}{r_s}+\frac{a_2}{{r_s}^{3/2}}+\frac{a_3}{{r_s}^2}+O({r_s}^{-5/2})\quad
r_s\gg 1
\end{equation}
where $a_1=-1.106103$ is the Madelung constant and $a_2$ is the
zero-point energy of the lattice.
We determined the coefficient $a_3$ by a least-square fit.
The results are summarized in Table~\ref{tab-123},
together with previous results.
\begin{table}
\caption{Coefficients $a_1-a_3$  in Eq.~\ref{etot-fit}
 fitting the CDA and LDA
total energy (for the range $r_s$=20 to 100) are compared
with previous work.
}
\label{tab-123}
\begin{ruledtabular}
\begin{tabular}{ccccccc}
  &CDA & LDA &BM\cite{bonsall}  & RS\cite{rapisarda} & TC\cite{tanatceper} \\
\hline
$-a_1$ &  1.1061  & 1.10610   & 1.1060  & 1.104715 &1.10610 \\
$a_2$  &  0.8142  & 0.8142     & 0.8142  & 0.7947  &0.8142  \\
$a_3$   & 0.2456  & 0.1194     & ...     & 0.07338  &0.0254 \\
\end{tabular}
\end{ruledtabular}
\end{table}
 These results justify
our use of the CDA and the LDA for evaluating the
total energy of quasi-2D Wigner crystal phases for which there
are no QMC calculations as yet.

\section{Influence of the thickness}
\label{gau-thick}
 We consider a
quasi-2D electron crystal where each electron is localized
at each lattice site with a gaussian distribution centered on each site
in the $(x,y)$-plane,
while the $z$-extension may typically have the form of a Fang-Howard density.
As before, such $z$-distributions can be replaced by a constant-density
form for ease of calculations. Also, we assume that the 2D layers
are in HIGFETS, and as such the FH-parameter $b$ is automatically
specified (via Eq.~\ref{fh2w} )when the $r_s$ parameter defining
the 2D-layer density is specified.

The kinetic energy and the harmonic energy of the quasi-2D
system are still given by $E_K(\alpha)=N\alpha$ since
this is a result of the assumed gaussian form of the wavefunction.
However, the simple Coulomb potential $1/r$ has changed to
 $F(r)/r$ where $F(r)$ is the form factor arising from the
subband distribution.  The Wigner-exchange energy, i.e.,
the exchange between two localized electrons is now even
weaker than in Eq.~\ref{excdef}. Hence this type of
exchange is totally negligible.

\subsection{The evaluation of $E_{xc}$ for thick-2D layers using
 CDA and LDA.}
 As  described in Eq.~\ref{fh2w}, the z-distribution
is mapped onto a uniform slab of width $a$; in HIGFETS
this is
directly related to the $r_s$ parameter in the 2-D plane.
The inhomogeneous 2-D distribution in the plane is also
mapped onto a homogeneous distribution via the CDA
as in Eqs.~\ref{rsCDA}
or as in Eq.~\ref{rsLDA} for the LDA.
Both CDA and LDA require a knowledge of the $E_{xc}(r_s,a)$
for quasi-2D uniform systems with a layer width $a$. Parametrized forms
of the exchange energy and the correlation energy
of uniform quasi-2D electron fluids have been given by
Dharma-wardana\cite{ssc}. The exchange energy $E_x(r_s,a)$
is given in the form $E_x(r_s,\zeta)Q(r_s,a,\zeta)$ where
$E_x(r_s,\zeta)$ is the well-known exchange energy of the
$\delta$-thin system, while $Q(r_s,a,\zeta)$ is a form factor.
The correlation energy of quasi-2D layers in HIGFETS
 is given in Ref.~\cite{ssc}
as an interpolation involving a form for electron ``rods'' interacting
via a logarithmic potential (as is the
case for small $r_s$), and for 3D-like electrons when $r_s$,
and the thickness $a$
become large. The Wigner crystallization regime involves
the latter regime. For details of these parametrizations,
the reader is referred to Ref.~\cite{ssc}. Since the WT involves
small energy differences, we have actually done an explicit
calculation instead of using the fits.

\begin{figure}
\includegraphics*[width=8cm,height=6cm]{wpt.eps}
\caption{(Color online) Comparison of liquid and solid-phase energies.
$(E-E_M){r_s}^{3/2}$ where
$E_M=-1.106103/r_s$ and $E$ is the unpolarized or
fully-polarized fluid energy, or the solid energy
$E_{cda}$,  $E_{lda}$ or from QMC.}
\label{figwpt}
\end{figure}

