text:
\section{Introduction}

Quantum transport under a time-dependent field in coherent
mesoscopic systems is the subject of many recent
studies\cite{pas,but1,vegvar,pieper,bruder,chen,wang1}.
Another problem of interest is the nonlinear conductance
of such a system, whether under a time-dependent field or
not\cite{but4}.
A difficult theoretical issue is the prediction, for a general
mesoscopic conductor, the transport coefficients as a function of
the AC field frequency and the bias voltage. Once these parameters
are known, one can predict useful information such as the nonlinear
current-voltage characteristics in the DC case, the emittance in
the linear frequency, linear voltage AC case, and further nonlinear
dynamic conductance. Indeed, it is now possible to experimentally
measure the nonlinear AC transport properties such as the second
harmonic generation, as have been demonstrated by several
laboratories\cite{webb,vegvar1,liu}.

When a conductor is subjected to time-varying external fields such as
an AC bias voltage, the total electric current flowing through the
conductor consists of the usual particle current plus the displacement
current. The presence of the latter is crucial such that the total
electric current is conserved. Hence for a theory to deal with AC
transport, in principle one should include the displacement current
into the consideration. Because a displacement current originates
from induction, and the necessary condition for electric induction is
the electron-electron (e-e) interaction, one thus concludes that an
important ingredient for AC transport theory should be the
consideration of e-e interactions. These issues have been emphasized
by B\"uttiker and co-workers\cite{review}.
On the other hand, for DC transport under {\it nonlinear} conditions,
a necessary requirement is the gauge invariance\cite{but4}: the
physics should not change when electrostatic potential
everywhere is changed by the same constant amount. Gauge invariance
puts severe conditions on the form of the nonlinear transport
coefficients. From these physical arguments, it is clear that AC as
well DC nonlinear transport contains ingredients which were not
needed when dealing with the familiar DC linear
transport\cite{review}.

The problems of current conservation and gauge invariance have been
recognized in the literature. For conductors which maintain quantum
coherence, B\"uttiker and his co-workers have developed an
approach\cite{but1} based on the single electron scattering matrix theory
to deal with the linear AC dynamic conductance as well as the
second order nonlinear conductance coefficients. The original scattering
matrix theory were invented to investigate DC linear transport
coefficients, as is represented by the Landauer-B\"uttiker
formulation\cite{landauer}. Such a theory calculates particle current
from the scattering matrix, thus a direct application to AC situation
would violate current conservation\cite{but1,review}.
To solve this problem, the scattering matrix theory for AC
transport consists of two steps\cite{but1,review}. First, it
calculates the particle current and finds
that this current is not conserved. Second, it considers the e-e
interaction which alters the scattering potential landscape, and this
effect generates an internal response which cancels exactly the
non-conserved part of the particle current thereby restores the current
conservation. For the DC second order nonlinear conductance
coefficient, similar considerations led to the desired gauge
invariance.

In a recent work, the authors have developed a microscopic and general
theoretical formalism for electric response which is appropriate for
both DC and AC weakly nonlinear quantum transport\cite{ma1}.  That
formalism was based on the response theory and it formalized the
connection of the response theory to the scattering matrix theory at
weakly nonlinear level. One of the useful conceptual advances
of the general formalism\cite{ma1} was the introduction of a
frequency dependent characteristic potential at the nonlinear level.
The characteristic potential describes the changes of scattering
potential landscape of a mesoscopic conductor when the electrochemical
potential of an electron reservoir is perturbed
externally\cite{but1}. It is the
nonlinear order characteristic potential which allowed us to analyze
weakly nonlinear AC response\cite{ma1}, as well as the nonlinear DC
conductance, order by order in the bias voltage. In contrast, so far
the scattering matrix theory can be applied up to the second order
nonlinearity and linear order AC.

Using the concept of nonlinear characteristic potential developed in
the response theory\cite{ma1}, we have found that the scattering
matrix theory can actually be further developed to apply to
higher order nonlinear DC situations.  In addition, recognizing that
an AC transport problem requires the self-consistent solution of the
Schr\"odinger equation coupled with Maxwell equations, we have found
a way to derive both the external and internal responses in
{\it equal-footing}
within the scattering matrix approach.  It is the purpose of this
article to report these results. In particular, we shall start from the
scattering matrix theory and formulate an approach which is appropriate for
analyzing linear order dynamic conductance and the weakly nonlinear DC
conductance beyond the second order. We emphasis the properties of electric
current conservation and gauge invariance, and these properties are maintained
by considering electron-electron interactions. The approach developed
here is particularly useful for nonlinear DC conductance calculation, and we
shall analyze the third order weakly nonlinear transport coefficient for
a double-barrier tunneling diode. Since the approach presented here
can be cast into a form which allows numerical computation, many further
applications of it to complicated device structures can be envisioned.

The rest of the article is organized as follows.  In the next section
we present the development of the formalism.  Section III presents two
applications of this formalism: the linear AC dynamic conductance and
the third order nonlinear conductance.  Finally a short conclusion is
included in section IV.

\section{Theoretical Formalism}

In this section we briefly go through the formal development of
our scattering matrix theory and concentrate more on the conceptually
important physical quantities which will be needed.

We start by writing the Hamiltonian of the system in the presence of an
external time-dependent field as
\begin{equation}
H = \sum_{\alpha m} (\bar{E}_{\alpha m} + eV_{\alpha} \cos{\omega t})
a^{\dagger}_{\alpha m}(\bar{E}_{\alpha m},t) a_{\alpha m}(\bar{E}_{\alpha m},t)
\label{eq1}
\end{equation}
where $a^{\dagger}_{\alpha m}$ is creation operator for a carrier
in the incoming channel $m$ in probe $\alpha$, $eV_{\alpha} \cos{\omega t}$
is the shift of the electrochemical potential $\mu_{\alpha}$ away from
the equilibrium state associated with $\mu^{eq}$, {\it i.e.}, $eV_{\alpha}
\cos{\omega t} = \mu_{\alpha} - \mu^{eq}$. The energy $\bar{E}_{\alpha m}$
is a functional of the internal electrical potential landscape
$U({\bf r},\{V_{\alpha}\})$ which depends on $V_{\alpha}$ in the low
frequency regime. Potential $U$ includes the internal response to
the external perturbation and it generates such effect as the displacement
current. In general $U$ is also an explicit function of time (or of the
AC frequency $\omega$) as discussed in Ref. \onlinecite{ma1}, but in this
work we shall only be concerned with the dynamic conductance to first
power of $\omega$ and for this case $U$ is static. Note we have
explicitly included $U$ into the Hamiltonian which helps in dealing with
both external and internal responses in equal-footing.
The self-consistent nature of this Hamiltonian is clear: $U$ must be
determined, in general, from the Maxwell equations where the charge
density is obtained from solving the quantum mechanical problem of the
Hamiltonian.

Next let's consider the series expansion of the energy in terms of the
potential landscape $U$,
\[\bar{E}_{\alpha m}+eV_{\alpha}cos(\omega t) =
E_{\alpha m} + e\hat{O}_{\alpha}^{(1)}
cos(\omega t)\]
\begin{equation}
+ e^2\hat{O}_{\alpha}^{(2)}(cos (\omega t))^2 +
\cdot\cdot\cdot
\label{eq2}
\end{equation}
where the operators $\hat{O}_{\alpha}^{(i)}$ is a spatial integration of
the $i$-th order {\it characteristic potential} (see below) folded with
the $i$-th order functional derivative of $E_{\alpha m}$ with respect to
the potential landscape $U({\bf r})$. For instance the linear order operator,
which is linear in voltage $V_{\beta}$, is given by
\begin{equation}
\hat{O}_{\alpha}^{(1)} \equiv \sum_{\beta} (\delta_{\alpha \beta}
+\partial_{V_{\beta}} E_{\alpha m}) V_{\beta}
\label{eq5}
\end{equation}
where
\[\partial_{V_{\beta}}E\ \equiv \ \int d^3 {\bf r}\ u_{\beta}({\bf r})
\ \frac{\delta E}{\delta eU({\bf r})} \]
with $u_{\beta}({\bf r})\equiv \frac{\partial U({\bf r})}{\partial V_{\beta}}$
the linear order characteristic potential\cite{but1}. The expressions
for higher order operators $\hat{O}_{\alpha}^{(i)}$ are more
difficult to write down in a general form, but they are proportional
to the $i$-th power of the bias. In addition they can be easily
determined after we formally obtain the transmission function and
then applying the current conservation and gauge invariance to the
results. Using Eq.(\ref{eq2}), the Hamiltonian now reads
\begin{eqnarray}
H &=& \sum_{\alpha m} \left[E_{\alpha m} + \sum_i\hat{O}_{\alpha}^{(i)}
(cos{\omega t})^i\right] \nonumber \\
& &\times
a^{\dagger}_{\alpha m}(\bar{E}_{\alpha m},t)
a_{\alpha m}(\bar{E}_{\alpha m},t)\ \ \ .
\label{eq4}
\end{eqnarray}
The operators $a_{\alpha m}(\bar{E}_{\alpha m},t)$ satisfies the equation
of motion
\begin{equation}
\dot{a}_{\alpha m}(\bar{E}_{\alpha m},t) = \frac{1}{i\hbar} [a_{\alpha m}
(\bar{E}_{\alpha m},t), H]\ \ ,
\label{eq6}
\end{equation}
which can be integrated because the time dependence of $H$ is simple.
For instance to linear order in voltage, we only need to use
$\hat{O}^{(1)}$ in the Hamiltonian and the result is
\begin{eqnarray}
a_{\alpha,m}(\bar{E}_{\alpha m},t)&=&
a_{\alpha m}(\bar{E}_{\alpha m}) \nonumber \\
&\times & \exp\left(-\frac{i}{\hbar} \left[E_{\alpha m} t +
\frac{e\hat{O}_{\alpha}^{(1)}}{\omega} \sin{\omega t}\right]\right)
\nonumber
\end{eqnarray}
Its Fourier transform is given by
\begin{eqnarray}
\tilde{{\bf a}}_{\alpha}(E) & & =
\int dt {\bf a}_{\alpha}(\bar{E}_{\alpha},t) e^{i Et/\hbar}
= {\bf a}_{\alpha}(E) \nonumber\\
& & -\frac{e}{2\hbar \omega} \hat{O}_{\alpha}^{(1)}
[{\bf a}_{\alpha}(E+\hbar \omega) -
{\bf a}_{\alpha}(E-\hbar \omega)]\nonumber\\
& & +\frac{e^2}{8\hbar^2 \omega^2}
\left(\hat{O}_{\alpha}^{(1)}\right)^2 \left[{\bf a}_{\alpha}
(E+2\hbar \omega) -2 {\bf a}_{\alpha}(E)\right.\nonumber\\
& &\left. + {\bf a}_{\alpha}(E-2\hbar \omega)\right]
+ \cdot\cdot\cdot\nonumber\\
& & = \sum_n \frac{1}{n!} (
\frac{-e\hat{O}_{\alpha}^{(1)}}{2\hbar \omega})^n
(e^{\hbar \omega \partial_E} - e^{-\hbar \omega \partial_E})^n
{\bf a}_{\alpha}(E)
\label{eq8}
\end{eqnarray}
where we have suppressed the index $m$ and ${\bf a}_{\alpha}$
is in a vector form of the operators $a_{\alpha m}$.
In Eq.(\ref{eq8}) the physics is transparent:
${\bf a}_{\alpha}(E \pm \hbar \omega)$ is just the one-photon sideband and
${\bf a}_{\alpha}(E \pm 2\hbar \omega)$ corresponds to the second
harmonic generation. More tedious expressions can be obtained
if higher order operators $\hat{O}^{(i)}$ are included in the
Hamiltonian.

