text:
\section{Introduction

Whether the 3D incompressible Navier-Stokes equations can develop
a finite time singularity from smooth initial data with finite
energy is one of the most challenging questions in nonlinear
partial differential equations \cite{Fefferman}. There have been
many previous studies devoted to this challenging question,
see e.g. \cite{Constantin86,CS04,CFM96,DHY05,DHY06,Chae07} and
two recent review articles \cite{BT07,Constantin07}.
There have been a number of attempts to investigate possible
finite time singularity formation of the 3D Euler equations
numerically, see e.g. \cite{GS91,Kerr93,BP94}. So far, the
numerical evidence for a finite time blow-up is not yet conclusive
\cite{HL06,HL07,Hou09}.

Global regularity
results for the 3D Navier-Stokes equations have been obtained
using energy estimates under some smallness assumption on the
initial data \cite{Lady70,MB02, LL11}. It is well known that the
convection term does not play an essential role in energy
estimates due to the incompressibility of the velocity field.
Thus, it is not clear how convection may contribute to global
well-posedness of the 3D incompressible Navier-Stokes equations.

In \cite{HL08}, Hou and Li investigated the stabilizing effect of
convection via an exact 1D model. They found that the convection
term plays an essential role in canceling the destablizing vortex
stretching terms in this 1D model. This observation enabled them
to obtain a pointwise estimate via a Liapunov function which
controls the dynamic growth of the derivative of vorticity.
Motivated by the work of \cite{HL08}, Hou and Lei further
investigated the role of convection by constructing the following
3D model of the axisymmetric Navier-Stokes equations with swirl
\cite{HL09}:
\begin{equation}\label{3DInviscidModel}
\begin{cases}
\partial_tu = \nu\big(\partial_r^2 + \frac{3}{r}\partial_r
  + \partial_z^2\big)u + 2 u\partial_z\psi,\\[-4mm]\\
\partial_t\omega = \nu\big(\partial_r^2 + \frac{3}{r}\partial_r
  + \partial_z^2\big)\omega + \partial_z(u^2),\\[-4mm]\\
- \big(\partial_r^2 + \frac{3}{r}\partial_r
  + \partial_z^2\big)\psi = \omega.
\end{cases}
\end{equation}
When $\nu=0$, we refer to the above model as the 3D inviscid model.
This model derived by using a reformulated Navier-Stokes
equations in terms of a set of new variables
$(u,\omega,\psi)=(u^\theta,\omega^\theta,\psi^\theta)/r$, where
$r=\sqrt{x_1^2+x_2^2}$, $u^\theta$ is the angular velocity,
$\omega^\theta$ the angular vorticity, and $\psi^\theta$ the
angular stream function, see \cite{HL08,HL09}. The only difference
between this 3D model and the reformulated Navier-Stokes equations
is that we neglect the convection term in the model. This new 3D
model shares several well known properties of the full 3D Euler or
Navier-Stokes equations \cite{HL09}. These include an energy
identity for smooth solutions, an artificial incompressible
constraint, a non-blowup criterion of Beale-Kato-Majda type
\cite{BKM84}, a non-blowup criterion of Prodi-Serrin type
\cite{Prodi,Serrin}, and a partial regularity result for the model
\cite{HL09b}, which is an analogue of the
Caffarelli-Kohn-Nirenberg theory \cite{CKN82,Lin88} for the full
Navier-Stokes equations.

Despite the striking similarity at the theoretical level, this 3D
model seems to have a very different behavior from that of the Euler
or Navier-Stokes equations. Numerical study in \cite{HL09} seems to
suggest that the model develop a potential finite time singularity
from smooth initial data with finite energy. However, the mechanism
that leads to the singular behavior of the 3D model seems to be
destroyed when the convection term is added back to the model.
In a recent paper \cite{HSW09}, Hou, Shi and Wang proved rigorously
that the inviscid model can indeed develop a finite time singularity
for a class of smooth initial data with some Neumann-Robin boundary
condition. Moreover, they proved a global well-posedness result for
a class of small smooth initial data. The analysis in \cite{HSW09}
was carried out for a rectangular domain, which does not
apply to the axisymmetric domain considered in this paper.

In this paper, we prove that the 3D inviscid model with some
appropriate boundary conditions of Neumann-Robin type can develop
a finite time singularity starting from smooth initial data on a
bounded or an unbounded exterior axisymmetric domain. Moreover, we
obtain a global well-posedness result for a class of large smooth
initial data under some Dirichlet boundary condition.

Our analysis in this paper is similar in spirit to that of
\cite{HSW09}. However, there are several new ingredients in this
work. The first one is that our blowup result applies to a bounded
or unbounded exterior domain in the axisymmetric geometry. The
local well-posedness of the 3D model with a boundary condition of
the Neumann-Robin type is more complicated than the case
considered in \cite{HSW09} and involves the use of the modified
Bessel function. The second ingredient is to construct a special
positive test function that satisfies several requirements. In the
case of a bounded domain, we use the first eigenfunction of the
Laplacian operator with homogeneous Dirichlet boundary condition.
In the case of an unbounded exterior domain, a positive and
decaying eigenfunction of the Laplacian operator does not exist.
This requires us to relax the constraints on the test function.
The third ingredient is an improved estimate which enables us to
establish the global regularity of the 3D inviscid model for a
class of initial boundary value problem with large initial data.

The paper is organized as follows: In Section 2 we will state our
main results and present our main ideas of their proofs.
Section 3 is devoted to proving the finite time singularity of the
3D inviscid model.  In Section 4 we present our global well-posedness
result. Finally, we prove the local well-posedness of the initial
boundary value problem in Section 5.

\section{Main Results}

In this section we set up our problem and state our main results.
First of all, let us recall that the 3D model
\eqref{3DInviscidModel} is formulated in terms of a set of new
variables
$u = \frac{u^\theta}{r}$, $\omega =\frac{\omega^\theta}{r}$,
$\psi = \frac{\psi^\theta}{r}.$
Due to this change of variables, the original three-dimensional
Laplacian operator for $\psi^\theta$ has been changed into a
five-dimensional Laplacian operator for $\psi$ in the axisymmetric
cylindrical coordinate in \eqref{3DInviscidModel}. Thus we can
reformulate our 3D inviscid model in the three-dimensional
axisymmetric cylindrical domain
\begin{equation}\nonumber
D(\gamma_1, \gamma_2) = \{(x_1, x_2, z) \in \mathbb{R}^3: \gamma_1
\leq r = \sqrt{x_1^2 + x_2^2} < \gamma_2; 0 \leq z \leq 1\}
\end{equation}
as a five-dimensional problem in the
axisymmetric cylindrical domain
\begin{equation}\nonumber
\Omega(\gamma_1, \gamma_2) = \{(x_1, \cdots, x_4, z) \in
\mathbb{R}^5: \gamma_1 \leq r = \big(\sum_{j =
1}^4x_j^2\big)^{\frac{1}{2}} < \gamma_2; 0 \leq z \leq 1\} \;.
\end{equation}
It is much more convenient to perform the well-posedness and the
finite time blow-up analysis for our 3D model in the
five-dimensional setting. In the remaining part of the paper, we
will carry out our analysis in this axisymmetric five-dimensional
domain.