\subsection{Minimization of the total energy $E_T$}

As in Sec.\ref{perfmin}, we minimize the total energy as a function of
$\alpha$ for a given $r_s$. Here, the
energy is more sensitive to the spin-polarization
$\zeta$  than in the perfect crystal even
if the difference is very small. The unpolarized crystal is more stable
than the polarized one. So we present results for the unpolarized
system.
The values of $\alpha$ which minimizes the energy can also be fitted by the
same form as in Sec.\ref{perfmin}. We obtain
\begin{equation}
\alpha_{cda}=\frac{0.619}{{r_s}^{3/2}} \quad\mathrm{and}\quad
\alpha_{lda}=\frac{0.627}{{r_s}^{3/2}}
\end{equation}
We have also fitted the total energy. Here the Madelung energy is
 the  $E_{Cou}$ given in Eq.(\ref{thick-madelung}) and we use the
usual expansion in inverse $r_s^{3/2}$ etc.
\begin{eqnarray}
E_{T}^{cda} & = &
E_{Cou}(r_s)+\frac{0.68597}{{r_s}^{3/2}}+\frac{0.321652}{{r_s}^2} \\
E_{T}^{lda} & = &
E_{Cou}(r_s)+\frac{0.708977}{{r_s}^{3/2}}+\frac{0.357242}{{r_s}^2}
\end{eqnarray}
We remark that the total energy has a minimum as a function of $r_s$. This
minimum is located around $r_s\sim 26$ and its value is $\sim -0.011$ a.u.
A comparison of  liquid phase and Wigner crystal in HIGFETS is given in
Table~\ref{tabpol2}. These total energies include the $2a/3r_s^2$ correction
arsing from the interaction of the quasi-2D layer with the unifrom background,
as discussed in subsection~\ref{gau-thin}. Since this depends on the
layer thickness $a$, this correction does not occur in the ideal 2D
system.
\begin{table}
\caption{Results of energy minimization for a hexagonal
  lattice and comparison with the unpolarized
  liquid phase energy $E_L$.
   The energies are measured in $10^{-3}$ atomic
  units.}
\label{tabpol2}
\begin{ruledtabular}
\begin{tabular}{ccccccc}
\hline
$r_s$ \rule{0pt}{2.6ex} &15& $20$ & 30& $50$   \\
\hline
$E_{cda}$ \rule{0pt}{2.6ex}&-6.7255 & -10.1581&-10.8576  & -9.1112
 \\
$E_{lda}$ \rule{0pt}{2.6ex}&-6.5036 & -9.8169&-10.7782 & -9.0306
 \\
$E_{L}$ \rule{0pt}{2.6ex}&-7.1324 & -10.0249 &-10.5995& -8.8939
\\
\end{tabular}
\end{ruledtabular}
\end{table}
\subsection{Phase transition Liquid$\to$ Wigner crystal.}
\label{wpt-sec}
According to quantum Monte Carlo simulations, the phase transition between a
$\delta$-thin 2D electron liquid  and a 2D electron Wigner crystal occurs
 around $r_s=
35\pm5$.
With our methods we find a transition for $r_s=32$ using the CDA  and
$r_s=38$ using the LDA.

In Figure \ref{figwpt}, we show the phase diagram of the system (in
order to have a clear display we present $(E-E_M){r_s}^{3/2}$ where
$E_M=-1.106103/r_s$ the Madelung energy). The fluid phase energy is calculated
using the fit given by\cite{attac}. Unlike in the $\delta$-thin
2D system, the total energy contains the term $\Delta_{be}=2a/3r_s^2$
arising from the interaction with the unifrom background,
(see subsection~\ref{gau-thin}). This has been removed from both the
liquid and the solid phase
energies as this improves the clarity of the display.

\begin{figure}
\includegraphics*[width=6cm,height=7.5cm]{r1p5.eps}
\caption{(Color online) $(E-E_M){r_s}^{3/2}$ where
$E_M=-1.106103/r_s$ and $E$ is the unpolarized or
fully-polarized fluid energy, or the solid energy
$E_{cda}$ or  $E_{lda}$. The spin-phase transition in
the fluid is labeled SPT. The onset of the Wigner crystal
in CDA and LDA are indicated by arrows.
}
\label{phaset}
\end{figure}

These results
tend
to show that both LDA and CDA provide an adequate evaluation of  $E_{xc}$ for
 electron solids, especially when we recall that the $E_c$ at $r_s$
values (200-8000),
way outside the fit range ($r_s\le 40$), are needed in the CDA and the
LDA evaluations.
Figure~\ref{phaset} displays the phase transitions
in the quasi-2D HIGFET system. The Wigner transition occurs at
$r_s=15.5$ for the CDA, and $r_s=20.5$ for the LDA, i.e,
before the spin-phase transition (marked SPT in the figure)
of the liquid phase. Since the $\delta$-thin 2D layer is
expected to have a WT near $r_s\sim 35$, the thickness effect
has brought the WT to smaller $r_s$ values. It should be noted
that if correlation effects are neglected, the WT occurs at very low
$r_s$. Hence the shift of the WT to low $r_s$ is a consequence
of the reduced correlations in the quasi-2D system.

\section{Conclusion}

We have investigated the crystallization of electrons under their
own interaction in infinitely-thin 2D electron layers, known
as Wigner crystallization, as well as
in 2D layers with a finite width. The case of
 infinitely-thin 2D electron layers has been extensively studied
in the past, and provides a bench mark to test our methods
for replacing inhomogeneous electron densities by equivalent
uniform-density models. Detailed Hartree-Fock
calculations with large plane-wave basis sets are shown to
be closely equivalent to the single-gaussian harmonic
lattice calculations. We show that the constant-density approximation,
CDA, as well as the local-density approximation, LDA, successfully
recover the total energy as well as the correlation energies of
the infinitely-thin 2D electron crystal. In particular, these
models predict a liquid$\to$solid phase-transition in the
range $30<r_s<40$, in good agreement with Quantum Monte Carlo
simulations. When these methods are applied to quasi-2D
layers with the thickness as in HIGFETS, the weakened
Coulomb correlations move the Wigner transition towards
high densities. The LDA and the CDA predict a
Wigner transition near $r_s\sim$15 to 21.

redpajama_set_name: RedPajamaArXiv


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text:
#import "GoogleSignIn.h"
#import <UnityAppController.h>

// Controller to handle Google SignIn.  The AppController methods are swizzled
// into the UnityAppController in order to avoid breaking other code that needs
// to handle these messages also.
@interface UnityAppController (GoogleSignInAppController)
// These are the implementations for GSI.  The signatures match the
// AppController methods.
- (BOOL)application:(UIApplication *)application
    didFinishLaunchingWithOptions:(NSDictionary *)launchOptions;

- (BOOL)application:(UIApplication *)application
            openURL:(NSURL *)url
            options:(NSDictionary<NSString *, id> *)options;