To calculate the total electrical current, we shall apply the formula
derived in Ref. \onlinecite{but2}, which is exact up to linear order of
$\omega$ and for larger frequency it is an approximation to a
space-dependent expression of the current operator,
\begin{eqnarray}
I_{\alpha}(t)&=& \frac{e}{h} \int dE dE' \left[ \tilde{{\bf
a}}_{\alpha}^{\dagger}(E) \tilde{{\bf a}}_{\alpha}(E')
\right.\nonumber\\
& -&\left. \tilde{{\bf b}}_{\alpha}^{\dagger}(E)
\tilde{{\bf b}}_{\alpha}(E') \right]\times \exp(i(E-E')t/\hbar)
\label{eq9}
\end{eqnarray}
where $\tilde{{\bf b}}_{\alpha}(E)$ is the operator which annihilates a
carrier in the outgoing channel in probe $\alpha$. The annihilation
operator in the outgoing channel, $\tilde{{\bf b}}_{\alpha}$, is related
to the annihilation operator in the
incoming channel $\tilde{{\bf a}}_{\alpha}$ via the scattering matrix
${\bf s}_{\alpha\beta}$: $\tilde{{\bf b}}_{\alpha}
= \sum_{\beta} {\bf s}_{\alpha \beta} \tilde{{\bf a}}_{\beta}$
where ${\bf s}_{\alpha\beta}$ is a function of energy $E$ and a functional
of the electric potential $U({\bf r},\{V_{\alpha}\})$.
Finally we comment that in evaluating Eq. (\ref{eq9}) we need to take
a quantum statistical average of
$<{\bf a}_{\alpha}^{\dagger}(E) {\bf a}_{\beta}(E')> = \delta_{\alpha
\beta} \delta(E-E') f_{\alpha}(E)$
where $f_{\alpha}(E)$ is the Fermi function of reservoir $\alpha$.
Because of the limitations of Eq. (\ref{eq9}), our theory will
be exact for transport coefficients linear in $\omega$ for AC situations.
However this is not a severe limitation for practical
calculations\cite{but2}.

One of the most important quantities of this theory is the determination
of characteristic potential which arrives naturally. As discussed
above, this quantity determines the operators $\hat{O}^{(i)}$.
Since the scattering matrix theory used here is exact to linear power of
$\omega$ which is the order we shall work on, we only need to consider
$\omega$-independent characteristic potentials.  On the other hand,
as we are interested in the weakly nonlinear coefficients, it is
crucial to consider higher order characteristic potentials\cite{ma1}:
$u_{\delta\gamma}({\bf r})\equiv \partial^2 U({\bf r})/\partial
V_{\delta}\partial V_{\gamma}$, $u_{\beta\delta\gamma}({\bf r})$, etc..
For any physical quantity beyond the terms linear in $\omega$ or second
order in voltage, including the second harmonic generation term (the term
of $\omega V^2$), these higher order characteristic potentials are
necessary.

We now discuss the solution of higher order characteristic potentials
by explicitly carrying out the calculation of $u_{\delta\gamma}$. In the
weakly nonlinear regime, the variation of the electric potential can be
expanded in terms of the variation of the electrochemical potential $d\mu$
\begin{equation}
edU({\bf r}) = \sum_{\beta} u_{\beta}({\bf r}) d\mu_{\beta}
+ \frac{1}{2} \sum_{\beta \gamma} u_{\beta \gamma}({\bf r})
d\mu_{\beta} d\mu_{\gamma} + ...
\label{dU}
\end{equation}
where $u_{\beta}$ is the characteristic potential, $u_{\beta \gamma}$
(which is symmetric in $\beta$ and $\gamma$) is the second order
characteristic potential tensor, and $(\cdot\cdot\cdot)$ are higher
order terms written in a similar fashion. Because we are only
interested in AC transport to the first power of frequency
$\omega$, the electrodynamics is solved by the Poisson equation,
\begin{equation}
-\nabla^2 dU({\bf r}) = 4\pi e^2dn({\bf r})
= 4\pi e^2\sum_{\alpha} dn_{\alpha}({\bf r})
\label{poisson}
\end{equation}
where $dn_{\alpha}$ is the variation of the charge density at contact
$\alpha$ due to a change in electrochemical potential at that contact.
There are two contributions to the charge density at contact $\alpha$:
the injected charge density due to the variation of the chemical
potential at contact $\alpha$, and the induced charge density
$dn_{ind,\alpha}$ due to the electro-static potential, hence
\begin{equation}
dn_{\alpha} = \frac{dn_{\alpha}}{dE} d\mu_{\alpha} + \frac{1}{2}
\frac{d^2n_{\alpha}}{dE^2} d\mu_{\alpha}^2 +\cdot\cdot\cdot\ +\
dn_{ind,\alpha}
\label{induce}
\end{equation}
where $dn_{\alpha}/dE$ is the injectivity which is the local density of
state at contact $\alpha$ and $d^2n_{\alpha}/dE^2$ is the energy
derivative of the injectivity. The induced charge density involves Lindhard
function. Using Thomas-Fermi approximation Eq.(\ref{induce}) takes a
compact and simple form
\begin{equation}
dn_{\alpha} = \frac{dn_{\alpha}}{dE} (d\mu_{\alpha} - edU) + \frac{1}{2}
\frac{d^2n_{\alpha}}{dE^2} (d\mu_{\alpha}-edU)^2\ +\ \cdot\cdot\cdot
\label{dn}
\end{equation}
From Eqs.(\ref{dU}), (\ref{poisson}), and ({\ref{dn}), we obtain the
equation satisfied by the second order characteristic potential tensor
\begin{eqnarray}
-\nabla^2 u_{\beta \gamma} + 4\pi e^2 \frac{dn}{dE} u_{\beta \gamma}
&=& 4\pi e^2 \left(\frac{d^2n_{\beta}}{dE^2} \delta_{\beta \gamma} -
\frac{d^2n_{\gamma}}{dE^2} u_{\beta}\right. \nonumber \\
&-& \left.\frac{d^2n_{\beta}}{dE^2} u_{\gamma} + \frac{d^2n}{dE^2} u_{\beta}
u_{\gamma}\right)\ .
\label{u11}
\end{eqnarray}
Since all the quantities involved in this equation are known from the
linear order calculation, $u_{\beta\gamma}$ can thus be determined.
Similarly,
order by order we can determine higher order characteristic potentials
from results obtained at lower orders, for instance the equation
satisfied by $u_{\beta\gamma\delta}$ is found to be:
\begin{eqnarray}
& & -\nabla^2 u_{\beta \gamma \delta} + 4\pi e^2
\frac{dn}{dE} u_{\beta \gamma \delta} = 4\pi e^2
\left(\frac{d^3n_{\beta}}{dE^3} \delta_{\beta \gamma}
\delta_{\beta \delta} \right.\nonumber\\
& & - \frac{d^3n}{dE^3} u_{\beta} u_{\gamma} u_{\delta}
+ \left\{ \frac{d^3n_{\beta}}{dE^3} u_{\gamma} u_{\delta}
- \frac{d^3n_{\beta}}{dE^3} \delta_{\beta \gamma} u_{\delta}
\right.\nonumber\\
& &\left.\left. + \frac{d^3n}{dE^3} u_{\beta \gamma} u_{\delta}
- \frac{d^3n_{\beta}}{dE^3} u_{\gamma \delta} \right\}_c \right)
\label{u111}
\end{eqnarray}
where the curl bracket $\{ ... \}_c$ stands for the cyclic permutation of
indices $\beta$, $\gamma$, and $\delta$.
Note that if better models are needed to deal with the
screening effect, the term with $dn/dE$ on the left hand side of
(\ref{u11}), (\ref{u111}) and higher order equations
is replaced by an integration over the appropriate
Lindhard function folded with the characteristic potential\cite{ma1}.

From Eq.(\ref{dU}) we can derive several important sum rules on the
characteristic potential tensor. If all the changes in the
electrochemical potentials are the same, {\it i.e.},
$d\mu_{\beta} = d\mu_{\gamma} = d\mu$, this corresponds to an overall
shift of the electro-static potential $edU = d\mu$. From this we have
$\sum_{\beta} u_{\beta} = 1$, $\sum_{\beta \gamma} u_{\beta \gamma} = 0$.
Due to gauge invariance, Eq.(\ref{dU}) remains the same if $dU$,
$d\mu_{\beta}$, and $d\mu_{\gamma}$ are all shifted by the same amount.
This leads to
$\sum_{\beta} u_{\beta \gamma} = \sum_{\gamma} u_{\beta \gamma} = 0$.
Using Eq.(\ref{u11}) we can confirm that these relations
are indeed satisfied. Similar sum rules can be derived for higher order
characteristic potentials.