Denote
\begin{align}\label{set-1}
S_{\rm exterior}\equiv\left\{\beta > 0 \quad | \quad \beta\neq\frac{
k\int_0^{\infty}e^{-k\cosh(\theta)}\cosh^2(\theta)d\theta}{
\int_0^{\infty}e^{-k\cosh(\theta)}\cosh(\theta)d\theta},\ \forall
k\in\mathbb{Z}^{+}\right\}.
\end{align}
Now we are ready to state the first result of this paper which is
concerned with the local well-posedness of classical solutions to
the 3D inviscid model with a Neumann-Robin
type boundary condition on the exterior domain $\Omega(1, \infty)$.
\begin{thm}\label{thm-local-exterior}
Let $S_{\rm exterior}$ be defined in \eqref{set-1} and $\beta \in
S_{\rm exterior}$. Consider the initial-boundary value problem of
the 3D model \eqref{3DInviscidModel} with the initial data
\begin{equation}\label{data-1}
u_0 \in H^3(\Omega(1, \infty)),\ \ \psi_0 \in H^4(\Omega(1,
\infty)),
\end{equation}
\begin{equation}\label{data-11}
u_0^2 > 0\ {\rm for}\ z \neq 0\ {\rm and}\ z \neq 1,\quad u_0|_{z
= 0} = u_0|_{z = 1} = 0
\end{equation}
and the Neumann-Robin type boundary condition
\begin{equation}\label{bd-1}
(\psi_r + \beta\psi)|_{r = 1} = 0,\quad {\psi_z}|_{z = 0} =
{\psi_z}|_{z = 1} = 0.
\end{equation}
Then there exists a unique smooth solution $(u, \psi)$ to the 3D
inviscid model with the initial data
\eqref{data-1}-\eqref{data-11} and the boundary condition
\eqref{bd-1} on $[0, T)$ for some $T
> 0$. Moreover, we have
\begin{equation}\label{2-4-1}
u \in C\big([0, T), H^3(\Omega(1, \infty))\big),\quad \psi \in
C\big([0, T), H^4(\Omega(1, \infty))\big).
\end{equation}
\end{thm}

The proof of Theorem \ref{thm-local-exterior} relies on an
important property of the elliptic operator with the mixed
Neumann-Robin type boundary condition. Note that the boundary
condition in \eqref{bd-1} is not the third type. To recover the
standard elliptic regularity estimate, we need to study the
spectral property of the differential operator which requires that
$\beta \in S_{\rm exterior}$. We remark that the local
well-posedness analysis for \eqref{3DInviscidModel} with a mixed
Dirichlet-Robin boundary condition has been established in
\cite{HSW09} where the non-standard boundary condition is imposed
on the axial direction. Here our non-standard boundary condition
is imposed on the radial direction. The local well-posedness in
such case involves the use of modified Bessel function and is more
involved. The proof of Theorem \ref{thm-local-exterior} will be
deferred to Section 5.

Next, we state the finite time blowup result of the exterior
problem \eqref{3DInviscidModel}, \eqref{data-1},\eqref{data-11}
and \eqref{bd-1}.
\begin{thm} \label{thm-bu-exterior}
Suppose that all the assumptions in Theorem
\ref{thm-local-exterior} are satisfied.
Let $\beta\geq2+2\sqrt{1+\frac{\pi^2}{4}}$,
$\alpha=\frac{\beta}{2}$ and
\begin{align}\label{2-4}
\phi(r,z)=\theta(r)\sin(\pi z),\ \theta(r)=e^{-\alpha r^2},\
\Phi(r,z)=\phi_{rr}+\frac{3}{r}\phi_r+\phi_{zz}.
\end{align}
Then the solution of the 3D inviscid model
will develop a finite time singularity in the $H^3$ norm provided
that
\begin{align}\label{2-5}
\int_0^1 \int_1^\infty \Phi\log (u^2_0) r^3 drdz > 0,\quad
\int_0^1 \int_1^\infty \Phi\psi_{0z} r^3 drdz > 0
\end{align}
and
\begin{eqnarray}\label{2-6}
\int_0^1 \int_1^\infty\partial_z\psi_0 \Phi r^3drdz\Big)^2
\geq \frac{16}{c_0}\Big(\int_0^1 \int_1^\infty(\log u_0^2)\Phi
r^3drdz\Big)^3,
\end{eqnarray}
where $c_0$ is a positive constant defined in \eqref{c0}.
\end{thm}
The proof of Theorem \ref{thm-bu-exterior} is in spirit similar to
that of Theorem 1.1 in \cite{HSW09}. The main ingredient here is
to construct a special positive test function which meets our
requirements on the unbounded domain case. In
\cite{HSW09}, the authors can take the product of sine
functions in the $x-y$ domain as a testing function since the
domain is a rectangular domain. In the case of a unbounded exterior
domain in the axisymmetric geometry, a positive and decaying
eigenfunction does not seem to exist. This requires us to relax
the constraints on the test function. We will present the details
of the proof of Theorem \ref{thm-bu-exterior} in Section 3.

\begin{rem}
We remark that similar results in Theorem \ref{thm-local-exterior}
and \ref{thm-bu-exterior} are also true in the bounded domain case
$\Omega(0, 1)$. We will not present this result here. A more interesting
result would be to obtain a similar result for the case of
$\Omega(0, \infty)$ with an initial boundary condition whose energy is
conserved in time. This would require a different technique.
We will report it in a forthcoming paper.
\end{rem}

In Theorem 1.1 of \cite{HSW09}, the authors proved the finite time
singularity of the 3D inviscid model in a
rectangular domain. Their Robin boundary condition is imposed on
the axial boundary $z = 1$.  Our next theorem extends their result
to the case of a bounded axisymmetric domain $\Omega(0, 1)$.

Let $(\lambda_k, \theta_k(r))$ be the eigenvalue-eigenfunction
pair of the following Dirichlet eigenvalue problem:
\begin{align}\label{eg1}
\begin{cases}
-(\partial_r^2 + \frac{3}{r}\partial_r)  \theta_k=\lambda_k \theta_k,\quad r\in[0,1),\\
\theta_k|_{r=1}=0.
\end{cases}
\end{align}
Define
\begin{eqnarray}\label{2-8}
S_{\rm interior} \equiv \{\beta > 0 \;|\; \beta\ne \lambda_k,
\beta \neq
\frac{\sqrt{\lambda_k}(e^{\sqrt{\lambda_k}}+e^{-\sqrt{\lambda_k}})}{e^{\sqrt{\lambda_k}}-e^{-\sqrt{\lambda_k}}}
\mbox{ for all } \; k=1, 2, \cdots\},
\end{eqnarray}
and
\begin{align}\label{phi-tf}
 \phi(r,z)=\frac{e^{-\alpha (z-1)}+e^{\alpha
(z-1)}}{2} \theta_1(r).
\end{align}
Moreover, we assume that $\alpha$, $\beta$ satisfy
\begin{equation}\label{2-10}
0<\alpha<\sqrt{\lambda_1},\quad \beta = \frac{\lambda_1}{\alpha}
\frac{e^{\alpha }-e^{-\alpha }}{ e^{\alpha }+e^{-\alpha }}
>{\sqrt{\lambda_1}}\left(\frac{e^{\sqrt{\lambda_1}}+e^{-\sqrt{\lambda_1}}}
{e^{\sqrt{\lambda_1}}-e^{-\sqrt{\lambda_1}}} \right ).
\end{equation}
We can prove the following local-well-posedness and finite time blow-up
results.
\begin{thm}\label{thm-bd}
(A) {\it Local well-posedness}.
Let $S_{\rm interior}$ be defined in \eqref{2-8} and $\beta \in
S_{\rm interior}$. Consider the initial-boundary value problem of
the 3D model \eqref{3DInviscidModel} with the initial data
\begin{equation}\label{data-2}
u_0 \in H^3(\Omega(0, 1)),\ \ \psi_0 \in H^4(\Omega(0, 1)),
\quad u_0|_{z = 0} = u_0|_{z = 1} = 0
\end{equation}
and the Dirichlet-Robin type boundary condition
\begin{equation}\label{bd-2}
\psi|_{r = 1} = \psi|_{z = 1} = 0,\quad {\psi_z + \beta\psi}|_{z =
0} = 0.
\end{equation}
Then there exists a unique smooth solution $(u, \psi)$ to the 3D
inviscid model with the initial data
\eqref{data-2} and the boundary condition \eqref{bd-2} on $[0, T)$
for some $T > 0$. Moreover, we have
\begin{equation}\label{2-13}
u \in C\big([0, T), H^3(\Omega(0,1))\big),\quad \psi \in
C\big([0, T), H^4(\Omega(0,1))\big).
\end{equation}
(B) {\it Finite time blow-up}.
Suppose \eqref{2-10} is satisfied and $u_0^2 > 0 $ for $0 < z < 1$.
If $u_0$ and $\psi_0$ satisfy
\begin{align}\nonumber
\int_0^1 \int_0^1 (\log u_0^2)\phi r^3\mathrm{d} {r}\mathrm{d} z > 0,\quad
\int_0^1 \int_0^1 \psi_{0z}\phi r^3\mathrm{d} {r}\mathrm{d} z
> 0,
\end{align}
and
\begin{eqnarray}\nonumber
\Big(\int_0^1 \int_0^1\partial_z\psi_0 \phi r^3drdz\Big)^2 \geq
\frac{1}{c_1}\Big(\int_0^1 \int_0^1 (\log u_0^2)\phi
r^3drdz\Big)^3,
\end{eqnarray}
for some absolute constant $c_1 > 0$, then the
solution of the 3D inviscid model will
develop a finite time singularity in the $H^3$ norm.
\end{thm}