- (BOOL)application:(UIApplication *)application
              openURL:(NSURL *)url
    sourceApplication:(NSString *)sourceApplication
           annotation:(id)annotation;

@end

redpajama_set_name: RedPajamaGithub


If you have a home that you are having built or just replacing your HVAC in Houston, there is a wide gamut of options for heating and cooling your home. Of course, being in Houston and the climate zone we are in, heating is not always a huge concern since we rarely see freezing temperatures. You are likely familiar though with the common furnace/air conditioner combo found in over 80% of Houston homes.
However, in keeping with covering modern HVAC technology this month, we would like to bring your attention to an alternative to a big bulky furnace that might be a better fit for your home. If you are looking for something that is more fuel efficient than a furnace and is stable to heat your home, a heat pump might be the right choice for you? But you may not know anything about a heat pump as the technology might be very new to you. Not to worry, HVAC in Houston is sort of our thing, so let us break it down for you.
What Is A Heat Pump & What Does It Do?
Heat pumps are not old technology but not the newest either. They have however advanced quite a bit in efficiency over the last several years and offer some great advantages to a furnace.
A heat pump is essentially a single unit that can not only provide heat but cooling as well. When your home needs to be heated or cooled a heat pump moves the air inside or outside of your home depending what your space needs—heating or cooling.
The reason heat pumps are more fuel efficient and better for the environment is that they don't burn fossil fuel to produce heat. Heat pumps have historically been primarily for warm weather climates such as Texas and the rest of the southern states that rarely see near or below freezing temperatures. This is because it used to be that heat pumps could not operate in regions with below freezing temperatures—but advancements in technology have changed that. However, we don't have to worry about with HVAC in Houston due to our climate.
Heat pumps are basically an air conditioning unit that can operate in reverse and provide heat during the colder months.
In warm weather, heat from inside your home is absorbed by the pump and moved outside which cools the home effectively.
In cooler weather, the process simply reverses and the heat pump brings heat from the air outside and distributes it throughout your home.
Yes, that may seem illogical—extracting heat from the outside, in cold temperatures, you don't believe it? Well, believe it. The truth is there is no such thing as "cold" it is merely a fabrication of our mind to define air that has little heat energy in it. In fact, air always contains heat, just at times, there is more of it. That being said, heat can always be extracted from cold air, but as far as heat pumps in Houston are concerned—it's a lot easier to extract in milder temperatures like Houston. However, as mentioned earlier, newer heat pumps sold mainly in the northeast, do have advanced technology that allows them to operate in freezing temperatures as well.
Even though there are several types of heat pumps there is really one main type of heat pump most often used in Houston.
With regards to HVAC in Houston, the heat pumps often used here are Air Source Heat Pumps. They are called this because they literally use external air as their source for heat. This is most practical for urban and suburban areas with developed areas.
Rural areas, on the other hand, can benefit from water sourced or geothermal heat pumps. These are complex installation because they use water pipes and heat from beneath the ground. They can be very efficient but are more practical in rural areas.
Similar to a split system HVAC in Houston, a split system pump has an indoor distributor connected to an outside unit. Here is where it gets different. A split system heat pump uses evaporator coils to absorb heat and condenser coils to A split system heat pump has two parts: an inside unit and an outside unit, just like a traditional residential central air unit.
The difference is, a split system heat pump has both coils that absorb heat (evaporator coils) and coils that release heat (condenser coils) in the inside and outside units.
That means that a split system pump can both cool and heat from either the inside or the outside. This makes it very versatile in that it is essentially reversible.
If you are installing in an older home where ducts are not an option—just as there are mini-split air conditioning units with distributors for each room, heat pumps come in mini-splits as well. When ducts are not feasible these ductless systems provide an energy efficient alternative. Be forewarned, however, that these ductless systems do not remove humidity as well as a ducted system and given Houston's humid climate, we typically do not recommend them unless you plan on using a supplemental dehumidifier.
What Are The Advantages Of Heat Pumps In Houston?
The question you have been asking since the beginning of this article is about to be answered, we saved this part for last so you would know about heat pumps, not just their advantages. You have to know how they work and what they are good for before making a case for their advantage. That being said the advantages for Houston residents and our mild climate do add up.
LOWER ENERGY EXPENSES: According to energy.gov, a heat pump in Houston can create almost three times as much heat energy for a given space than the electricity it uses. That means a significant reduction in your energy bill year after year. On average, a Houston home can save up to $1,000 a year!
CHEAPER MAINTENANCE AND REPAIRS: Since you are using one system for heating and cooling, there is only one unit to maintain and one system diagnostic if something goes awry. This lowers the cost of ownership and makes maintenance fairly straightforward and easy to diagnose.
FRIENDLIER TO THE ENVIRONMENT: Even though heat pumps use electricity to operate, they don't use fossil fuels to heat as a furnace does. This does your part to reduce fossil fuel usage.
Looking to upgrade your home's heating and cooling but want to cut the costs down? Don't feel the need for a big bulky furnace for a climate zone that rarely gets bone-chilling cold? You need to contact one of our consultants today and have Airteam show you the options we have in quality heat pumps by Trane. Contact us for a free consultation!