Let's summarize the scattering matrix theoretical procedure. With the
characteristic potential tensor calculated, we explicitly derive
the Hamiltonian in a series form Eq. (\ref{eq4}). The Hamiltonian
determines the creation and annihilation operators via equation of
motion Eq. (\ref{eq6}) and the scattering matrix
${\bf s}_{\alpha\beta}$. Finally, using Eq. (\ref{eq9}) we compute the
electric current as a function of voltage.

\section{Applications}

In the following we apply the scattering matrix formalism developed in
the last section to two examples: the linear order emittance and the third
order DC nonlinear conductance. The first example has been examined by
B\"uttiker and co-workers\cite{but1}, our result is in exact agreement
with theirs. The second example has not been studied and we shall
provide further numerical results for a resonant tunneling diode.

\subsection{Linear Dynamic Conductance}

The linear dynamic conductance (called emittance) is the transmission
function of the terms proportional to $V_\beta$ and $\omega V_{\beta}$
in the electric current. From Eq. (\ref{eq9}) we expand every thing in
these variables and obtain

\begin{eqnarray}
I_{\alpha}(\omega') &=& \sum_{\beta} \hat{O}_{\beta}^{(1)} \int dE
(-\partial_E f) \{ \frac{e^2}{h} A_{\beta \beta}(\alpha,E,E) \nonumber \\
& -& \frac{e^2}{2h} \hbar \omega' [{\bf s}_{\alpha \beta}^{\dagger}
\partial_E {\bf s}_{\alpha \beta} - (\partial_E {\bf s}_{\alpha \beta})
{\bf s}_{\alpha \beta}] \}
\label{eq16}
\end{eqnarray}
where we have used notation $A_{\alpha \beta} \equiv A_{\beta
\beta}(\alpha,E,E)$ and ${\bf s}_{\alpha \beta} \equiv {\bf s}_{\alpha
\beta}(E,U)$. The transmission function $A$ is defined in the usual
form as
\begin{eqnarray}
A_{\beta \beta'}(\alpha, E, E',U)& =&
{\bf 1}_{\alpha} \delta_{\alpha \beta} \delta_{\alpha \beta'}
\nonumber\\
& -& {\bf s}_{\alpha \beta}^{\dagger}(E,U)
{\bf s}_{\alpha \beta'}(E',U)
\label{eq12}\ \ .
\end{eqnarray}
In deriving Eq. (\ref{eq16}), we have used the fact that
$\sum_{\beta} A_{\beta \beta} (\alpha, E,E,U)=0$. All quantities
such as $A_{\alpha \beta}$, ${\bf s}_{\alpha \beta}$, and
$u_{\beta}=(\partial U({\bf r})/\partial V_{\beta})_{eq}$
are taken at equilibrium, {\it i.e.}, at $V_{\alpha}=0$.
Using Eq.(\ref{eq5}), we separate the operator according to
$\hat{O}_{\beta}^{(1)}
\partial_E = V_{\beta} \partial_E + \sum_{\gamma} V_{\gamma}
\partial_{V_{\gamma}}$, thus (\ref{eq16}) can further be simplified to,
\begin{eqnarray}
I_{\alpha}(\omega') &=& \int dE (-\partial_E f) \{ \sum_{\beta} V_{\beta}
\frac{e}{h} A_{\alpha \beta} \nonumber \\
& -& \frac{e^2}{2h} \hbar \omega' \sum_{\beta} V_{\beta}
[{\bf s}_{\alpha \beta}^{\dagger} \partial_E {\bf
s}_{\alpha \beta} - (\partial_E {\bf s}_{\alpha \beta}) {\bf
s}_{\alpha \beta}] \nonumber \\
& -& \frac{e^2}{2h} \hbar \omega' \sum_{\gamma} V_{\gamma}
\sum_{\beta} [{\bf s}_{\alpha \beta}^{\dagger}
\partial_{V_{\gamma}} {\bf s}_{\alpha \beta} - (\partial_{V_{\gamma}}
{\bf s}_{\alpha \beta}) {\bf s}_{\alpha \beta}] \}
\label{eq17}
\end{eqnarray}
From this result, we immediately realize that the first term on the right
hand side is just the DC contribution to the electric current. From the
second and third terms which are linear in $\omega'$ and $V_{\beta}$,
we obtain the linear order emittance
\begin{eqnarray}
E_{\alpha \beta} &=& \int dE (-\partial_E f) \frac{e^2}{4\pi i} \{
[{\bf s}_{\alpha \beta}^{\dagger} \partial_E {\bf s}_{\alpha \beta}
- (\partial_E {\bf s}_{\alpha \beta}) {\bf s}_{\alpha \beta}]
\nonumber \\
&+& \sum_{\gamma}[{\bf s}_{\alpha \gamma}^{\dagger} \partial_{V_{\beta}}
{\bf s}_{\alpha \gamma} - (\partial_{V_{\beta}}
{\bf s}_{\alpha \gamma}) {\bf s}_{\alpha \gamma}] \}\ \ .
\label{eq18}
\end{eqnarray}
This result exactly agrees with the that obtained previously\cite{but1}.
The first term of $E_{\alpha\beta}$ describes the external contribution
to the AC current, while the second term is from internal response.
They are obtained simultaneously from the scattering matrix theory
developed here. Finally, from the gauge invariance condition\cite{but1}
$e\partial_E A_{\alpha \beta} + \sum_{\gamma} \partial_{V_{\gamma}}
A_{\alpha \beta} = 0$, it is easy to show
$\sum_{\beta} E_{\alpha \beta} = 0$, which is a direct consequence of
$\hat{O}_{\beta}^{(1)}$ in Eq. (\ref{eq16}). It is
also easy to show that the electric current is conserved, {\it i.e.},
$\sum_{\alpha} E_{\alpha \beta} = 0$.

\subsection{Third Order DC Nonlinear Conductance}

The scattering matrix theory developed here can be applied to compute
DC weakly nonlinear conductance to any order in bias. As an example we
now calculate the third order DC nonlinear conductance
$G_{\alpha \beta \gamma \delta}$, which is defined by expanding the
electric current in powers of voltage to the third power,
\begin{eqnarray}
I_{\alpha}& =& \sum_{\beta} G_{\alpha \beta}V_{\beta} +
\sum_{\beta \gamma} G_{\alpha \beta \gamma}V_{\beta}V_{\gamma}
\nonumber\\
&+& \sum_{\beta \gamma \delta} G_{\alpha \beta \gamma \delta}
V_{\beta}V_{\gamma}V_{\delta} +\ \cdot\cdot\cdot\ \  .
\end{eqnarray}
Following the same procedure as above in deriving the linear
emittance $E_{\alpha \beta}$, by expanding the electric current Eq.
(\ref{eq9}) and other quantities to third order in bias,
it is tedious but straightforward to derive
\begin{eqnarray}
G_{\alpha \beta \gamma \delta} &=& \frac{e^3}{3h}
\int dE (-\partial_E f) \left[\left\{\partial_{V_{\gamma}}
\partial_{V_{\delta}} A_{\alpha \beta}\right.\right.\nonumber\\
&+&\left.\left. e\partial_{V_{\gamma}} \partial_E A_{\alpha \beta}
\delta_{\beta \delta}
\right\}_c + e^2\partial_E^2 A_{\alpha \beta}
\delta_{\beta \gamma} \delta_{\gamma \delta}\right]\ .
\label{g4}
\end{eqnarray}
Note that the second order characteristic potential
tensor has been implicitly included in Eq.(\ref{g4}), because
\begin{eqnarray}
\partial_{V_{\gamma}} \partial_{V_{\delta}} A_{\alpha \beta} &=&
\partial_{V_{\gamma}} \int \frac{\delta A_{\alpha \beta}}{\delta
U({\bf r}_1)} \frac{\partial U({\bf r}_1)}{\partial V_{\delta}}
d{\bf r}_1 \nonumber \\
&=& \int \left(\frac{\delta}{\delta U({\bf r}_2)}
\frac{\delta A_{\alpha \beta}}{\delta U({\bf r}_1)}\right)
\ u_{\delta}\ u_{\gamma}\ d{\bf r}_1 d{\bf r}_2 \nonumber \\
&+& \int \frac{\delta A_{\alpha \beta}}{\delta U({\bf r}_1)}
\ u_{\delta \gamma}\ d{\bf r}_1 \ \ .
\label{relation}
\end{eqnarray}
Again, we emphasis that other higher order nonlinear conductance
can be calculated in a similar fashion. In general, the n-th order
characteristic potential tensor is needed for the $(n+1)$th order
nonlinear conductance.  Finally we point out that this result
Eq.(\ref{g4}) can in fact be obtained by expanding the following electric
current expression to the third order in voltage,
$I_{\alpha} = \frac{2e}{h} \sum_{\beta} \int dE f(E-E_F-eV_{\beta})
A_{\alpha \beta}(E,\{V_{\gamma}\})$.