The local well-posedness of the initial-boundary value problem for
3D model in Theorem \ref{thm-bd} can be carried out using almost
the same argument as that in \cite{HSW09} by replacing the first
eigenfunction $\sin \pi x_1\sin\pi  x_2\sin\pi  x_3\sin\pi  x_4$
of the rectangular domain by the first eigenfunction $\phi_1(x)$ of the
unit ball in $\mathbb{R}^4$. The finite time blow-up result can
be proved in exactly the same way as in \cite{HSW09}.
Since the analysis is essentially the same as that in \cite{HSW09},
we will omit the proof of Theorem \ref{thm-bd} in this paper.

The last theorem extends the global existence result in Theorem
6.1 in \cite{HSW09} to the axisymmetric domain $\Omega(0, 1)$.
The most interesting aspect of this result is that the initial
condition can be made as large as we wish in the Sobolev space.
This is achieved by effectively imposing a sufficiently large
negative boundary
condition for $\partial_z\psi |_{\partial \Omega(0, 1)} = -M$
with $M$ being a large positive constant.

\begin{thm}\label{thm1.2}
Let $M>0 $ an arbitrarily large constant and $s \geq 3$.
Assume that $u_0 \in H^s(\Omega(0, 1))$,  $\psi_0 \in
H^{s+1}(\Omega(0, 1))$ with $u_0(r, 0) = u_0(r, 1) = 0$ and
$\psi_0|_{r = 1} = - Mz$, $\partial_z\psi_0|_{z = 0} =
\partial_z\psi_0|_{z = 1} = - M$. Then the 3D inviscid model
with the initial and boundary data
\begin{equation}\label{data-3}
u(0, \cdot) = u_0(\cdot),\quad \psi(0, \cdot) = \psi_0(\cdot),
\end{equation}
and
\begin{equation}\label{data-31}
\psi(t, 1, z) = - Mz,\ \partial_z\psi(t, r, 0) = \partial_z\psi(t,
r, 1) = -M
\end{equation}
admits a unique global smooth solution $(u, \psi)$ with $u \in
C\big([0, \infty); H^s(\Omega(0, 1))\big)$, $\psi \in C\big([0,
\infty); H^{s+1}(\Omega(0, 1))\big)$ provided that
\begin{eqnarray}\label{data-4}
\|\nabla \partial_z\psi_0\|_{H^{s-1}} \leq M/(8C_s^2), \quad
\|u_0^2\|_{H^s} \leq M^2/(4C_s^3),
\end{eqnarray}
where $C_s$ is an absolute positive constant depending on $s$ and
$\Omega$ only. Moreover, we have
\begin{equation}\label{ap-3}
\|u(t)^2\|_{H^s(\Omega(0, 1))}\le
C_s\|u_0^2\|_{H^s(\Omega(0, 1))}e^{-2Mt},
\end{equation}
and
\begin{equation}\label{ap-4}
\|\nabla\partial_z\psi\|_{H^{s-1}(\Omega(0, 1))}\le
\|\nabla\partial_z\psi_0\|_{H^{s-1}(\Omega(0, 1))} +
\frac{C_s}{2M}\|u_0^2\|_{H^{s}(\Omega(0, 1))}.
\end{equation}
\end{thm}

We will present the proof of Theorem \ref{thm1.2} in Section 4.

\section{Finite Time Singularity in the Exterior Domain}

In this section, we present the proof of Theorem
\ref{thm-bu-exterior}, which shows that the 3D inviscid model develops
a finite time singularity in the exterior domain.

\noindent
{\bf Proof of Theorem \ref{thm-bu-exterior}}.
We will prove Theorem \ref{thm-bu-exterior} by
contradiction, as in \cite{HSW09}. By the local well-posedness result,
we know that the initial boundary value problem of the 3D inviscid model
has a unique solution $u \in H^3(\Omega(1, \infty))$ and
$\psi \in H^4(\Omega(1, \infty))$ for $ 0 \leq t \leq T$ for some $T>0$.
Let $T_b$ be the largest time for which our 3D inviscid
model has a unique smooth solution $u \in H^3(\Omega)$ and
$\psi\in H^4(\Omega)$ for $ 0 \leq t < T_b$. We will prove that
$T_b < \infty$. Suppose that $T_b = \infty$. Then we have
\begin{equation}\label{3-1}
u \in C\big([0, \infty), H^3(\Omega(1, \infty))\big),\quad \psi
\in C\big([0, \infty), H^4(\Omega(1, \infty))\big).
\end{equation}
We will prove that \eqref{3-1} would lead to a contradiction.

Define $\phi$ and $\Phi$ as in Theorem \ref{thm-bu-exterior}.
By a straightforward calculation, we have
\begin{align}\label{3-2}
\Phi(r,z)=[4\alpha^2r^2-(8\alpha+\pi^2)]\phi(r, z).
\end{align}
For $\alpha\geq1+\sqrt{1+\frac{\pi^2}{4}}$, it is easy to get that
\begin{equation}\nonumber
4\alpha^2r^2-(8\alpha+\pi^2) \geq 4\alpha^2-(8\alpha+\pi^2) \geq
0\quad {\rm for}\ r \geq 1.
\end{equation}
Consequently, we have
\begin{align}\label{3-3}
\Phi(r,z) \geq 0\quad {\rm for}\  1 \leq r, 0 \leq z \leq 1.
\end{align}
On the other hand, due to the boundary condition on the initial
data $u_0$ in \eqref{data-11}, one can use the first equation in
\eqref{3DInviscidModel} with $\nu=0$ to solve $u$:
\begin{equation}\nonumber
u^2(t, r, z) = u_0^2(r, z)\exp\{4\int_0^t\partial_z\psi(s, r, z)
ds\}\quad {\rm for}\ z \neq 0, 1.
\end{equation}
Hence, by continuity, as long as the solution is smooth, one also
has
\begin{equation}\label{3-4}
u(t, r, 0) = u(t, r, 1) = 0.
\end{equation}