Managing a project correctly can often make or break a company's reputation. Individual teams are assigned to their corresponding team leaders and the managerial staff above them often simply hopes for the best. However, several project management mistakes can truly harm a company, both financially and publicly.
Some of those mistakes can really cause downtime, a loss of morale and even a project's failure. Though, the truth is that sometimes they can be really easy to avoid. If you wish to know more about the most predominant project management mistakes and `how to tackle them, keep on reading.
Proper management can have a large number of benefits for a business. First and foremost, successful team management can help you increase and improve your customers' satisfaction. The more in sync you are with your team and the more you work together in order to improve your results and your services, the easier it will be for you to keep your customers happy.
On top of that, proper project management will help you be more flexible when it comes to dealing with problems and unexpected situations. You will be able to find the right opportunities you need to expand your business and help your team grow and evolve, the more you work together in unison.
The very first thing you should be doing is making sure every team member is assigned the correct task. Sometimes, even if someone has more experience in a field, there might be another member of your team who is more creative, interested or knowledgeable in a certain topic.
The best way to make sure you assign the right person the right task is by communicating with your team and giving them the chance to express whether they would prefer to take up a task or not. This way, everyone will be able to have the chance to work on a project they will enjoy, and this will help you increase your team's productivity and success.
Trust is very important in every team. If you are the leader of a team, you will have to put your trust in their powers and not try and control them constantly.
Giving your team members some freedom, especially when it comes to their creativity can really help them perform better and have more trust in you and the team as a whole.
One of those mistakes you should definitely avoid is not putting enough time and effort into making sure your project is planned and will run smoothly. Sometimes, not planning or even explaining a project correctly to your team can really set you back and create big misunderstandings.
Milestones and goals will always be helpful when it comes to keeping track of your team's progress. They are the best way for you to know whether everything is running smoothly or not and how according to plan everything goes.
Goals will also be a great source of motivation for your team as they will know what they are working hard to achieve. Milestones are a great reminder of how simple everyday steps can bring the entire team a step closer to its final goal for a certain project.
In order for a project to run successfully, you will need to have some resources available for your team to use without having to look for them at the very last minute. For example, one of the resources that are always needed for any smaller or bigger project is a good editing and proofreading tool.
Instead of looking for a good one while the project is almost done, you should make your team's job a little easier and provide them with an easy-to-use tool such as Grammarly, Hemingway Editor or TrustMyPaper from the very beginning.
When things start not going too well, improvisation is always needed and can be a great source of help in order to help you and your team get back on track. The truth is though that it can be too much of a good thing. Each company has a certain set of rules the employees must follow and they are supposed to help teams work better under certain occasions and situations.
If a project is not as successful and improvisations need to take place, you need to be sure that all of them are compatible with the company's point of view and goals. This will help the team know exactly which steps to take and you will be able to teach them even more about the company procedure.
Apart from delivering great results, a project is supposed to help your team learn how to work better in unison, adapt to new situations, work by the company rules and of course obtain new skills.
After the completion of a project, you should always find some time to talk to your team members about their personal growth throughout it and how it has and will affect their future working experience in the company.
Good project management will help you work with more ease with your team and rid yourself of any small mistakes which can hinder your progress. Even the smallest of miscommunication issues or misunderstandings can make a project run slower and that can ultimately harm your company's sales, plans and future goals.
Which of these 7 mistakes do you believe you will be able to avoid during your next project?


There has been a lot of speculation over Callum Hudson-Odoi's future at Chelsea. The 18-year-old has reportedly handed in a transfer request which has been rejected by the club.
A £35m offer from Bayern Munich is believed to have already been turned down for the teenager, despite the fact that the winger only has 18 months remaining on his current deal.
Many Chelsea fans are keen to see England Under 19 international more regularly and after yesterday's poor display, there will be more pressure on the manager to make sweeping changes to the starting lineup.
It will be interesting to see whether Hudson-Odoi features against Huddersfield on Sunday unless the decision is made before then to offload him.


Illustration showing that if one diameter is conjugate to a second, the second is conjugate to the first.
A graph of tan ellipse with Foci and Center.
Illustration of an ellipse with foci F' and F, major axis A' to A, minor axis B' to B, and center O.
Illustration showing that tangents drawn at the ends of any diameter are parallel to each other.
Illustration of ellipse with parts labeled.
Illustration of how to draw a tangent to an ellipse from an external point.
A section of the human eye.
Diagram depicting a cone with both nappes intersected by plane J to form a hyperbola.
Illustration showing how the a hyperbola is symmetrical with respect to its conjugate axis.
Two concave mirrors facing each other to concentrate light.


Cornerstone Credit Union League is delighted to announce that Valwood Park Federal Credit Union has re-affiliated this year, and is now eligible for all the membership benefits the association provides, including advocacy, asset/liability management, chapter and council programs, compliance and regulatory guidance and support, communications and outreach, league representatives, research, small credit union development, and training and events.
"During our recent NCUA exam," said Tammy Perkins, CEO of Valwood Park FCU, "we were told we needed some help with our policies—specifically to adopt a few new ones, clean up some existing ones, and get some compliance assistance. Our NCUA examiner, Yvonne, recommended I join the Cornerstone Credit Union League to get the assistance I needed. She indicated the League has many resources that would benefit me and would be useful to my credit union."
"I don't get out to conferences and seminars much because of our size, and the League has many resources available that can be used in-house," said Perkins. "I took my examiner's recommendation and joined the League. I am now am able to utilize all the tools and services the League offers and get the help I need."
"We are excited to welcome Valwood Park FCU to the Cornerstone family," said Cornerstone SVP Credit Union Relations Mike Delker. "I view it as a validation of our commitment to advancing the success of all credit unions, and I am very pleased they are once again a member. I am also grateful that the NCUA recognizes the benefit of league membership as well and very much appreciate the reinforcement of this to the credit union."
Originally chartered in 1974, Valwood Park FCU is located in Carrollton, Texas. The credit union has since grown to $19 million in assets and serves more than 350 companies. Their field of membership includes people, businesses, and other legal entities that live, work, worship, or attend school in Carrollton, Farmers Branch, and Addison. For more information, please visit valwoodpark.com.