In the following we calculate $G_{1111}$ from the general result of Eq.
(\ref{g4}) for a double barrier tunneling diode. For simplicity let's
consider an one-dimensional double barrier tunneling system
where the two barriers are $\delta$-functions located
at positions $x=-a$ and $x=a$. The barrier strength is $V_1$ and $V_2$
respectively. When $V_1=V_2$, this is a symmetric system, hence the
second order nonlinear conductance vanishes. In the symmetric case the
first nonlinear coefficient comes from the third order, as specified by
Eq. (\ref{g4}). If we approximate the scattering matrix by the Breit-Wigner
form\cite{but4} near a resonance energy $E_r$,
$s_{\alpha\beta}(E)\sim
[\delta_{\alpha\beta}-i\sqrt{\Gamma_\alpha\Gamma_\beta}/\Delta]$,
where $\Gamma_\alpha$ is the decay width of barrier $\alpha$,
$\Delta=\Delta E+i\Gamma/2$ with $\Gamma=\Gamma_1+\Gamma_2$ and
$\Delta E\equiv E-E_r$, we obtain a simple expression,
\begin{eqnarray}
& & G_{1111} = \frac{2e^3}{3h{\Gamma}^2}[(3(\Delta E)^2-
\frac{\Gamma^2}{4})(\Gamma_1^2+\Gamma_2^2-\Gamma_1 \Gamma_2)
\Gamma_1 \Gamma_2\nonumber\\
& &-6\Gamma_1^2 \Gamma_2^2 (\Delta E)^2]
\left[(\Delta E)^2+\frac{\Gamma^2}{4}\right]^{-3}
\label{breit}
\end{eqnarray}
For the symmetric case, this expression reduces to
\begin{equation}
G_{1111} = -\frac{e^3 \Gamma_1^2}{6 h} \frac{3(\Delta E)^2+
\Gamma_1^2}{[(\Delta E)^2 + \Gamma_1^2]^3}
\label{breit1}
\end{equation}
which is negative definite and has one minimum at $\Delta E = 0$.
Because of the simple nature of the scattering matrix within the
Breit-Wigner form, a general electric current expression has been
obtained\cite{but4}: $I_{\alpha}=I_{\alpha}(V_{\beta})$. We have
thus calculated $G_{1111}$ from this exact I-V relation, and it
agrees exactly with the result (\ref{breit1}) which comes from
Eq. (\ref{g4}).

Most practical transport problems can not be solved analytically. It is
thus very important to be able to solve them numerically.
Indeed, a distinct merit of the scattering matrix theory presented here
is that it allows numerical computation, {\it e.g.} Eqs. (\ref{eq18}),
and (\ref{g4}) can be numerically evaluated for explicit
scattering potentials of a conductor. We only mention that the functional
derivatives of the transmission function $A_{\alpha\beta}$ with respect
to the potential landscape $U({\bf r})$ as appeared in Eq. (\ref{g4}), the
potential derivatives, and the partial local density of states which is
needed in the emittance calculation, can all be determined via
the scattering Green's function.

For the double-barrier diode just discussed, if we do not use the
Breit-Wigner scattering form, $G_{1111}$ can only be obtained numerically.
For this system the Green's function $G(x,x')$ can be calculated
exactly\cite{yip} thus from the Fisher-Lee relation\cite{lee}
we obtain the scattering matrix ${\bf s}_{\alpha\beta}(E)$ and hence the
transmission function $A_{\alpha\beta}$ from its definition (\ref{eq12}).
To compute $\delta A_{11}/\delta U$ and the higher order functional
derivative, we use Fisher-Lee relation and the fact\cite{gasparian}
that $\delta G(x_1,x_2)/\delta U(x) = G(x_1,x) G(x,x_2)$.
Hence,
\begin{equation}
\frac{\delta {\bf s}_{11}}{\delta U(x)} = i\hbar v G(x_1,x) G(x,x_1)
\end{equation}
and
\begin{eqnarray}
& & \frac{\delta^2 {\bf s}_{11}}{\delta U(x) \delta U(x')}
=i\hbar v \left[G(x_1,x') G(x',x) G(x,x_1)\right.\nonumber\\
& & \left. + G(x_1,x) G(x,x') G(x',x_1)\right]\ \ ,
\end{eqnarray}
where $v$ is the velocity of the particle. The energy and
$V_\gamma$ derivatives of Eq. (\ref{g4}) can be evaluated explicitly
using the numerical procedures documented before\cite{wang1,wang2}.
Finally, the nonlinear characteristic potential $u_{11}$ is obtained
from Eq. (\ref{u11}).

\begin{figure}
\narrowtext
{\epsfxsize=7cm\epsfysize=7.0cm\centerline{\epsfbox{fig.ps}}}
\vspace{-2.5cm}
\caption{
$G_{1111}$ as a function of the scattering electron energy $E$ for a
double barrier tunneling diode with symmetrical barriers.  Solid line:
numerical results by solving the full quantum scattering problem using
Green's functions.  Dashed curve: using the approximate Breit-Wigner
form of the scattering matrix. The units of the quantities are set by
$\hbar=1$, $e=1$ and $m=1/2$.
}
\label{fig1}
\end{figure}

The numerical result for $G_{1111}$ as a function of the scattering electron
energy $E$ is plotted as the solid curve in Fig. (1). Around the resonance
energy $E_r\approx 2.0$, $G_{1111}$ takes large but negative values.
Thus for electron Fermi energy in this range, the current-voltage
characteristics will be nonlinear and this may result to negative
differential resistance. Such a behavior has important significance for
practical purposes\cite{datta}. Notice that the two dips of $G_{1111}$ are
not exactly the same, such an asymmetrical behavior has been observed in
other quantities\cite{yip}. For comparison we also plotted (dashed line)
the result from the Breit-Wigner approximation of the scattering matrix, Eq.
(\ref{breit1}). While the negative nature of $G_{1111}$ and the overall
magnitude are similar to the numerical result, the Breit-Wigner result
shows only one dip.  This inconsistency is completely due to the simple
form of the Breit-Wigner approximation as it gives a space-independent
and constant characteristic potential. The accurate solution using the
Green's function generates space-dependence of various quantities.

\section{Summary}

In summary, we have extended the scattering matrix theory which is
now appropriate to analyzing linear dynamic conductance to first order in
frequency, and weakly nonlinear DC conductance order by order in
external bias. The crucial ingredient of this development is the
characteristic potential at weakly nonlinear orders and these potentials
appear naturally from the self-consistent Hamiltonian. The theory is
current conserving and gauge invariant. The physical quantities involved
in this theory are numerically calculable, hence the present approach
can be used to conductors with complicated scattering potential landscape for
quantitative predictions. The formal connection of the scattering
matrix theory and the response theory, at the weakly nonlinear AC level,
has been clarified in our recent work\cite{ma1}. While the response theory
is very general\cite{ma1} and can be used to analyze weakly nonlinear DC and
AC transport order by order in bias, and for AC case to all orders of
frequency, we expect that the scattering matrix theory should be able to
do the same. This paper partially fulfills this expectation by
extending the scattering matrix theory to higher orders of nonlinearity.
We point out that to go beyond the linear frequency, the expression for
electric current, Eq. (\ref{eq9}), should be extended. In addition we
should use the Helmhotz equation (in Lorentz gauge) for the
electrodynamics instead of the Poisson equation.
Finally, it is important to note that the theoretical
approach of scattering matrix developed here is appropriate to transport
problems near equilibrium. Far from equilibrium, one may employ the Keldysh
Green's functions\cite{keldysh}.

\noindent
{\bf Acknowledgments}.
We thank Mr. Q.R. Zheng for a useful discussion concerning the
electrodynamics used in this work. We gratefully acknowledge financial
support by various organizations. J.W. is supported by a research
grant from the Croucher Foundation, a RGC grant from the SAR
Government of Hong Kong under grant number HKU 261/95P, and a
CRCG grant from the University of Hong Kong; Z.M. is supported by
the Foundation of Advanced Research Center of Zhongshan University
and NSF-China; H.G. is supported by NSERC of Canada and FCAR
of the Province of Qu\'ebec. We thank the Computing Center of The
University of Hong Kong for CPU allocations.