Multiplying the second equation in \eqref{3DInviscidModel} with
$\nu=0$  by
$\phi_z$ and integrating over $\Omega(1, \infty)$, we have

\begin{align}\label{3-4-a}
- \int_0^1 \int_1^\infty (\partial_r^2 + \frac{3}{r}\partial_r +
\partial_z^2)\psi_t \phi_z r^3drdz = \int_0^1 \int_0^\infty
\partial_zu^2\phi_zr^3drdz.
\end{align}
On one hand, using \eqref{3-4} and performing integration by parts,
we get
\begin{align}\label{3-4-b}
\int_0^1\int_1^\infty \partial_zu^2\phi_zr^3drdz = -
\int_0^1\int_1^\infty u^2\partial_z^2\phi r^3drdz = \pi^2
\int_0^1 \int_1^\infty u^2\phi r^3drdz.
\end{align}
On the other hand, using the boundary condition \eqref{bd-1}
and performing integration by parts, we obtain by
noting that $\theta_r(1)+\beta\theta(1) = 0$ that
\begin{eqnarray}\label{3-4-c}
&&- \int_0^1 \int_1^\infty (\partial_r^2 + \frac{3}{r}\partial_r
  + \partial_z^2)\psi_t \phi_z r^3drdz\\\nonumber
&&= \frac{d}{dt}\int_0^1(\psi_r\phi_z - \psi\partial_{rz}^2\phi)|_{r=1}dz
  - \frac{d}{dt}\int_0^1 \int_1^\infty \psi(\partial_r^2 +
  \frac{3}{r}\partial_r) \phi_z r^3drdz\\\nonumber
&&\quad +\ \frac{d}{dt}\int_0^1 \int_1^\infty \psi_z\partial_z^2
  \phi r^3drdz\\\nonumber
&&= \pi\theta(1)\frac{d}{dt}\int_0^1(\cos\pi z)\big(\psi_r
  + \beta \psi \big)|_{r=1} dz
  + \frac{d}{dt}\int_0^1 \int_1^\infty \psi_z\Phi r^3drdz\\
&&= \frac{d}{dt}\int_0^1 \int_1^\infty  \psi_z\Phi r^3drdz.
\end{eqnarray}
Combining \eqref{3-4-c} with \eqref{3-4-a}-\eqref{3-4-b} gives
\begin{eqnarray}\label{3-5}
\frac{d}{dt}\int_0^1 \int_1^\infty \psi_z\Phi r^3drdz = \pi^2
\int_0^1 \int_1^\infty u^2\phi r^3drdz.
\end{eqnarray}

Multiplying the first equation in \eqref{3DInviscidModel}
with $\nu=0$ by $\Phi$ and integrating on $\Omega(1, \infty)$ yield
\begin{align}\label{3-6}
\frac{d}{dt}\int_0^1 \int_1^\infty (\log u^2) \Phi r^3drdz =
4\int_0^1 \int_1^\infty  \psi_{z} \Phi r^3drdz.
\end{align}
Since $\int_0^1 \int_1^\infty \partial_z\psi_0\Phi r^3drdz > 0$,
we conclude from \eqref{3-5} that
\begin{eqnarray}\label{3-7}
\int_0^1 \int_1^\infty \psi_z\Phi r^3drdz > 0\quad {\rm for\
all}\ t \geq 0.
\end{eqnarray}
It follows form \eqref{3-6}-\eqref{3-7} and the condition
$\int_0^1 \int_1^\infty (\log u_0^2)\Phi r^3drdz > 0$ that
\begin{align}\label{3-8}
\int_0^1 \int_1^\infty (\log u^2)\Phi r^3drdz > 0\quad {\rm for\
all}\ t \geq 0.
\end{align}
Consequently, we obtain by using \eqref{3-2} and \eqref{3-8} that
\begin{eqnarray}\label{3-9}
&&\Big(\int_0^1 \int_1^\infty (\log u^2)\Phi
  r^3drdz\Big)^2 \leq \Big(\int_0^1 \int_1^\infty (\log^+ u^2)\Phi
  r^3drdz\Big)^2\\\nonumber
&&\leq 4\Big(\int_0^1 \int_1^\infty  |u|\Phi
  r^3drdz\Big)^2\\\nonumber
&&\leq 4 \int_0^1 \int_1^\infty |u|^2\phi
  r^3drdz \int_0^1 \int_1^\infty \big(\frac{\Phi}{\phi}\big)^2\phi
  r^3drdz\\\nonumber
&&\leq \frac{8c_0\pi^2}{3}\int_0^1 \int_1^\infty |u|^2\phi
  r^3drdz,
\end{eqnarray}
where $c_0$ is defined by
\begin{eqnarray}\label{c0}
c_0 = \frac{3}{2\pi^2}\int_0^1 \int_1^\infty \big(4\alpha^2r^2-(8\alpha+\pi^2)\big)^2\phi
  r^3drdz < \infty.
\end{eqnarray}
Using \eqref{3-5}, \eqref{3-6} and \eqref{3-9}, we get
\begin{eqnarray} \label{3-10}
\frac{d^2}{dt^2}\int_0^1 \int_1^\infty (\log u^2)\Phi r^3drdz &= &
  4\pi^2 \int_0^1 \int_1^\infty  u^2\phi r^3drdz\\\nonumber
&\geq & \frac{3}{2c_0}\Big(\int_0^1 \int_1^\infty (\log u^2) \Phi
  r^3drdz\Big)^2.
\end{eqnarray}
Let
\begin{equation}
\label{def-Y}
Y(t) \equiv \int_0^1 \int_1^\infty (\log u^2) \Phi r^3drdz\;.
\end{equation}
Then \eqref{3-10} implies
\begin{equation}
\label{3-11}
Y''(t) \geq \frac{3}{2c_0} Y(t).
\end{equation}
It follows from \eqref{3-6}-\eqref{3-7} that $Y'(t) > 0$.
Multiplying \eqref{3-11} by $Y'(t)$ and integrating in
time from 0 to $t$, we get
\begin{eqnarray} \nonumber
&&\Big(Y'(t)\Big)^2 \geq \Big(Y'(0)\Big)^2 - \frac{1}{c_0} Y(0)^3
+\ \frac{1}{c_0} Y(t)^3\\\nonumber
&&= \Big(4\int_0^1 \int_1^\infty \partial_z\psi_0 \Phi
  r^3drdz\Big)^2 - \frac{1}{c_0}\Big(\int_0^1 \int_1^\infty
  (\log u_0^2)\Phi r^3drdz\Big)^3
+\ \frac{1}{c_0} Y(t)^3 \;.
\end{eqnarray}
The condition \eqref{2-6} implies
\begin{eqnarray} \label{dY(t)}
\Big(Y'(t)\Big)^2 \geq \frac{1}{c_0} Y(t)^3.
\end{eqnarray}
Since $ Y'(t) >0$, it is easy to solve \eqref{dY(t)} to
conclude that
\begin{eqnarray}\label{4-5}
\int_0^1 \int_1^\infty (\log u^2)\Phi r^3drdz \geq
\frac{4c_0\int_0^1 \int_1^\infty (\log u_0^2) \Phi
r^3drdz}{\Big(2\sqrt{c_0} - t\sqrt{\int_0^1 \int_1^\infty
(\log u_0^2) \Phi r^3drdz}\Big)^2} \;\;.
\end{eqnarray}
Note that \eqref{3-2} gives
\begin{equation}
\Phi(r,z)=[4\alpha^2r^2-(8\alpha+\pi^2)]\phi(r, z)
= [4\alpha^2r^2-(8\alpha+\pi^2)] e^{-\alpha r^2} \sin(\pi z).
\end{equation}
Since $r\geq 1$, it is easy to show that $\Phi$ satisfies
\begin{equation}
0 \leq \Phi(r,z) \leq 4\alpha^2r^2 e^{-\alpha r^2} \leq
 4\alpha^2 e^{-\alpha}, \quad r \geq 1.
\end{equation}
Thus, we have
\begin{eqnarray}
\label{4-6}
\int_0^1 \int_1^\infty (\log u^2)\Phi r^3drdz &\leq &
\int_0^1 \int_1^\infty (\log^+ u^2)\Phi r^3drdz \\ \nonumber
&\leq & 4\alpha^2 e^{-\alpha} \int_0^1 \int_1^\infty u^2 r^3drdz .
\end{eqnarray}
Combining \eqref{4-5} with \eqref{4-6} gives
\begin{equation}
\label{4-7}
4\alpha^2 e^{-\alpha} \int_0^1 \int_1^\infty  u^2 r^3drdz \geq
\frac{4c_0\int_0^1 \int_1^\infty (\log u_0^2)\Phi
r^3drdz}{\Big(2\sqrt{c_0} - t\sqrt{\int_0^1 \int_1^\infty
(\log u_0^2)\Phi r^3drdz}\Big)^2} \; .
\end{equation}
On one hand,  we have $\int_0^1 \int_1^\infty u^2 r^3drdz < \infty$
for all times by \eqref{3-1}. On the other hand, the right hand side
of \eqref{4-7} will blow up as
$t \rightarrow \frac{2\sqrt{c_0}}{\sqrt{\int_0^1\int_0^\infty(\log u_0^2)\Phi r^3drdz}}$. This is clearly a contradiction. This contradiction implies
that the assumption \eqref{3-1} can not be valid and the solution
must blow up in a finite time in the $H^3$ norm no later than
$T^* = \frac{2\sqrt{c_0}}{\sqrt{\int_0^1\int_0^\infty (\log u_0^2)\Phi r^3drdz}}$. This completes the proof of Theorem \ref{thm-bu-exterior}.