text:
HomeNewsArchivesCommittee Approves Potter for Fire Service Director
Committee Approves Potter for Fire Service Director
July 1, 2004 – Merwin Potter, Fire Service acting director, was approved by the Senate Rules Committee on Wednesday to become the agency's permanent director. The committee proceeded with Potter's confirmation hearing contrary to the advice of its legal counsel, Yvonne Tharpes.
At the hearing Tharpes offered a second opinion backing the one she had delivered in a Rules session last week, saying Potter and Kevin Rodriguez, the governor's nominee for Personnel director, had been confirmed by default because the time frame for Senate action had expired. The committee on Wednesday also approved Rodriguez's nomination. (See "Rules Does Confirm Fire Service, Personnel Nominees".)
The senators were more interested in hearing what the nominees had to say than in rehashing the legal opinion. Sen. Carlton Dowe didn't essentially go along with either opinion. "When it's convenient, we go with a legal opinion," he said. "We should be able to hear the nominees, but we shouldn't have to hide behind legal opinion."
Potter, surrounded by Fire Service personnel, embraced the occasion to recount strides he said the service has made in the last year. He noted the just-announced plan to reopen the Dorothea fire station on St. Thomas in September once a new class of firefighter recruits completes training. While the Fire Service is currently 31 years behind in its level of service, he said, it is moving ahead.
This year, he said, the Cotton Valley fire station on St. Croix and the Tutu station on St. Thomas have already reopened. He said the keys to the fire engine shelter on Water Island have been turned over to the Fire Service, and on his "wish list" is a Fire Service presence on the island.
Potter said fire departments in the States have been merging with other safety services since the terrorist attacks of Sept 11, 2001. He called for merging the Fire Service with the territory's Emergency Medical Services and Fire Rescue units, saying this can be done by executive order or legislation. The merger would mean a significant financial savings for the government, he said, asking the senators for their support.
Also, he said, the territory's Homeland Security Council has recommended that the EMS and Fire Rescue functions as well as those of the Hazardous Materials and Weapons of Mass Destruction Response unit be placed under the Fire Service. EMS now falls within the Health Department and the Hazmat unit is within the Planning and Natural Resources Department.
Sen. Usie Richards asked Potter the status of two new fire captain positions for St. Croix included in legislation enacted on the Senate override of a veto by the governors earlier this year. Potter said the positions are included in the administration's proposed fiscal year 2005 budget.
Richards also asked about the Fire Service conducting fire inspections. Potter said such inspections, carried out by the Arson Prevention and Investigation Unit, bring in about $200,000 annually now but with increased staffing could generate up to $2 million a year. Potter also said the unit is understaffed. "Manpower issues, computerization of the unit, lack of adequate vehicles and local laws" prevent its full functioning, he said.
Potter's nomination, like that of Rodriguez earlier in day, was approved on a 4-0 vote, with Sen. Lorraine Berry not voting. Berry said she approved of both nominations but declined to vote because she went along with Tharpes' opinion.
The nominations now go the full Senate for a vote.
Committee members present were the chair, Sen. Roosevelt David, and Sens. Berry, Douglas Canton Jr., Dowe and David Jones. The other two members, Sens. Louis Hill and Ronald Russell, were excused. Also present were Sens. Richards and Celestino A. White Sr., who are not members of the committee.
Publisher's note : Like the St. Thomas Source now? Find out how you can love us twice as much — and show your support for the islands' free and independent news voice … click here.
V.I. to Seek 'Clear Rules' for Tax-Incentive Program

redpajama_set_name: RedPajamaCommonCrawl


text:
package com.helger.commons.lang.proxy;

import org.junit.Test;

import com.helger.commons.collection.impl.CommonsArrayList;
import com.helger.commons.collection.impl.ICommonsList;

import edu.umd.cs.findbugs.annotations.SuppressFBWarnings;

/**
 * Test class for class {@link LoggingInvocationHandler}.
 *
 * @author Philip Helger
 */
public final class LoggingInvocationHandlerTest
{
  @Test
  @SuppressFBWarnings ("RV_RETURN_VALUE_IGNORED")
  public void testBasic ()
  {
    final ICommonsList <String> aList = LoggingInvocationHandler.proxying (ICommonsList.class, new CommonsArrayList <> ());
    aList.add ("a");
    aList.add ("b");
    aList.subList (0, 1).isEmpty ();
    // String result is not proxied because it is no interface
    aList.remove (0).length ();
  }

  public interface ITest
  {
    default int foo ()
    {
      return 1;
    }
  }

  public static class TestImpl implements ITest
  {
    public int foo ()
    {
      return 2;
    }
  }

  public static class TestImpl2 implements ITest
  {}

  @Test
  @SuppressFBWarnings ("RV_RETURN_VALUE_IGNORED_NO_SIDE_EFFECT")
  public void testDefaultMethod ()
  {
    LoggingInvocationHandler.proxying (ITest.class, new TestImpl ()).foo ();
    LoggingInvocationHandler.proxying (ITest.class, new TestImpl2 ()).foo ();
  }
}


text:
Shunichi Suzuki may refer to:

, Japanese politician and bureaucrat
, Japanese politician

See also
Shin'ichi Suzuki (disambiguation)

redpajama_set_name: RedPajamaWikipedia


text:
Liturgusidae est une petite famille d'insectes appartenant à l'ordre des Mantodea. On retrouve 65 espèces divisées en 17 genres. Les espèces de cette famille se camouflent à merveille sur l'écorce des arbres. On retrouve les Liturgisidae en Australie, en Indonésie, en Amérique centrale, en Amérique du Sud et dans le sud-est des États-Unis

Description
Chez les Liturgusidae, la tête est de forme triangulaire et les yeux sont nettement exorbités. Les antennes sont filiformes et relativement fines. Les pièces buccales sont de type broyeur et elles se retrouvent à l'avant de la tête.