redpajama_set_name: RedPajamaArXiv


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Welcome! USEAdmin1 2023-01-23T13:53:37-05:00
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As the nation's oldest and largest non-partisan citizens' action group dedicated to preserving the unifying role of the English language in the United States, we hope you will join us in our efforts to make English its official language!
The "English Language Unity Act" is legislation to make English the official language in the U.S. House of Representatives (H.R. 997) and the U.S. Senate (S. 678). Visit our Action Center to learn about ways to tell your legislators to support Official English!
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In a ballot referendum on November 2, more than two thirds of residents in Allentown, Pennsylvania voted to keep an Official English provision in the town charter that has been on the books since 1995.
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A new Rasmussen Poll published on April 14, 2021 has again shown compelling support for English as America's common and
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Art Assembled: New This Week in May
Guest Post: David Ling
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Home / Blue/Green
Category: Blue/Green
Art Assembled: New This Week May
May 31, 2018	arttextstyle0 Comment
Reflect, Ulla-Maija Vikman, painted viscose and linen, 62.5" x 54", 2017. Photo by Tom Grotta
May was quite a busy and exciting month here at browngrotta arts. We ended April and kicked off May with our annual Art in the Barn Exhibition, Blue/Green: color/code/context. The exhibition attracted a record-breaking crowd that swarmed from all areas near and far. In addition to the opening itself, we hosted "Art-Ocean-Energy" a fundraiser for Ports of Cause as well as an IDCEC accredited presentation "Material Matters: Integrating Art Textiles and Fiber Sculpture in Architecture and Interior." We also published our new catalog Blue/Green: color/code/context. The catalog–our 48th volume–features work by 57 artists from over 15 countries. Blue/Green: color/code/context is available for purchase on our online store and Amazon.
To kick off May's New This Week we shared Ulla-Maija Vikman's Reflect. Made by hand-painting viscose yarn and linen, Vikman's Reflect falls freely into space and forms varying color surfaces as air flow causing the uniquely painted fibers to move. Vikman found combining the color blue with textiles very interesting because of the way in which they juxtapose each other. "Textile is material and tactile. Blue is immaterial, airy and spacious," explains Vikman.
Changing Tides, Wendy Wahl, Encyclopedia Britannica pages, 27" x 42" x 1.75", 2018. Photo by Tom Grotta
Next up we had Changing Tides by Wendy Wahl. Made of 275 pages of 1988 Encyclopedia Britannica Annual of World Data, Changing Tides continues a series Wahl developed from her interest in expressing our station in time through the use of materials that have been a part of a particular collective consciousness. Wahl cut the encyclopedia pages into seven sections, for each of the continents, and thoughtfully scrolled and compressed into 1,925 whirls to symbolize the reality of rising water around the globe.
Blue Wave, Ferne Jacobs, coiled and twined waxed linen thread, 19" x 17.5" x 6", 1994. Photo by Tom Grotta.
Lastly, Ferne Jacobs' Blue Wave. Jacobs, who began making sculptural baskets in 1970, uses waxed linen to create intricate, coiled designs that evoke organic forms. Jacobs' commitment to fiber sculptures grows out of a fascination that thread can be made solid, that by using only her hands and thread, she can create a form that can physically stand on its own.
Blue/Green: color/code/context Catalog
Blue/Green: color/code/context
The companion catalog for Blue/Green: color/code/context is now available for purchase in the browngrotta arts online store and on Amazon. The catalog— our 48th volume—contains 148 pages, 158 color photographs of work by 57 artists from over 15 countries.
The pieces featured in the exhibition and catalog were made using traditional materials such as cotton, linen and wool as well as a wide array of untraditional materials. For example, Tamiko Kawata uses small black safety pins and cardboard in Green Blue Screen One. Gyöngy Laky's Our Egg, which references our precious, life-giving and life-sustaining blue/green orb, is made of telephone wire, wine bottle wire, and a light green chicken egg. In making Real, John Mcqueen used cut up plastic bottles and sticks.
The catalog's essay, "Analogous Artistry: Blue/Blue Green/Green," is written by Leatrice Eiseman, a color specialist whose expertise is recognized worldwide. In addition to heading the Pantone® Color Institute, Eiseman is the director of the Eiseman Center for Color Information and Training. She is the author of 10 books on color, including Color: Messages and Meanings a Pantone® Color Resource and most recently, The Complete Color Harmony, Pantone® Edition. In her essay, Eiseman delves into the cultural, historical and emotional references to blue and green. The catalog features two-page spreads of each work in the exhibition. The essay and back pages are illustrated with more-than 20 photographs of additional works of blue and green.
In summary, Blue/Green: color/code/context is a wide-ranging survey of ways that artists interpret these colors and the influence they exert.
Recap: Whirlwind Art Week in Wilton at browngrotta arts
VIP-opening, photo by Carter Grotta
We had record crowds in attendance and a record number of sales at browngrotta arts in Wilton last week for Blue/Green: color/code/context. At our VIP preview event on Friday, we hosted our clients, collectors and art appreciators and our event sponsors from Litchfield Distillery, venü Magazine and Country Club Homes.
Karl Dolnier parking cars at Blue/Green opening. Photo by Carter Grotta
Artist Dinner after Artist Reception. Photo by Carter Grotta
Saturday we hosted 10 artists from the exhibition (Keiji Nio and family all the way from Japan, Kiyomi Iwata from Virginia, Pat Campbell from Maine, Lewis Knauss, Nancy Koenigsberg, Polly Barton and Tamiko Kawata from New York, Wendy Wahl from Rhode Island and Dawn MacNutt from Nova Scotia) and loads of visitors, too. Sunday and Monday we were busy all day.
Surface Design Association Talk. Photo by Carter Grotta
Tuesday we hosted a good crowd of appreciative and knowledgable members of the Surface Design Association.
Mae Colburn presentation of Helena Hernmarck work at the Architecture and Designer Talk. Photo by Carter Grotta
Wednesday was educational — we presented Material Matter: Integrating Art Textiles and Fiber Sculpture into Interiors and Architecture with the help of Mae Colburn from Helena Hernmarck's studio and some interior shots from Walter Cromwell at Country Club Homes. Those in attendance were eligible to get Continuing Education Credit from the Interior Design Continuning Education Council.
westport arts center
Thursday brought the Westport Arts Council Board and patrons another educated and interested audience.
Ports of cause fundraiser. photo by Harrison James O'Brien
Friday was Art•Ocean•Energy, an immersive art experience for supporters of Ports of Cause, a 501(c)3 driven to promote, inspire and accelerate innovative and sustainable solutions and practices that reduce the impact luxury living and everyday lifestyles have on our oceans. Those who joined us on Friday, heard Tom speak about our artists' dedication to sustainable art and art practices and
Arthur Bavelas talking at Ports of Cause fundraiser. photo by Harrison James O'Brien
Arthur Bavelas, Founder of the Bavelas Group Family Office & Family Office Insights of New York City, speak about How sustainable innovation is driving the blue economy while benefiting our oceans and natural resources. A lively discussion followed. Saturday was a full day as was Sunday. Sunday evening we concluded our 10-day annual opening with a informed and engaged group from the Aldrich Museum in Ridgefield, Connecticut. Hope we'll see you at browngrotta arts in 2019 at one or more of our annual events. In the meantime, you can find us online at browngrotta.com; talking about events and acquisitions and other art stuff at arttextstyle.com and on Facebook, posting items and images on Twitter and Instagram and videos on the browngrotta arts YouTube Channel.
Artists in the House: Who's attending the Opening of Blue/Green: color/code/context on Saturday
April 25, 2018	arttextstyle0 Comment
Keiji Nio, Rough Sea of Sado,polyester, aramid fiber, 48.25" x 47.5", 2016. Photo by Tom Grotta
The Artists Reception and Opening for Blue/Green: color/code/context occurs this Saturday at browngrotta arts, 276 Ridgefield Road, Wilton, Connecticut 06897. Eleven of the participating artists will be in attendance, enhancing what is always an energizing opportunity to experience our annual Art in the Barn event. Keiji Nio and his family are coming from Japan, Pat Campbell from Maine, Wendy Wahl from Rhode Island, Kiyomi Iwata from Virginia, Norma Minkowitz and Helena Hernmarck from Connecticut and Polly Barton, John McQueen, Nancy Koenigsberg, Lewis Knauss and Tamiko Kawata from New York. Wendy Wahl's work is made of blue Encyclopedia Britannica pages; John McQueen used plastic bottles — a departure for him. Norma Minkowitz has created a detailed and magical stitched drawing and Lewis Knauss a work of pale, pale green and natural reed and twigs. Join us from 1-5 pm to see their work and that of 50 more artists. The artists will be available throughout the Barn, to answer questions about their work, their favorites or about the work of others. They'll be wearing name tags — feel free to say hello. For more info: http://www.browngrotta.com/Pages/calendar.php; 203-834-0623. Or visit us during the week — Sunday April 29th – Sunday May 6th, 10-5 pm.
John McQueen
Nancy Koenigsberg
Lewis Knauss
Wendy Wahl
Pat Campbell
Norma Minkowitz
Kiyomi Iwata
Helena Hernmarck
Make a Day of It: Area Events to Visit on Your Way to Blue/Green at browngrotta arts
In planning your trip to browngrotta arts in Wilton, Connecticut for Blue/Green: color, code, context between April 28th and May 6th take some time out of your schedule to visit a few other exhibitions going on in the area.
A short 15-minute drive from browngrotta arts, the Westport Arts Center's current exhibition HandMade: Women Reshaping Contemporary Art features a diverse array of work from 15 leading female fiber and textile artists, including Ghada Amer, Anna Betbeze, Ligia Bouton, Orly Cogan, Lesley Dill, Terri Friedman, Sermin Kardestuncer, Sophia Narrett, Faith Ringgold, Miriam Schapiro, Judith Scott, Beverly Semmes, Rosemarie Trockel and Margo Wolowiec. The exhibition also features work by three browngrotta arts artists, Chiyoko Tanaka, Carolina Yrarrázaval and Norma Minkowitz. Curated by Elizabeth Gorayeb, the Executive Director of the Wildenstein Plattner Institute, Inc—a New York-based non-profit committed to art historical research—the exhibition examines the role of women in reshaping what has historically been considered "fine art." Additionally, the exhibition demonstrates how fiber and textile materials allow artists such as Faith Ringgold and Sophia Narre to examine topics such as race, gender and sexuality. HandMade: Women Reshaping Contemporary Art will be on view at the Westport Arts Center through June 2nd. For more information visit the Westport Arts Center website HERE.
Ala Ebtekar's Zenith V at Long, Winding Journeys: Contemporary Art and the Islamic Tradition. Photo: Katonah Museum of Art
Next stop, the Katonah Museum of Art's exhibition Long, Winding Journeys: Contemporary Art and Islamic Tradition. The exhibition looks at a group of artists of Middle Eastern and South Asian descent whose work engages the diverse forms of Islamic visual tradition to explore religion, culture and socio-political issues today. The title of the exhibition "Long, Winding Journeys: Contemporary Art and the Islamic Tradition" was inspired by Pulitzer Prize-winning playwright Ayad Akhtar's essay The Breath of Miraj. Akhtar's The Breath of Miraj conveys the manner in which Islam and its history can inspire creative life to become a "long, winding journey." While making the pieces included in the exhibition, artists utilized some of the century-old forms that define Islamic art, such as calligraphy, miniature painting, geometric patterning, textiles and architecture. Long, Winding Journeys: Contemporary Art and Islamic Tradition will be available for viewing until June 17th, for more information on the exhibition visit the Katonah Museum of Art's website HERE.
Boris Mikhailov (Ukrainian, b. 1938), Untitled from the series Sots Art, 1975-1990, Gelatin silver print hand-colored with aniline dyes on paper at Hot Art in a Cold War: Intersections of Art and Science in the Soviet Era
Hot Art in a Cold War: Intersections of Art and Science in the Soviet Era will be on view until May 20th at the Bruce Museum in Greenwich, Connecticut. The provocative exhibition probes into the consequences of innovation in science, technology, mathematics, communications and design during the Cold War. The exhibition juxtaposes the art made during the Cold War in opposition to state-sanctioned Socialist Realism with artifacts from the nuclear and space programs to explore the triumphs and tragedies unleashed by humankind as it gained the power to both leave the Earth and to destroy it. Produced from the 1960s to the 1980s, the items on view in Hot Art in a Cold War address themes of international supremacy and hegemonic power during a turbulent period marked by the ever-escalating competition for nuclear supremacy and the space race. "The Bruce Museum prides itself in being a museum of both art and science and in finding the interconnections between the two," states Dr. Daniel Ksepka, Bruce Museum Curator of Science and co-curator of Hot Art in a Cold War. The exhibition allows visitors to "see how the triumphs of the space program and anxieties about nuclear arms were captured by period artists. Likewise, many of the scientific objects are works of art in their own right. The elegance of Sputnik, for example, is as striking and undeniable as its impact on the space race." For more information on Hot Art in a Cold War: Intersections of Art and Science in the Soviet Era visit the Bruce Museums website HERE.
Last but not least, the Wilton Historical Society's new permanent exhibition Connecticut History, Wilton's Story is now available for viewing. Through artifacts and objects, the Wilton Historical Society aims to shine a light on Wilton's roots and connections, as well as the evolution of the town since the colonial period. For more information on Connecticut History, Wilton's Story visit their website HERE or call the Wilton Historical Society at 203-762-7257.
Who is new in Blue/Green: code/color/context — Micheline Beauchemin and Polly Barton
Blue/Green: color/code/context opens at browngrotta arts, 276 Ridgefield Road, Wilton, Connecticut on April 28th (1 pm to 6 pm). Featured in the exhibition are more than 50 artists, including two new to browngrotta arts, Micheline Beauchemin of Canada and Polly Barton from the US.
Details of Totem aux Millefleurs Bleues by Micheline Beauchemin and Synapse by Polly Barton
Beauchemin began her career making stained-glass windows but early on turned to weaving and embroidering spectacular wall hangings in vibrant colors, including blues and greens. traveled and studied in Japan, China, India, North Africa, the Canadian Arctic and the Andes, adding depth and mystery to the love of light, water, wings and nets that is evident in her body of work. She created a number of important commissions throughout Canada, including an acrylic curtain for the Grande Salle of the Théâtre Maisonneuve at Place des Arts in Montréal (1963-1967) a curtain for the National Arts Centre in Ottawa (1966-1969), tapestries for Queen's Park in Toronto (1968-1969), the Hudson's Bay Company in Winnipeg (1970) and the Canadian pavilion at the 1970 World's Fair in Osaka, Japan. She participated in the 10th Lausanne Biennial, was elected to the Royal Canadian Academy of Arts and was awarded the Governor General's Award in Visual and Media Arts. A book about Beauchemin, her life and works, Micheline Beauchemin: Je rêvais de tapisseries à la grandeur des cathédrales, à la largeur de nos rivières (roughly, I dreamed of tapestries, as wide as rivers, throughout cathedrals) can be purchased through our website at http://store.browngrotta.com/books/
Polly Barton is a US artist known for adapting the ancient weaving technique of ikat into contemporary woven imagery. She has provided an ikat of silk, Pillar of Cloud, for Blue/Green: color/code/context. As a young artist, Barton worked as a personal assistant to Helen Frankenthaler. She cites that experience as a formative one, where she learned firsthand the inner drive, resilience, and intention necessary for an artist. The year also introduced her to the challenges and rewards of the New York art world. In 1981, she moved to Kameoka, Japan and lived in the religious heart of the Oomoto Foundation to study with master weaver, Tomohiko Inoue. In Kameoka, she practiced tea ceremony, calligraphy and Noh Drama with Oomoto's master teachers. Barton has shown her woven ikats on both coasts. Her works are in the permanent collections of the Art Institute of Chicago, the Boston Museum of Fine Arts, and the Mint Museum among others.
Blue/Green: color/code/context opens on April 28th for just 10 days. The 140-page color catalog will be available on the 28th at browngrotta.com.
Details: Opening and Artists Reception, Saturday, April 28th, 1-6 pm; Sunday April 29th – Sunday May 6th, Hours: 10-5 pm. For more info: http://www.browngrotta.com/Pages/calendar.php; 203-834-0623.
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The Hope College men's basketball team bounced back from Saturday's loss to Calvin by holding off Kalamazoo 87-83 on Monday on the road.
The Flying Dutchmen improved to 12-9 and 5-5 in the MIAA. Kalamazoo dropped to 6-15 and 3-7 in the MIAA after upsetting Olivet last week.
Riley Lewis made five 3-pointers and scored a game-high 24 points.
Preston Granger added 20 points and nine rebounds. Dennis Towns had a double-double with 13 points and 11 rebounds.
Calvin Hackert came off the bench and hit three 3s, scoring 11 points. Teddy Ray had seven points and seven rebounds.
Jason Beckman struggled from the field, going 2-for-11 with five points. That leaves him four points short of reaching 1,000 career points.
Hope shot 53 percent from the field in the game, including 47.8 percent (11-for-23) from 3-point range.
The Flying Dutchmen managed just 31.6 percent from the free-throw line, going 6-for-19.
Hope won the rebounding battle 39-33.
The Hornets shot 46.2 percent and went 12-for-28 (42.9 percent) from 3-point range. Kalamazoo also went 11-for-13 from the free-throw line.
Ben Reiter led the Hornets with 23 points and Tanner Blyly added 19.
The Flying Dutchmen will travel to Adrian for a 7:30 p.m. tip on Wednesday, Feb. 6.