\section{Global Regularity with Large Data}

This section is devoted to proving Theorem \ref{thm1.2}.

\noindent
{\bf Proof of Theorem \ref{thm1.2}.}
First of all, the local well-posedness of the initial boundary value
problem
can be established by using an argument similar to that of \cite{HSW09}.
Now let us assume that $(u, \psi)$ is a local smooth solution
satisfying boundary condition \eqref{data-31} such that
$u \in C\big([0, T); H^s(\Omega(0, 1))\big)$,
$\psi \in C\big([0, T); H^{s+1}(\Omega(0, 1))\big)$ for some $T > 0$.
We are going to show that $T = \infty$.

Denote by
\begin{equation}\nonumber
\widetilde{v} = - \partial_z\psi,\quad \widetilde{u} = u^2.
\end{equation}
It is easy to see that
\begin{equation}\nonumber
\widetilde{v} \in C\big([0, T); H^s(\Omega(0, 1))\big),\quad
\widetilde{u} \in C\big([0, T); H^s(\Omega(0, 1))\big).
\end{equation}
Differentiating the second equation in \eqref{3DInviscidModel} with
$\nu=0$ with respect to $z$, we get
\begin{equation}\nonumber
(\partial_r^2 + \frac{3}{r}\partial_r +
\partial_z^2)\partial_t\widetilde{v} = \partial_z^2\widetilde{u}.
\end{equation}
Note that $\partial_t\widetilde{v}|_{\partial\Omega(0, 1)} = 0$.
We define $g \equiv \Delta_5^{-1} f$ as the solution of the
Laplacian equation with the homogeneous Dirichlet boundary condition:
\begin{equation}\nonumber
(\sum_{i = 1}^4\partial_{x_i}^2 +
\partial_z^2) g = f,\quad g|_{\partial\Omega(0,
1)} = 0,\quad \forall f \in L^2(\Omega(0, 1)).
\end{equation}
Then, we can reformulate the 3D inviscid model as follows:
\begin{align}\nonumber
\begin{cases}
\widetilde{u}_t =-4\widetilde{u}\widetilde{v},  \\
\widetilde{v}_t= \Delta_5^{-1}\partial_z^2\widetilde{u}.
\end{cases}
\end{align}
Note that the boundary condition in \eqref{data-31} implies that
\begin{equation}\nonumber
\widetilde{v}|_{\partial\Omega(0, 1)} = M .
\end{equation}
If we further denote
\begin{equation}\label{def-v}
v = \widetilde{v} - M,
\end{equation}
we obtain an equivalent system for $\widetilde{u}$ and $v$:
\begin{eqnarray}
\label{eqn-u}
&&\widetilde{u}_t = - 4M\widetilde{u} -4\widetilde{u}v ,  \\
\label{eqn-v}
&&v_t = \Delta_5^{-1}\partial_z^2\widetilde{u},\\
\label{BC-v}
&&v|_{\partial\Omega(0, 1)} = 0.
\end{eqnarray}

Recall the following well-known Sobolev inequality \cite{Foland95}.
Let $u,v \in H^s(\Omega)$ with $s>n/2$ ($n$ is the dimension of
$\Omega$). We have
\begin{eqnarray}
\label{Sobolev-1}
\|uv\|_{H^s(\Omega)}\le C_s \|u\|_{H^s(\Omega)}\|v\|_{H^s(\Omega)}.
\end{eqnarray}
We will also use the Poincar\'e inequality \cite{Evans98}:
\begin{eqnarray}
\label{Sobolev-2}
\|v\|_{H^s(\Omega)}\le C_s \|\nabla v\|_{H^{s-1}(\Omega)} \;,
\end{eqnarray}
if $v|_{\partial\Omega(0, 1)} = 0$. Here $C_s$ is an absolute positive
constant depending on $s$ and $\Omega$ only.

Taking the $H^s$ norm to the both sides of \eqref{eqn-u} and using
\eqref{Sobolev-1}-\eqref{Sobolev-2}, we obtain
\begin{eqnarray}
\label{eqn-4-1}
\frac{d}{dt} \|\widetilde{u}\|_{H^s} &\leq &  -4 M \|\widetilde{u}\|_{H^s}
+ 4C_s \|\widetilde{u}\|_{H^s} \|v \|_{H^s} \\ \nonumber
&\leq & -4 M \|\widetilde{u}\|_{H^s} + 4 C_s^2 \|\widetilde{u}\|_{H^s}
\|\nabla v \|_{H^{s-1}} \\ \nonumber
& \leq & (-4M + 4 C_s^2 \|\nabla v \|_{H^{s-1}}) \|\widetilde{u}\|_{H^s},
\end{eqnarray}
where we have used \eqref{BC-v}.

Next, we apply $\nabla$ to the both sides of \eqref{eqn-v} and take
the $H^{s-1}$-norm. We get
\begin{eqnarray}
\label{eqn-4-2}
\frac{d}{dt} \|\nabla v\|_{H^{s-1}} &\leq  &
\|\nabla \Delta_5^{-1}\partial_z^2 \widetilde{u} \|_{H^{s-1}} \\ \nonumber
&\leq &
\|\Delta_5^{-1}\partial_z^2 \widetilde{u} \|_{H^{s}} \\ \nonumber
&\leq & C_s\|\partial_z^2 \widetilde{u} \|_{H^{s-2}} \leq C_s \|\widetilde{u} \|_{H^{s}},
\end{eqnarray}
where we have used the standard elliptic regularity estimate for
$\Delta_5^{-1}$.

By the local well-posedness result and the assumption on the initial
condition \eqref{data-4}, we know that there exists a positive $T>0$ such
that we have
\begin{equation}
\label{eqn-4-3}
\|\nabla v (t)\|_{H^{s-1}} \leq \frac{M}{2 C_s^2} , \quad 0 \leq t \leq T.
\end{equation}
Let $T^*$ be the largest time such that \eqref{eqn-4-3} holds. We will
prove that $T^* = \infty$. Suppose $T^* < \infty$. Substituting
\eqref{eqn-4-3} into \eqref{eqn-4-1}, we obtain
\begin{equation}
\label{eqn-4-4}
\frac{d}{dt} \|\widetilde{u}\|_{H^s} \leq  -2 M \|\widetilde{u}\|_{H^s},
\quad 0 \leq t < T^*,
\end{equation}
which implies
\begin{equation}
\label{eqn-4-5}
\|\widetilde{u}\|_{H^s} \leq  \|\widetilde{u_0}\|_{H^s} e^{-2M t},
\quad 0 \leq t < T^*.
\end{equation}
Now substituting \eqref{eqn-4-5} into \eqref{eqn-4-2} yields
\begin{eqnarray}
\label{eqn-4-6}
\|\nabla v\|_{H^{s-1}} &\leq&  \|\nabla v_0\|_{H^{s-1}} +
C_s \|\widetilde{u_0}\|_{H^s} \int_0^t e^{-2Ms} ds \\ \nonumber
&\leq & \|\nabla v_0\|_{H^{s-1}} + \frac{C_s}{2M} \|\widetilde{u_0}\|_{H^s} \\ \nonumber
&\leq &\frac{M}{4 C_s^2} < \frac{M}{2 C_s^2}, \quad 0 \leq t < T^*,
\end{eqnarray}
where we have used the condition \eqref{data-4}. Since
$\|\nabla v\|_{H^{s-1}} \leq \frac{M}{4 C_s^2} < \frac{M}{2 C_s^2}$
for $t < T^*$ and
$\|\widetilde{u}\|_{H^s} \leq  \|\widetilde{u_0}\|_{H^s} e^{-2M T^*}
< \|\widetilde{u_0}\|_{H^s}$ for $t < T^*$, we can use
our {\it a priori} estimates \eqref{eqn-4-1}-\eqref{eqn-4-2} to
show that \eqref{eqn-4-3} remains valid for $ 0\leq t \leq T^* + \delta$
for some $\delta >0$. This contradicts with the assumption that $T^*$
is the largest time such that \eqref{eqn-4-3} holds. This contradiction
implies that $T^* = \infty$ and estimates \eqref{eqn-4-5}-\eqref{eqn-4-6}
remain valid for all times. This completes the proof of
Theorem \ref{thm1.2}.