Chez cette famille, le corps et les ailes antérieures sont de coloration brune à verte et imitent à merveille l'écorce d'un arbre.

Comme tous les représentants des Mantodea, ils possèdent des pattes ravisseuses ou raptoriales. Elles s'en servent pour capturer et maintenir leur proie. Chez ce groupe, l'épine antérieure du fémur est sensiblement semblable aux autres et il y a une fosse entre la première et la seconde épine externe.

Cycle de vie
Comme tous les membres de l'ordre des Mantodea, ils ont un développement hémimétabole qui se déroule en trois étapes principales : l'œuf, la nymphe et l'adulte. La nymphe est relativement similaire à l'adulte. Elle est cependant plus petite, ses ailes ne sont pas développées et ses organes sexuels ne sont pas encore à maturité. Dans certaines cas, elles ont une coloration différente des adultes. Au cours de sa croissance, la nymphe augmente en taille et mue cinq à 10 fois. Elle ressemblera de plus en plus à l'adulte et c'est à la dernière mue, que les ailes finissent par se déployer complètement.

Comportements
Liturgusidae présentent les mêmes comportements généraux que ceux décrient sur la page des Mantodea.

Camouflage
Les Liturgusidae font usage de leur coloration pour se fondre dans leur environnement. Elles imitent à la perfection l'écorce d'un arbre.

Alimentation
La plupart des mantes sont exclusivement des prédatrices généralistes. Elles se nourrissent d'autres insectes et la composition de leur régime alimentaire varie avec l'âge.

Systématique
La famille des Liturgusidae a été décrite par l'entomologiste italien Ermanno Giglio-Tos en 1919.

Taxinomie
Sous-famille : Liturgusinae Giglio-Tos, 1915.

Liste des genres
 Ciulfina Giglio-Tos, 1915
 Dactylopteryx Karsch, 1892
 Gonatista Saussure, 1869
 Gonatistella Giglio-Tos, 1915
 Hagiomantis Audinet-Serville, 1839
 Humbertiella Saussure, 1869
 Liturgusa Stål, 1877
 Liturgusella Giglio-Tos, 1915
 Majanga Wood-Mason, 1891
 Majangella Giglio-Tos, 1915
 Mellierella Giglio-Tos, 1915
 Pseudogousa Tinkham, 1937
 Scolodera Milledge, 1989
 Stenomantis Saussure, 1871
 Theopompa Stål, 1877
 Theopompella Giglio-Tos, 1915
 Zouza Rehn, 1911

Notes et références

Articles connexes
 Mante religieuse
 Liste des genres et des espèces de mantes

Liens externes

Famille de Mantoptères (nom scientifique)


How are Endothermy, Climate Change, and Increased White Shark Sightings Related? Endothermy is a pretty special physical feature of white sharks, but did you know they aren't born with this capability!? Instead, it develops as they get older. I learned that for the first time at a lecture where both Dr. Chris Lowe and Dr. Aaron Carlysle presented their research regarding the movements of white sharks (and other lamnid sharks) along the California coast and how water temperature affects these movements. Why is that significant?
5 Hammerhead Facts in 60 Seconds!
The USS Indianapolis is often referred to as the "worst shark attack" in history. After examining the story it seems more appropriate to call it the "biggest clean up job" sharks ever had to do in the aftermath of humans attempting to kill each other.
In this Shark Minutes episode we look at Hollywood's latest portrayal of the events and compare them to to other accounts of the event.
.Cage diving is a heavily debated topic with pros and cons on both sides. Some arguments are legitimate, some are misinformed, and some are yet to be proven one way or another. But there is one argument that may just trump all others.
Footage by Skyler Thomas and Andy Dellios. Thumbnail photo by Maarten Jozef Billen Additional brief clips taken from news sources under fair use policy. Watch the video below.
Shark Minutes Season 3 Episode 3. Teaching Sharks to Eat People.
Is the cage dive industry teaching sharks to associate humans with food and consequently hunt them? How about shark ecotourism in general? What about any human / shark interaction where bait and scent is used? There's no shortage of heated debates on this topic, but I think I found two new arguments to consider on the matter. Watch the episode below.
Shark Minute shirts are now available. Support the production of these videos with a purchase.
Shark Minutes Season 3 is here. Kicking off this season, Skyler Thomas condenses a lecture by Stanford's Dr. Sal Jorgensen, explaining how the white shark's massive liver plays a crucial role in their trans-oceanic migrations. Buoyancy, energy, and "gliding like birds" are only a few of the intriguing parts of this episode.
If you enjoy Shark Minutes, consider supporting the project with the purchase of a shirt.


Ronald Poulton-Palmer was born in Headington on 12th September 1889. Educated at Oxford University he played rugby union for the Barbarians and Harlequins. He eventually became captain of England and in a match against France in 1914 he scored four tries.
He became chairman of the Huntley and Palmer biscuit business in Reading but on the outbreak of the First World War he immediately volunteered for the Royal Berkshire Regiment. He arrived on the Western Front in March, 1915.
Ronald Poulton-Palmer was killed at Ploegsteert Wood on 5th May, 1915. A fellow officer reported that when he went round the company at dawn "almost every man was crying". Poulton-Palmer was one of 26 England rugby international players killed in the war. A further 30 Scottish internationals also lost their lives during the conflict.