text:
13,000-Year-Old Tracks Found On Remote Canadian Island Are The Earliest Human Footprints In North America
Walter KopplingerShutterstock
Alexandra Lozovschi
The earliest human footprints in North America have been unearthed off the coast of Canada, on Calvert Island, reveals a study published yesterday in the journal PLOS One.
The astounding discovery — "29 footprints of at least three different sizes," according to the paper — was made by archaeologists at the Hakai Institute and University of Victoria in British Columbia, led by anthropologist Duncan McLaren.
The footprints, estimated to be 13,000-years-old, were possibly left behind by two adults and a child, all barefoot, reports the New York Times, and are believed to be the oldest preserved human track marks ever found in North America.
The 29 human footprints were buried under sediment layers at an ancient archeological site dating back to the late Pleistocene and offer important clues "about the ice age human occupation of the Pacific Coast of Canada," the researchers wrote in their study.
The PLOS One paper was edited by Michael Petraglia, an archaeologist from the Max Planck Institute for the Science of Human History in Germany, who commented on the importance of this discovery.
"It's not only the footprints themselves that are spectacular and so rare in archaeological context, but also the age of the site."
Petraglia told the New York Times that the ancient human footprints uncovered on Calvert Island in British Colombia, 62 miles north of Vancouver Island, suggest "an early entrance into the Americas."
Dr. McLaren agrees with this hypothesis.
"It is possible that the coast was one of the means by which people entered the Americas at that time," he pointed out.
According to the study, the footprints were made in the wet clay near the water's edge during the end of the last ice age, at a time when the sea level in the area was six to ten feet lower.
In Dr. McLaren's opinion, their presence in the area at that point in time is a clear sign the island was inhabited at the end of the last ice age.
"As this island would only have been accessible by watercraft 13,000 years ago, it implies that the people who left the footprints were seafarers who used boats to get around, gather and hunt for food and live and explore the islands," he said.
His team discovered the human footprints "impressed into a 13,000-year-old paleosol beneath beach sands," the study notes, while digging for sediments.
The first footprint recovered at this site was found as early as 2014, about 24 inches below the beach's surface. Next to the footprint, the team also unearthed two pieces of ancient wood, which radiocarbon analysis revealed were between 13,300 and 13,000 years old.
It took three years for the archaeologists to dig up all the 29 human footprints, which have clear arch, toe, and heel marks. This prompted the researchers to be "certain that they were left by human feet," they show in the study.
According to LiveScience, the prehistoric footprints were so well preserved that the team was even able to assign modern-day U.S. shoe sizes to the three individuals that left them behind.
Judging by today's standards, the three people that walked the beach on Calvert Island 13,000 years ago had small feet and would have worn some of the smallest shoe sizes: a junior size eight, a junior size one (or a woman's size size), and a woman's size eight or a man's size seven.


text:
Mrs. X and Ors. v. Union of India and Ors.
This case summary and analysis was prepared with generous pro bono support from White & Case and was reviewed by National Law University Delhi.
Request Resource
The Medical Termination Act 1971 authorizes termination of pregnancy up to 20 weeks (Section 3(2)). Mrs. X, who was about 22 weeks into her pregnancy, petitioned the Court to permit her to terminate her pregnancy after learning that the fetus had a severe medical condition of bilateral renal agenesis that may prevent it from surviving after birth, and may endanger her life during delivery.
The Court ordered verification of the petitioners' claims by a medical board consisting of seven doctors. The report was reviewed by a doctor from the Ministry for Health who agreed with the findings. The medical board found that there was a risk of intrauterine fetal death/still birth and there was no chance of long-term post-natal survival and no curative treatment was available. The medical board further found that there was risk to the pregnant woman, as continuing the pregnancy could endanger her physical and mental health.
The Court relied upon the case of Suchita Srivastava and Anr. v. Chandigarh Administration [(2009) 9 SCC 1], where in it was held that a woman's right to make reproductive choices is also a dimension of personal liberty under Article 21 of the Constitution. The Court noted that a pregnant woman had the right to bodily integrity and to preserve her life if there was foreseeable danger in the case of continuing a pregnancy to term. It further noted that the report of the medical board warranted the abortion under the law, Section 3(2)(i) of the Medical Termination of Pregnancy Act 1971, as continuing the pregnancy would pose a risk to the petitioner's life and a possible grave injury to her physical or mental health. The Court further noted that Section 5 of the act enables termination where not less than two doctors consider it immediately necessary to save the life of the pregnant woman.
On this basis, the Court found that notwithstanding that Mrs. X was by this point approximately 24 weeks pregnant, she should be permitted to terminate the pregnancy under the provisions of the Medical Termination of Pregnancy Act 1971.
The Court further recognized that the affidavit for the petition was not signed by Mrs. X but by a doctor (and fellow petitioner). While the Court found no sign of coercion, it nonetheless made clear that an affidavit from Mrs. X would be required and that the hospital would also need her consent prior to carrying out the termination.


Certificate for one share of four pounds to bearer in this London-based company which owned Nicaraguan plantations. Very decorative certificate with engraving of four persons picking bananas. Border in green and yellow, with yellow bananas and tree leaves; attached complete coupon sheet. Three original signatures of directors and company secretary. Text in French and English.
Certificate size is 25 cm high x 36.5 cm wide (10" x 15").