\section{Local Well-Posedness in the Exterior Domain}

The local well-posedness theory of the initial-boundary value
problem of the 3D model \eqref{3DInviscidModel} with
\eqref{data-1} and \eqref{bd-1} is based on the following lemma
\ref{lemA-1}. Once the lemma is proved, the proof can be carried
out in exactly the same way as the local well-posedness analysis
presented in \cite{HSW09}. Hence, we will only present the
proof of the lemma \ref{lemA-1} in a slightly modified domain
with $1 < r < \infty$ and $0 < z < \pi$.
\begin{lem}\label{lemA-1}
For any given $\omega\in H^{s-2}(\Omega(1, \infty))$ with
$s\geq2$, there exists a unique solution $\psi\in H^s(\Omega(1,
\infty))$ to the boundary value problems
\begin{align}\label{A-2}
\begin{cases}
- \big(\partial_r^2 + \frac{3}{r}\partial_r
  + \partial_z^2\big)\psi = \omega,\quad 1 < r,\; 0 < z < \pi,\\
\psi_r +\beta\psi|_{r=1}=0,\quad \psi_z|_{z=0} = \psi_z|_{z=\pi} =
0,
\end{cases}
\end{align}
where $\beta \in S_{\rm exterior}$ is a constant. Furthermore, we
have the following estimate:
\begin{align}\label{A-est}
\|\psi\|_{H^s(\Omega(1, \infty))} \leq
C\|\omega\|_{H^{s-2}(\Omega(1, \infty))},
\end{align}
where $C$ is an absolute positive constant.
\end{lem}
\begin{proof}
Let us decompose
$\psi=\psi^{(1)}+\psi^{(2)},$
where $\psi^{(1)}$ is the solution of the elliptic equation
with the following mixed Dirichlet-Neumann boundary condition:
\begin{align}\label{A-3}
\begin{cases}
- \big(\partial_r^2 + \frac{3}{r}\partial_r
  + \partial_z^2\big)\psi^{(1)} = \omega,\quad {\rm in}\ \Omega(1, \infty),\\
\psi_z^{(1)}|_{z=0} = \psi_z^{(1)}|_{z=\pi}= 0, \quad \psi^{(1)}|_{r=1} = 0, \quad \psi^{(1)}
\rightarrow 0\ {\rm as}\ r \rightarrow \infty.
\end{cases}
\end{align}
Then $\psi^{(2)}$ satisfies
\begin{align}\label{A-4}
\begin{cases}
- \big(\partial_r^2 + \frac{3}{r}\partial_r
  + \partial_z^2\big)\psi^{(2)} = 0,\quad {\rm in}\ \Omega(1, \infty),\\
[\psi^{(2)}_r +\beta\psi^{(2)}]|_{r=1}= - \psi^{(1)}_r|_{r=1},\\
\psi^{(2)}_z|_{z=0}= \psi^{(2)}_z|_{z=\pi} = 0.
\end{cases}
\end{align}
The standard elliptic theory gives that $\psi^{(1)}\in
H^s(\Omega(1, \infty))$ and $\|\psi^{(1)}\|_{H^s(\Omega(1,
\infty))}\leq \|\omega\|_{H^{s-2}(\Omega(1, \infty))}$. It remains
to show that the Neumann-Robin problem \eqref{A-4} is
well-posed.

Let us perform the cosine transform to \eqref{A-4} with respect to
$z$ variable, which gives
\begin{align}\label{A-5}
\begin{cases}
- \big(\partial_r^2 + \frac{3}{r}\partial_r)\widehat{\psi^{(2)}} + k^2\widehat{\psi^{(2)}} = 0,\\
[\widehat{\psi_r^{(2)}}
+\beta\widehat{\psi^{(2)}}]|_{r=1}=-\beta\widehat{\psi^{(1)}_r}(1,k),
\end{cases}
\end{align}
where the cosine transform $\ \widehat{\cdot}\ $ is defined as:
\begin{align}
\widehat{\psi^{(2)}}(r,k)=\frac{2}{\pi}\int_0^{\pi}\psi^{(2)}(r,z)\cos(kz)dz.
\end{align}
Let $\widehat{\psi^{(2)}}(r,k)=\frac{1}{r}f(rk, k)$.
Then \eqref{A-5} can be written in terms of $f$ as
\begin{align}\nonumber
k^2\frac{d^2}{dr^2}f(rk)+\frac{k}{r}\frac{d}{dr}f(rk)-(k^2+\frac{1}{r^2})f(rk)=0,
\end{align}
which is equivalent to the following modified Bessel equation
\begin{align}\nonumber
r^2f''(r, k)+ rf'(r, k)-(1+r^2)f(r, k)=0.
\end{align}

The general solution of the modified Bessel equation with the
decaying property as $r \rightarrow \infty$ is given by modified
Bessel function:
\begin{align}\nonumber
f(r, k)= C(k)K(r),
\end{align}
where $K(r)$ is the modified Bessel function and can be
represented in an integration form as follows
\begin{align}\nonumber
K(r) = \int_0^{\infty}e^{-r\cosh(\theta)}\cosh(\theta)
d\theta,\quad K(r) \rightarrow 0\ {\rm as}\ r \rightarrow \infty.
\end{align}
In fact, we have $0 < K(r) \leq c_2r^{-1/2}e^{-r}$ as
$r \rightarrow \infty$ for some positive constant $c_2$. Thus, the
general solution of $\widehat{\psi^{(2)}}(k,r)$ is given by
\begin{align}
\widehat{\psi^{(2)}}(r,k)=\frac{C(k)}{r}K(rk).\label{A-10}
\end{align}
The boundary condition of $\psi^{(2)}$ in \eqref{A-5} can be used
to determine $C(k)$ as follows:
\begin{align}
C(k)=\frac{-\beta\widehat{\psi^{(1)}}(k,1)}{(\beta-1)K(k)+kK'(k)}.\label{A-11}
\end{align}
Note that $C(k)$ in \eqref{A-11} is well-defined for
$\beta\in S_{\rm exterior}$. The remaining part of the proof is
exactly the same as in \cite{HSW09}. We can show that
$\psi^{(2)}$ will have the same regularity property as $\psi^{(1)}$.
This proves our lemma. We will omit the details here.
\end{proof}

\section*{Acknowledgement}
This work was supported in part by NSF by Grant DMS-0908546. Zhen
Lei would like to thank the Applied and Computational Mathematics
of Caltech and Prof. Thomas Hou for hosting his visit and for
their hospitality during his visit. Zhen Lei was in part supported
by NSFC (grant No.11171072), the Foundation for Innovative
Research Groups of NSFC (grant No.11121101), FANEDD, Innovation
Program of Shanghai Municipal Education Commission (grant
No.12ZZ012) and SGST 09DZ2272900. The research of Dr. S. Wang was
supported by China 973 Program(Grant no. 2011CB808002), the Grants
NSFC 11071009 and PHR-IHLB 200906103.