For Saddam, Where's the Carrot?
2.What happens to Iraq if it withdraws?
Sanctions definitely do inflict economic and social pain on Iraq. But what can Saddam expect if he withdraws? This second half of the equation has been ignored.
If Iraq withdrew tomorrow from Kuwait, sanctions would undoubtedly continue as we demanded the release of foreign nationals. If he then released the nationals, would he feel safer? Could he be confident sanctions would stop? Might he not expect that US armed forces would occupy Kuwait and then try to overthrow him? Might he not expect sanctions to continue as he faced more demands: an end of Iraq's nuclear program; destruction of its biological and chemical weapons; return of looted property; compensation to Kuwait; compensation to detainees; forfeiture of frozen assets; etc.
The issue isn't whether demands are unreasonable. Rather, we need to recognize that sanctions produce no incentive to withdraw or to release foreign nationals if Saddam can expect that sanctions might well continue anyway and that he would be worse off - more vulnerable, and facing new demands with no bargaining chips. The frying pan is warming up, but Saddam has no incentive to jump into the fire.
If sanctions are to have a chance of working we need to provide Saddam with a way out. He needs to see both a more attractive prospect than unending sanctions and a way to a better outcome. He needs to know the consequences of the action we want him to take. He should be confident that if he withdraws from Kuwait and releases all foreign nationals then sanctions will stop and Iraq will not be attacked.
The Security Council's formal demand for ``unconditional'' withdrawal should not bar us from working out conditions that turn sanctions into real pressure. It may not be easy. Saddam's alternative ought to be such that although he finds it more attractive than sanctions, he is not rewarded for his aggression, nor paid any blackmail. A good standard would be that Saddam receives no more than he could achieve through peaceful negotiations or to which he is otherwise entitled under international law.
Beyond the release of foreign nationals, withdrawal from Kuwait, and the ending of sanctions, there are plenty of bargaining points. These might include: a transitional Arab peacekeeping force in Kuwait to follow Iraqi withdrawal; an invited Soviet presence in Iraq under UN auspices to guarantee Iraq against attack; President Bush's reassurance that the US will leave the Gulf when the area is stable; arms control negotiations among Iraq, the US, and Saudi Arabia to reduce Iraqi military potential in exchange for US withdrawals; appointing a distinguished Arab mediator to work on the Iraq-Kuwait disputes over the Ramaila oil field and Iraq's Gulf access; establishing a procedure for dealing with all financial issues over frozen assets, debts, and claims for compensation; an invitation from Kuwait for Arab assistance in moving toward internal democratization consistent with Islamic values. Such an agreement is best developed by a third party through private discussion in which no one is committed until the end.
Negotiation doesn't mean giving in. The US should continue to work on alternatives - what to do if sanctions and an open door don't work. Fighting a bloody war would cost billions, may end the UN consensus, destroy the oil facilities of Saudi Arabia, Kuwait, and Iraq, wreck economies, and so on. It might be better simply to deprive Iraq of a benefit from invading Kuwait by maintaining indefinitely the blockade on Iraqi oil. We could also let oil flow through the blockade if the purchase price were deposited in escrow in Switzerland. Such alternatives can be explored along with ``building a golden bridge'' for Saddam's retreat.
The US needs to be both persistent in pursuit of our interests and flexible as to how they are met. Future security arrangements, financial claims, and territorial disputes cannot be settled without discussion. It is far better to have discussions before rather than after a bloody war. With the benefit of such talks, the UN can offer Saddam a package of terms which should be more attractive to him than ongoing sanctions. Only when there are better terms will sanctions constitute pressure.
Iran nuclear talks: Are sanctions on the table?


During one of the videos, Kanye claims people are trying to dictate what he says and does. He also says he just took an I.Q. test and his scores were genius level.
"I just want to talk about mind control," he says. "You know, when people try to influence you through social media and try to tell you what to do or if you post something that's positive on Instagram and it gets taken down, if it's not a part of a bigger agenda, that's like mind control. That's the echo chamber. That's them trying to control you … that's the poison happening with social media.
'Ye also explains that he's attempting to buy back his publishing from Sony ATV for $8 or $9 million but the powers that be refuse to sell it to him. He insinuates he's a slave to the music industry — much like Prince who famously changed his name to a symbol and wrote "slave" across his face.
Finally, he explains how he's like Afro-beat pioneer Fela Kuti, late reggae legend Bob Marley and Hip Hop luminary Tupac Shakur.
"The spirit of Fela [Kuti], the spirit of [Bob] Marley, the spirit of 'Pac flow through me. We free. Our minds are free.
Kanye is currently in East Africa to finish his forthcoming album Yandhi. Now that he's back on social media, we'll likely be hearing a lot more from him before its completion.
To watch a replay of 'Ye's video, head to Periscope.


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2021 Hyundai Tucson 'NX4' envisioned, could be very accurate (video)
Brett Davis May 19, 2020
Car News, Hyundai, Renderings, SUV, Videos
We saw some detailed digital depictions of what Hyundai's upcoming Santa Cruz pickup could look like over the weekend. And now we've found an educated guess on the design of the all-new 2021 Hyundai Tucson, codenamed NX4.
According to a purported Hyundai production schedule for 2020 the South Korean company is intending to start producing the all-new Tucson in August. However, this doesn't factor in possible delays brought on by the COVID-19 pandemic, so it might not commence until a few months later.
Using various prototypes and the Vision T concept car as inspiration, a digital designer has posted up a prediction of the new model's design on YouTube channel KKS STUDIO.
At the front the designer has adopted Hyundai's latest grille and headlight layout which was first seen on the Nexo, and more recently on the fresh Elantra/i30 sedan. The new layout consists of much smaller and slimmer headlights with a grid-like pattern for the main grille. In this case the designer has also included a four-box cluster of LED lights in the corners.
Along to the sides, the Vision T concept hinted that a new set of panel creases and shapes were on the way for the popular mid-size SUV. These include four contour lines for the bonnet, hexagonal-style wheel arches bulges with prominent crease lines, and a curvier roofline to suit the coupe profile that seems to be the trend these days.
While the front end looks like it could be quite accurate to us, judging by the prototypes we've seen and that Vision T concept, the rear might be a bit off in our opinion. The designer has implemented a full-width taillight that uses unique twin shards on each end for the main beams. Most prototypes and test mules out there have featured lots of camouflage and black sheeting, particularly at the back, concealing the true design.
No further specs or concrete details have been uncovered as yet. Hyundai has confirmed the new model will be offered with hybrid power, at least in some markets, and there's talk of the company's latest 2.5-litre Smartstream turbo being introduced for the first time on the SUV. The Hyundai Motor Group engine, which currently produces up to 224kW in the latest Genesis G80, would be the most powerful unit offered for the Tucson – surpassing the current 1.6 turbo option that develops 130kW. Again though, no official details have been confirmed yet.
Check out the video below to see how the designer came up with the renderings. It is in Korean but there are English subtitles available.
Hyundai Santa Cruz pickup rendered, based on new Tucson NX4 September 18, 2020
Hyundai production plans leaked; Kona N, new Tucson, Santa Fe hybrid April 7, 2020
Hyundai Santa Cruz prototype ute spotted with production body? August 28, 2020
2021 Hyundai 'Santa Cruz' pickup rendered, most accurate yet? May 16, 2020