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Tag Archives: Orlando
A cold chill for Florida residents
Luke 21:25,26 "There will be signs in sun and moon and stars, and on the earth dismay among nations, in perplexity at the roaring of the sea and the waves, men fainting from fear and the expectation of the things which are coming upon the world; for the powers of the heavens will be shaken.
Arctic chill to bring 30's for first time in 11 years to Miami
In some areas, the duration of temperatures of 32 degrees or below could be as much as 4 hours
A 1966 record in Lakeland could be broken Sunday morning when temperatures reach a low of 27 degrees. Orlando, Fort Myers and Fort Lauderdale could also see record cold.
Temperatures in Orlando will struggle to reach 50 degrees
Tagged Arctic chill, Florida, Fort Lauderdale, Fort Myers, Miami, Orlando | Leave a comment
Air taxi startup Lilium's first U.S. hub to be in Florida
By Douglas Busvine
BERLIN (Reuters) – Flying taxi startup Lilium will set up its first U.S. hub near Orlando, putting more than 20 million Floridians within range of the winged electric aircraft that can take off vertically and cover 300 km (185 miles) in a single one-hour hop.
Munich-based Lilium said on Wednesday its first U.S. Vertiport would be at Lake Nona, a futuristic smart city being built near Orlando International Airport by the Tavistock Development Group.
The hub, due to start operations in 2025, would be Lilium's second after a similar Vertiport planned in Duesseldorf, capital of Germany's most populous state of North Rhine-Westphalia.
Startups are racing to develop, certify and manufacture electric aircraft in a bid to revolutionize short-range travel. Five-year old Lilium – with $375 million in investor funding – is one of the best backed.
Its five-seater Lilium Jet has undergone flight tests and, if approved for service, would offer travelers a way to skip traffic and quickly reach their destinations for around the cost of an Uber, said Chief Operating Officer Remo Gerber.
The fixed-wing aircraft, powered by 36 electric engines which point down for takeoff and tilt to the rear for horizontal flight, would be steered by a qualified pilot.
"It's a hundred times safer than helicopters. Pricing is five to 10 times cheaper," Gerber told Reuters in an interview.
Power use for distance covered is similar to electric vehicles while, because there is no runway, the cost of a Vertiport is far lower than a traditional airport, ranging from 1-2 million euros for a basic landing zone to 7-15 million euros ($8-$18 million) for a major rooftop hub.
"Lilium's core mission of transport which not only supports bringing the region together, but also provides a solution to environmental issues, is incredibly impressive," said Tavistock Managing Director Ben Weaver.
The City of Orlando is also backing the project, which Mayor Buddy Dyer described as an "expansion of safe, efficient and environmentally friendly transportation options throughout one of the fastest growing regions in the country".
(Reporting by Douglas Busvine; Editing by Mark Potter)
Tagged Air taxi, Duesseldorf, electric aircraft, Lilium, Orlando, Vertiport | Leave a comment
United Airlines bets on Florida, adding dozens of flights a day starting November
(Reuters) – United Airlines is adding up to 28 daily nonstop U.S. flights to Florida starting Nov. 6 as the Chicago-based airline bets on a rebound in leisure travelers heading to sunny skies.
The direct flights are from non United hub cities in Boston, Cleveland, Indianapolis, Milwaukee, New York/LaGuardia, Pittsburgh and Columbus, Ohio to four Florida destinations.
United said it is part of its "continuing strategy to aggressively, and opportunistically manage the impact of COVID-19 by increasing service to destinations where customers most want to fly." But the carrier said it could reduce the number of flights if COVID-19 infections in Florida remain high.
New Florida flights will go to Fort Lauderdale, Fort Myers, Orlando and Tampa.
Ankit Gupta, United's vice president of domestic network planning, said the new flights represent "United's largest expansion of point-to-point, non-hub flying and reflects our data driven approach to add capacity where customers are telling us they want to go."
United can adjust up or down. Gupta said the added Florida flights could amount to more than 400,000 additional seats this winter season. He said many U.S. travelers are picking Florida instead of international destinations.
There are modest signs of improving air travel demand. The Transportation Security Administration said it screened 831,789 people on Sunday — the first time it screened more than 800,000 people since March 17. That is still down 70% over prior year figures.
Still, Florida has reported 542,792 coronavirus cases, the second most of any U.S. state behind only California, according to a Reuters tally, and more than 10% of all reported U.S. cases. If coronavirus cases in Florida remain high, "we will adjust our plans," Gupta said.
Southwest Airlines chief executive Gary Kelly said at a Texas Tribune forum on Wednesday the airline is still trying to figure how many flights to offer as it works to reduce its $20 million a day losses. "It is pure guesswork at this point" Kelly said.
(Reporting by David Shepardson; Editing by David Gregorio)
Tagged Boston, Cleveland, Columbus, Coronavirus, COVID-19, Florida, Fort Lauderdale, Fort Myers, Indianapolis, Milwaukee, New York, Orlando, Pittsburgh, Tampa, Travel, TSA, United Airlines | Leave a comment
Disney to shut Hong Kong Disneyland again as coronavirus cases rise
By Helen Coster
(Reuters) – Walt Disney Co. is temporarily closing its Hong Kong Disneyland theme park from July 15 amid rising coronavirus cases in the Chinese-ruled city, the company said Monday.
The announcement came two days after Disney reopened its biggest resort, Walt Disney World in Orlando, Florida, as coronavirus cases surged in the state.
"As required by the government and health authorities in line with prevention efforts taking place across Hong Kong, Hong Kong Disneyland park will temporarily close from July 15," a Disney spokeswoman said in a statement.
The Hong Kong Disneyland Resort hotels will remain open with adjusted services. They have put in place enhanced health and safety measures, the company said.
Hong Kong recorded 52 new cases of coronavirus on Monday, including 41 that were locally transmitted, according to health authorities. Since late January, Hong Kong has reported 1,522 cases and local media reported an eighth death on Monday.
Hong Kong is tightening social distancing measures amid growing worries about a third wave of coronavirus infections. The government will limit group gatherings to four people – from 50 – a measure last seen during a second wave of the outbreak in March.
Hong Kong Disneyland reopened in June. Hong Kong Tokyo reopened in July; Disneyland Shanghai reopened in May.
Disney's reopening of its parks in Asia helped provide assurance about moving ahead in Florida, Josh D'Amaro, chairman of Disney's parks, experiences and products division told Reuters in an interview on Saturday.
Florida has emerged as an epicenter of COVID-19 infections. Over the past two weeks, the state reported 109,000 new coronavirus cases, more than any other U.S. state.
(Reporting by Helen Coster in New York. Additional reporting by Lisa Richwine in Los Angeles, Editing by Nick Zieminski)
Tagged China, Coronavirus, COVID-19, Disneyland, Hong Kong, Orlando, shanghai | Leave a comment
Local hero: Florida hotelier Harris Rosen keeps his giving close to home
By Beth Pinsker
NEW YORK (Reuters) – Harris Rosen has a chain of eight hotels bearing his name in the Orlando area, but he makes most of his headlines these days for giving away his fortune.
The 80-year-old entrepreneur of Rosen Hotels & Resorts, who grew up on the Lower East Side of New York, adopted the Tangelo Park neighborhood near his hotels and has paid for preschool programs and college for local students. Among some of his other many causes: He endowed the Rosen College of Hospitality Management at the University of Central Florida, and he has been involved in charity efforts in Haiti, the home country of many of his staff.
Rosen's business also recently expanded its generous, self-funded health plan called RosenCare to cover the health clinic for teachers in Osceola County.
Rosen spoke to Reuters about how he came to make his fortune and then give it away.
Q: Who first taught you money values?
A: It came from my two granddads. Both of them came from Eastern Europe. One had a little restaurant on Lower East Side; the other made wooden barrels.
When my mom and dad got married, they went into business together to purchase little apartments where immigrants stayed. Unfortunately, there was a fairly significant depression in 1920s. They lost everything because they would not ask anyone to leave.
One night they came over, and said, essentially, you have something in your genes. You are going to be a businessperson, but don't ever borrow money.
I've lived with that all my life: I'm going to be a businessperson, and I can't borrow money. That's impossible! The first hotel I bought, I put down $20,000 and assumed a $2.5 million mortgage.
I will tell you now with great pride 45 years later, though, with 7,000 rooms, we don't have a penny of debt.
Q: What did your first job teach you?
A: When I was 10, I overheard fishermen talking about how badly they needed worms. So I went into the night crawler business. I hunted them with a flashlight, and then arrived early at fishing pier.
I learned that you try to find something that people need and want, charge a fair price and save as much as you can.
Q: Once you got some money together, what was your investing philosophy?
A: One of the first stocks I bought was Avon, because I met some of the ladies who ran the company. They said, "Harris, Buy the stock." I couldn't buy more than 10-15 shares, but I'd look at Avon every morning, and I did very well.
Then I bought Automatic Data Processing, because the grandmother of the company founder worked as a clerk in their sales office at the Waldorf Astoria where I also worked.
I don't think I've owned anything other than my company for about maybe 45 years. I invest only in Rosen.
Q: When did you start getting very generous with employee benefits?
A: Early on, about 30 years ago, I discovered I wasn't very happy with our whole health plan. I didn't understand why our premiums would go up year after year.
We had a tiny little office where our accounting folks stayed, but they outgrew it. I said, we'll convert it to primary care health center. I called a friend who knew insurance and said, 'Help me start my own insurance company.' Then I said: 'Let's look for a doctor.'
We focus on keeping people healthy.
Q: You have many charity projects, how do you decide how to give away your money?
A: About 25 years ago, sitting at my desk, I heard a voice and it said, "Harris, you have been blessed beyond anything you imagined, and now it would be appropriate to offer a helping hand to those in need."
Q: How do you pass along this legacy of giving to your children and grandchildren?
A: I just think they need to do the kind of work that they enjoy. They need to be honest and treat people with respect, and if they are in the position to become philanthropic, what they need to do is express that generosity by helping others.