\frenchspacing
\bibliographystyle{plain}

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I have a degree in aircraft engineering. I just got a job in an airline ( 145 aproved) as a cabin technician. Could anyone tell me how to obtain my easa license and how long will it take ? I havent done easa exams . But going to start my exams. The school I completed my degree is not a 147 approved organisation.


text:
PhysicalGeography.net | FUNDAMENTALS eBOOK
OF TERMS
CHAPTER 10: Introduction to the Lithosphere
(i). Plate Tectonics
In the 19th and early 20th centuries, several scientists suggested that the continental masses had the ability to move across the Earth's surface. These early theories of continental drift were based on the following evidence:
Locations of fossil occurrences suggested that some of the continental masses may have been connected in the geological past.
Paleoclimatic evidence indicates that now tropical regions on some continents had polar climates in the past. This may indicate that these regions were located at different latitudes.
Some continents seem to fit together like a jigsaw puzzle.
Some geologic deposits of rocks on the East coast of North and South America are similar to deposits found on the West coast of Africa and Europe.
During the first 30 years of this century the theory of continental drift was actively debated among geo-scientists. However, during the following 30 year period, debate on this theory waned because of the inability of scientists to propose a mechanism to cause the movement of the continental masses.
In the 1960s, the theory was resurrected with the discovery of alternating patterns of rock magnetism in surface sea-floor rocks. Scientists had previously discovered that the magnetic orientation of certain crystals in rocks varies from normal to reversed polarity depending on the date that the rock was formed and solidified. It was also discovered that these magnetic reversals were common and occurred on a regular basis. The polarity patterns found in the rocks at the ocean floor seemed to mirror themselves either side of the mid-oceanic ridge found at the centers of the ocean basins. Further, geologic dating of the rocks indicated the age of the sea-floor rocks increase as one moved away from the mid-oceanic ridge (see Figure 10i-1). Based on this information, scientists developed the theory of sea-floor spreading which suggested that volcanic rift zones at the mid-oceanic ridge represent areas of crustal creation. The following diagram illustrates the process of crustal creation and the magnetic striping process. In Figure 10i-2, illustrations "a" to "c" represent a sequence in time from the past to the present. In illustration a, rocks of normal polarity are being deposited at the rift zone located along the mid-oceanic ridge. As new rock is created, older rock is pushed away from the ridge. The reversed polarity rock shown in this diagram was created before the current normal polarity layer. Illustration b shows the process some time later. In this diagram, we now have four layers of rock with alternating polarity. By the third illustration, sea-floor spreading and changes in magnetic polarity have created six recognizable layers of rock either side of the rift zone.
Figure 10i-2: Creation of oceanic crust on the ocean floor. (Source: U.S. Geological Survey).
The theory of sea-floor spreading started a revolution in the Earth Sciences. Subsequent research discovered that the Earth's surface was composed of a number of oceanic and continental plates that float on top of the asthenosphere (see Figure 10i-3). Other research suggested that convection currents within the Earth's mantle were responsible for the creation of oceanic crust and the drifting of the continents (Figure 10i-4). In this diagram, it is theorized that convection currents within the Earth's mantle cause the creation of new oceanic crust at the mid-oceanic ridges. Oceanic crust is destroyed at areas where this crust type becomes subducted under lighter continental crust. This process also creates the deep oceanic trenches.
Figure 10i-4: Convection currents in the Earth's mantle and their role in oceanic crust formation and destruction. (Source: U.S. Geological Survey).
The theory of plate tectonics offered new and more scientifically sound explanations for a number of observed geologic phenomena. For example, the following diagrams illustrate the three types of plate convergence and describe some of the geologic repercussions of these processes. The first diagram models the tectonic convergence of two oceanic plates (Figure 10i-5).
Figure 10i-5: Collision of two oceanic plates. (Source: U.S. Geological Survey).
In this type of a collision, one of the plates is subducted under the other creating a deep oceanic trench. The Marianas trench in the Pacific ocean is created by the collision of the fast-moving Pacific Plate against the slower moving Philippine Plate. Convergence of two oceanic plates also creates chains of volcanic islands called island arcs. Island arcs are created by the friction of subduction which creates hot plumes of magma at the interface of the two plates. These hot plumes of magma then rise to the Earth's surface to form volcanoes. Another phenomena associated with collision and subduction of the plates is earthquakes. The gliding of one plate under the other is not smooth but jerky producing seismic waves.
The next diagram shows the collision of an oceanic and a continental plate (Figure 10i-6). In this illustration, the oceanic plate subducts under the lighter continental plate. Once again we get the formation of a trench, volcanoes, and earthquakes. Collision causes sediment deposited on the ocean floor to be piled up at the continental plate boundary. The creation of hot magma plumes also causes the continental crust to deform producing mountains.
Figure 10i-6: Collision of a oceanic plate with a continental plate. (Source: U.S. Geological Survey).
In the final illustration two continental plates collide (Figure 10i-7). Once again one of the crustal plates is subducted under the other producing earthquakes. A mountain range is produced at the plate boundaries because of the deformation of rocks. Some of the rocks in the mountain range may be sedimentary and may have been set down in an ocean environment that existed between the two continental crusts prior to collision.
Figure 10i-7: Collision of two continental plates. (Source: U.S. Geological Survey).
In summary, modern plate tectonic theory states that the surface crust of the Earth is composed of many independent segments called plates. These plates have the ability to move horizontally by gliding over the plastic asthenosphere (see Figure 10i-8). In some cases, plates can collide with each other at the plate boundaries causing subduction and the production of earthquakes, volcanoes, mountain building, and oceanic trenches. At other plate boundaries, plates may move away from each other because of sea-floor spreading or horizontally move past one another creating transform faults and earthquakes.
Additional Readings
Internet Weblinks
Citation: Pidwirny, M. (2006). "Plate Tectonics". Fundamentals of Physical Geography, 2nd Edition. Date Viewed. http://www.physicalgeography.net/fundamentals/10i.html
Created by Dr. Michael Pidwirny & Scott Jones University of British Columbia Okanagan
Email Corrections and Suggestions to:
Copyright © 1999-2018 Michael Pidwirny

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text:
Q: Getting reference key after posting after creating a post, its post id is a primary key. how do i get this post id and post it to a date time database table and its a reference key of this table
if (isset($_POST['submit'])) {
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A: No idea what technology you're using, but assuming the createpost method returns the created post info, you can do something like this:
if ($newPost = $post->createpost()){
        global $datetime;
        $datetime->post_id = $newPost['id'];
        ...