Pago Pago, AMERICAN SAMOA — Of the $1.6 million in unpaid payroll for Argosy University campuses, more than $7,000 is for the institution's American Samoa branch, while an accreditation commission is preparing to fully withdraw Argosy's accreditation, according to latest filings at the federal court in Cleveland, Ohio, which is overseeing a complaint against the school's owner, Dream Center Education Holdings.
DCEH has provided an online link for local students who are now left in limbo, after Argosy closed Mar. 8. Three local students have told Samoa News that they have no one to turn to for help, since the school's closure.
Responding to Samoa News inquiries, DCEH provided a link for students to the Argosy University Closed School Information page, where they can find contacts for assistance.
Local students have also voiced with Samoa News concerns over the possible loss of Argosy's accreditation, which was placed in January this year on a Show Cause order by the WASC Senior College and University Commission (WSCUC).
The concern is that a full withdrawal of accreditation puts in jeopardy their credit transfers to other accredited institutions.
A Mar. 20th letter from WSCUC president Jamienne S. Studley shows a deadline to withdraw the accreditation. The letter is addressed to US District Court Judge Dan Aaron Polster at the federal court in Cleveland, Ohio.
Studley reminded the court that it was on Jan. 19th that WSCUC placed Argosy on Show Cause to explain why its accreditation should not be withdrawn. On Feb. 26, WSCUC requested plans for student transition in the event of closure and information to determine whether Argosy's accreditation could continue.
Following the full closure of the schools on Mar. 14th, "without plans by the [court-appointed] Receiver for transfer of programs or students to other institutions, WSCUC acted to withdraw accreditation from Argosy," Studley wrote.
"In the interest of promoting students' interest in completing their programs, WSCUC provided that Argosy's accreditation will continue to May 12, 2019 for the exclusive purposes of (1) issuing degrees to students in their final term, provided those students have been certified — by faculty employed by Argosy as of March 8, 2019 — as having completed their degree requirements; and (2) providing students with access to academic transcripts and services to facilitate transfer and articulation of programs and credits to other institutions," Studley explained.
He offered suggestions from the WSCUC. One of them is for the court to direct the Receiver to keep the information line for students — 855.758.5660 — open as long as students are continuing to call for information about transfer, transcripts, financial status, loan discharges, and other necessary information.
"It would be very helpful to have counts from Argosy of the number of students and their fields who are awaiting academic placements, and those who have transferred, are seeking closed school discharges, will graduate this term, and so on," Studley points out.
"As we have advised the Receiver many times, we would welcome the opportunity to assist you in any way to help students maintain their academic pursuits and reduce further uncertainty, distress, and loss," he wrote to Judge Polster, who yesterday directed the Receiver, Mark E. Dottore, to respond to WSCUC by Apr. 2nd and inform the court.
Meanwhile, WSCUC encourages Argosy students to check its website (www.wscuc.org) for updates on Argosy, and helpful information, such as links to the US Department of Education for financial aid students, and an updated list of colleges and universities, which are WSCUC-accredited and will welcome inquiries from Argosy students.
Dottore submitted Monday this week, the payroll status for Argosy, saying that due to the "sudden loss" of US Department of Education Title IV funding for Argosy, the Receiver was unable to make payroll for Argosy for the two-week period ending Mar. 1, 2019 and scheduled to be paid Mar. 8, 2019.
Total unpaid payroll for Argosy is just over $1.5 million, according to the Receiver, who submitted a separate report breaking down unpaid payroll for each campus. The American Samoa branch has unpaid payroll totaling $7,353.62 — which includes $2,501.01 for "Admin" and $4,084.62 for "Faculty".
The Receiver has identified various sources of funding for the payrolls and among them are Argosy bank accounts, which have since moved to the Receivership accounts. Total amount is over $1.18 million, and the Receiver is trying to determine if he can apply the funds to the unpaid payroll balances.
Receiver is also holding $1.5 million upon the court's order, until it is determined whether it will be held in trust or be paid to students.
The Receiver proposed the priority of paying unpaid payroll, but the move requires court approval.


With all of the different accounts, emails, social media, etc out there checking your privacy settings can be a daunting task. Now you can use AdjustYourPrivacy.com. This site is very cool. It provides direct links to the privacy pages for most of the social media sites. It is an easy way to check all of these at the same time. It also allows you to look at your account from a the 'public' view and your view. Finally it has a database of information to help you in making your decisions. I highly recommend you try AdjustYourPrivacy.com.
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