I'm very happy with the way things are working out. I love the opportunity that I have had to offer a helping hand to so many people.
(Follow us @ReutersMoney or at http://www.reuters.com/finance/personal-finance. Editing by Lauren Young and Cynthia Osterman)
Tagged College, Florida, Hotel owner, Orlando, preschool programs, Rosen College University of Central Florida | Leave a comment
Judge denies motion to drop case against widow of Orlando gunman
By Joey Roulette
ORLANDO, Fla. (Reuters) – A judge on Monday denied a defense motion to dismiss charges against the widow of the gunman in the 2016 massacre at Orlando's Pulse nightclub, saying that the gunman's father's work an FBI informant was not relevant to the case.
Over the weekend, prosecutors disclosed that Omar Mateen's father, Seddique, had worked with the Federal Bureau of Investigation before his son carried out the massacre of 49 people at the Pulse nightclub in June 2016.
In opening their case, lawyers for Mateen's widow, Noor Salman, argued that the judge should dismiss the charges against her or declare a mistrial because prosecutors had failed to reveal the FBI's relationship to Mateen's father and other evidence related to him beforehand.
Salman, 31, is accused of helping her husband carry out surveillance of possible attack sites and doing nothing to stop him. Mateen, a U.S. citizen of Afghan descent who claimed allegiance to a member of the Islamic State militant group, was killed by police after more than three hours in the Pulse nightclub.
An FBI agent on Monday testified that years before Mateen carried out the attack, the agency considered using him as an informant, like his father.
Those discussions took place while the FBI was investigating comments made by the younger Mateen about overseas links to militants, Special Agent Juvenal Martin said in federal court in Orlando. That investigation closed without charges, he said.
Martin did not say why the FBI decided against enlisting Omar Mateen as an informant.
Salman's attorneys say that the disclosure by prosecutors that Seddique Mateen had been an informant from January 2005 to June 2016 violated a Supreme Court ruling barring prosecutors from withholding evidence.
After resting their case, prosecutors said agents probing the nightclub rampage found receipts of money transfers made from the United States to Turkey and Afghanistan made by the elder Mateen. An active investigation was under way, they said.
If the defense had known about the transfers, it would have investigated whether Seddique Mateen was involved in the attack or had prior knowledge of it, Fritz Scheller, a lawyer for Salman, said in the motion to dismiss.
But U.S. District Judge Paul Byron said, "It is not clear whether the purpose of the transfers was illegal."
He said the omission of any evidence related to Seddique Mateen had no bearing on the culpability of Salman.
Salman faces possible life in prison if convicted on charges of aiding her husband in the attack and obstructing an investigation.
(Reporting by Joey Roulette; Additional reporting and writing by Frank McGurty; Editing by James Dalgleish and Leslie Adler)
Tagged FBI, gunman, Judge, Massacre, Noor Salman, Omar Mateen, Orlando, Pulse nightclub, Wife | Leave a comment
Wife of Orlando nightclub gunman arrested on federal charges
By Daniel Levine
SAN FRANCISCO (Reuters) – The FBI on Monday arrested the wife of the gunman who killed 49 people at an Orlando gay nightclub last year, a massacre that intensified fears about attacks against Americans inspired by Islamic State, officials said.
Noor Salman, 30, is being charged with obstruction of justice and aiding and abetting by providing material support to a terrorist organization, Orlando Police Chief John Mina said in a statement.Salman's arrest came seven months after her husband, Omar Mateen, went on a hours-long siege at the Florida club that ended when police killed him. She was due to appear in federal court in Oakland, California on Tuesday morning.
"Certainly I can confirm that an arrest did occur in this case," Attorney General Loretta Lynch told MSNBC.
"We said from the beginning we were going to look at every aspect of this case, every aspect of this shooter's life to determine – not just why did he take these actions, but who else knew about them, was anyone else involved?" Lynch said.
Salman, who has a young son by Mateen, was arrested at her home outside San Francisco, The New York Times reported, citing an unnamed law enforcement official. Salman has moved at least three times since the attack, attempting to avoid the news media, The Times said.
The daughter of parents who immigrated from the West Bank in 1985, Salman was repeatedly questioned by law enforcement interrogators after the club attack, telling them she was with Mateen when he bought ammunition and conducted surveillance of the club.
But she denied any involvement in the attack or any knowledge of her husband's plans, she told the Times in an interview published on Nov. 1.
"I was unaware of everything," Salman told the Times. "I don't condone what he has done. I am very sorry for what has happened. He has hurt a lot of people."Her husband, who was 29 at the time of his death, claimed a connection to or support for multiple Islamist extremist groups, including al Qaeda, Hezbollah, al Nusra and Islamic State, Federal Bureau of Investigation Director James Comey told reporters a few days after the attack.
During the siege, Mateen spoke to a 911 emergency dispatcher and expressed solidarity with an al Nusra suicide bomber as well as Islamic State, also known as ISIS, ISIL or Daesh.
Representatives of the FBI could not be reached immediately for more details.
The Orlando massacre came about seven months after a husband and wife who sympathized with Islamic extremists opened fire in December 2015 on a holiday party in San Bernardino, California, killing 14 and wounding 22 others.
(Additional reporting by Frank McGurty and Daniel Trotta; Editing by Marguerita Choy and Cynthia Osterman)
Tagged Arrest, FBI, Florida, gunman, ISIS, Islamic State, Islamic Terrorism, Orlando, Orlando Massacre, Shooting, Terrorism, West Bank, Wife | Leave a comment
Orlando 911 calls tell of fear inside and outside of Pulse club
By Barbara Liston
ORLANDO, Fla. (Reuters) – Panicked callers to 911 during June's mass shooting in Orlando told police of buildings hit by stray bullets and wounded friends stuck inside the gay nightclub where a gunman pledging allegiance to Islamic State killed 49 people.
"Gun shots were just like crazy," one caller outside the club told 911 operators, according to partial transcripts of the calls that were released on Tuesday.
Shooter Omar Mateen killed 49 people and wounded 53 at the Pulse nightclub in the deadliest mass shooting in modern U.S. history.
One neighbor near Pulse told 911 operators people were banging on his door to escape the shooting and others were seeking cover behind parked cars.
People reported on the carnage inside the club.
"One of our friends sent us a text and he said that he's been shot and he's in the bathroom and no one sees him," one caller told 911.
A woman told an operator her husband was in the club and he reported shooting.
"He told me he cannot get out. He's over there (and) he said he cannot get out," the woman said.
A man said: "I just got home from the Pulse club … My friends texted me (to) tell me there is a shooting going (on) A lot of my friends got shot."
The operator responds by saying not to text or call the friend.
Authorities did not release the names of those who called 911 or those who were mentioned as being inside the club.
Mateen, 29, was killed by police inside the nightclub.
He pledged allegiance to the leader of the Islamic State militant group during the rampage in which he used an assault rifle and pistol that had been legally purchased although he had twice been investigated by the FBI for possible connections with militant Islamist groups.
U.S. authorities believe that Mateen, who lived in Fort Pierce, Florida, with his wife and young child, was self-radicalized and acted alone without assistance or orders from abroad.
(Reporting by Barbara Liston; Writing by Jon Herskovitz; Editing by Alistair Bell)
Tagged Islamic State, nightclub, Orlando, Orlando shooting | Leave a comment
Florida gator that killed boy likely removed: authorities
(Reuters) – The Florida alligator that killed a vacationing 2-year-old boy at Disney World Resort has likely been removed from the area of the attack, authorities said on Wednesday.
The Florida Fish and Wildlife Conservation Commission said it had suspended trapping activities near where the boy, Lane Graves, of Elkhorn, Nebraska, was attacked last week.
The commission "is confident that the alligator responsible for the attack has been removed," it said in a statement. Trappers have taken six alligators from the area.
The alligator snatched the toddler on June 14 as he played at the edge of the Seven Seas Lagoon, a manmade lake at the Walt Disney Co resort.
Police divers found Lane's body underwater the following afternoon, not far from where he was taken. An autopsy found that he died from drowning and traumatic injuries.
At the time, the resort had "No Swimming" signs that did not mention alligators. Disney has since installed signs by the lagoon warning guests of alligators and snakes.
(Reporting by Laila Kearney; Editing by Daniel Wallis and David Gregorio)
Tagged alligator, Death, Disney World, Florida, Orlando | Leave a comment
Full Orlando 911 transcript released; gunman pledged allegiance to Islamic State
ORLANDO, Fla. (Reuters) – The U.S. Justice Department and the FBI on Monday released what they said was the complete transcript of the phone conversation between the Orlando, Florida, shooter and 911 police operators as he threatened to strap explosives to his hostages.
The release of the full transcript came a few hours after the FBI had issued an edited transcript of the calls.
In the full transcript, the gunman, Omar Mateen, is quoted pledging allegiance to Islamic State leader Abu Bakr al-Baghdadi.
Mateen, 29, killed 49 people at a gay nightclub in Florida on June 12, in the deadliest mass shooting in modern U.S. history. He threatened to detonate a car rigged with bombs and to strap hostages into explosive vests, according to transcripts of the 911 calls he made while police tried to rescue people trapped in the club.
The FBI and Justice Department said they had released a redacted transcript of the conversations because of sensitivity to the interests of survivors and victims' families, and the integrity of the investigation.
But the first transcript led U.S. House of Representative Speaker Paul Ryan and other politicians to call for the release of a full transcript after a political battle over gun violence brewed in the U.S. Congress.
Mateen's conversations with a dispatcher and crisis negotiators were made public as police sought to fend off criticism that they may have acted too slowly to end a three-hour standoff at the Pulse nightclub in Orlando.
"You people are gonna get it and I'm gonna ignite it if they try to do anything stupid," Mateen said during one of the calls, according to the FBI transcript.
(Additional reporting by Letitia Stein in Tampa, Frank McGurty in New York, and Eric Beech, Mohammad Zargham and Patricia Zengerle in Washington; Writing by Fiona Ortiz and Daniel Wallis; Editing by Bill Trott)
Tagged Death, FBI, Florida, Islamic State, Orlando, Orlando shooting, Pulse Massacre, Shooting | Leave a comment