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text:
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PHABLABS 4.0 for Photonics
PHABLABS 4.0 was created with the goal of achieving a lasting, positive impact on the way photonics is integrated into the rapidly expanding ecosystem of European Fab Labs and Makerslabs, resulting in a larger and better skilled photonics workforce with superior innovation capacity in photonics to support the next revolution in digitization.
By combining the synergies and know-how of top experts from 11 European photonics institutes with the Fab Lab stakeholders, PHABLABS 4.0 will devise and deliver a set of 33 Photonics Workshops, 11 Photonics Challenger projects and Photonics Toolkits aimed at stimulating creativity, hands-on design, fabrication, experiments, and the building of innovative systems with photonics. All these tools will be created and developed to enhance Fab Labs and Makerslab with photonics activities tailored for 3 different target audiences: young minds (10-14y), students (15y-18y) and young professionals and technicians.
ICFO has become an active member of this European initiative, with the role of leading the WP2 (Photonics challenger projects @ photonics-enhanced Fablabs) as well as coordinating and developing workshops, gender action teams, dissemination activities, and providing support throughout the whole project.
ICFO has selected "Photonics for Life" as the central topic for its workshops and Challenger project, since it will allow participants to understand how photonics is at the very core of imaging devices, diagnostic technologies and a broad range of healthcare applications. ICFO has a consolidated "Light for Health" focus programme, and several research groups working in different topics around "Photonics for Life" and biophotonics, concentrating photonics technologies and applications in fields such as early diagnosis sensor, quality control systems, imaging technologies, and medical devices among others. ICFO collaborates with local hospitals, health care centers, biomedical research centers, Universities and corporations.
The PHABLABS 4.0 project intends to harness the power of the growing innovation ecosystem of the Fab Labs and equip it with sufficient material to really engage, excite and educate youngsters, students, technicians and young professionals alike in the skills of working and innovating with light. The ultimate impact of PHABLABS 4.0 will be seen in the emergence of a much larger and better trained workforce with 21st Century skills capable of translating the potential of photonics as a key enabling technology into tangible products for the benefit of society.
Coming soon…Eduball
Generating energy through team work while promoting science and sport. Can you imagine it? ICFO, together with Fundació Catalunya La Pedrera and the school in Oms i de Prat, have made it a reality. Stay tuned for more information, but meanwhile...check this out! OTHER...
ICFO launches the third edition of the Young Photonic Congress
ICFO has launched the third edition of the Young Photonics Congress, which will take place on 13 April 2018 at ICFO. This congress, which aims to bring together young scientists for their first scientific conference while introducing them to the scientific community,...
UNESCO endorses annual International Day of Light
ICFO, as co-founder and acting coordinator of the ECOP alliance (European Centres for Outreach in Photonics), will participate and have an acting role on the steering committee of the new International Day of Light, to be proclaimed at the General Conference of UNESCO...
More than 100,000 people challenge Einstein in a unique worldwide Quantum Physics experiment
•On November 30th, more than 100,000 people participated in the BIG Bell Test, a global experiment to test the laws of quantum physics. •Participants were able to complete more than half a million levels of the video game that generated more than 90 million bits, a...
ICFO's Outreach activities aim to inspire students, teachers, fellow scientists, the general public and industry at large, demonstrating the power of light as a tool for research, technology, industry and society.
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ICFO - The Institute of Photonic Sciences
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Q: Get notification to the currently logged users I want to add a notifications to my asp.net application. when place an order to order table,automatically popup should come to the currently logged users such as facebook notification.
please help with sample codes
Thanks.

A: You can use Query Notifications to achieve this.
To enable this option in your database you have to enable  Service Broker which is not enable by default. Have a look  how to Enabling Query Notifications
Also have a look how you can use SqlNotificationRequest and Detecting Notifications


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The Best Places to Live with Low Humidity
The Cumberland Gap Fall Festival
10 Things To Know About Colorado Springs, CO
by Hannah Wickford
A Winter Vacation to Italy
Most Beautiful Winter Destinations in New England
Mountain West Region Facts
Most Visited Landmarks in Colorado
Whether you're an outdoor enthusiast, history buff or urban adventurer, you'll find plenty to see and do in Colorado Springs. Intended as a high-end resort community when General Palmer founded it in 1871, Colorado Springs has grown into the state's second-largest city. The region welcomes more than 5 million visitors each year, and many of them choose to stay in Colorado Springs to enjoy all it has to offer.
Summers in Colorado Springs are usually warm, with temperatures peaking at 85 degrees Fahrenheit, making it an ideal time to visit the area. Early fall is also a good time to travel to the city, as most of the summer crowds are gone, but the weather is still balmy. Avoid early spring, as snow is not uncommon during March and April.
If you find it difficult to breathe when you arrive in Colorado Springs, it might be because the city sits at an elevation of 6,035 feet. In fact, Colorado Springs has only two-thirds of the typical level of oxygen found sea-level destinations. While this isn't a dangerously high altitude, many visitors experience mild altitude sickness after arrival. Staying hydrated and rested and avoiding alcohol may help to lessen the altitude's effects.
Explore Colorado Springs' colorful neighborhoods by foot, but have some transportation nearby, as it is a significant walk to get from one neighborhood to another. If you don't have a car, you can hail a taxi or use affordable public transportation like the Mountain Metropolitan Transit.
Olympic Spirit
Colorado Springs has been the official home of the U.S. Olympic Committee since 1978. Take a free tour of the Olympic Training Center (teamusa.org) and you might be lucky enough to see some budding Olympians in training.
Biking is big in Colorado Springs, and the city government has gone out of its way to put together a city biking plan. Bring your own bike or rent one at any of the city's bike shops and take off on Colorado Springs' 90 miles of on-street bike lanes, 118 miles of urban bike trails and 61 miles of mountain bike trails.
Those who plan to fly into Colorado Springs normally fly into the Colorado Springs Municipal Airport (springsgov.com) roughly 10 miles southeast of the downtown area. The airport offers nonstop service to and from Salt Lake City, Denver, Chicago, Atlanta, Orlando, Dallas, Houston, Phoenix, San Diego, Las Vegas, Los Angeles, San Francisco and Washington, D.C.
Just west of the city, Pikes Peak is said to be the most-visited mountain in the country. With an elevation of 14,000 feet, Pikes Peak offers expansive views of Colorado and, on a clear day, you can see all the way to Kansas. The view from Pikes Peak is what inspired Katherine Lee Bates to write the poem that inspired the song "American the Beautiful."
Underground Adventures
Just six miles outside of the city's center, the Cave of the Winds (caveofthewinds.com) was discovered in 1869. Since 1881, when it was opened to the public, it has offered visitors a chance to explore this vast subterranean formation. In addition to guided daily tours, guests can experience nighttime lantern tours and laser shows during the summer.
While Colorado Springs seems to always have something going on, three annual events draw tens of thousands of people each year to the city. The three-day Colorado Balloon Classic is held on Labor Day weekend and is the largest hot-air balloon show in the Rocky Mountain region. The two-day Springs Spree, which takes place in June, draws more than 70,000 people to enjoy music, dance and food with Pikes Peak as a backdrop. Territory Days, one of the largest outdoor festivals in Colorado, is usually held on Memorial Day weekend and has a variety of activities for both young and old.
Steep yourself in the rich history of the area when you say at the Broadmoor Hotel (broadmoor.com). What is now a luxury resort dates to 1891 when it opened as a small hotel and casino. Although it was already a very popular area resort, the Broadmoor underwent a $160-million improvement project beginning in 2003 that added a golf course, rooftop tennis courts and more to the hotel's list of amenities.
Current Results: Colorado Springs Snowfall Totals & Accumulation Averages
Frommer's: Planning a Trip
Princeton University: Outdoor Action Guide to High Altitude - Acclimatization and Illnesses
The Wall Street Journal: Colorado Springs, Colo.
COhomepages.com: Colorado Springs Annual Events & Festivals
Fast Company: How Colorado Springs Became The Heart Of The U.S. Olympic Movement
The Broadmoor, Colorado Springs: Overview
Meridian Ranch: Things You Should Know about Colorado Springs
After attending Fairfield University, Hannah Wickford spent more than 15 years in market research and marketing in the consumer packaged goods industry. In 2003 she decided to shift careers and now maintains three successful food-related blogs and writes online articles, website copy and newsletters for multiple clients.
Rainier Ehrhardt/Getty Images Sport/Getty Images
How to Get Discount Silver Dollar City Tickets
Places to Visit in Autumn in Tennessee
Points of Interest on Interstate 80 in Nevada
Promotion of Tourism in India


Figure 1: A natural gas flare on top of a 15 meter rig.
Natural gas is a colourless, odorless gas that burns easily (see flaring in Figure 1) and typically consists mostly (90% or more) of methane.  Unprocessed, or raw, natural gas is one of the main primary energy sources in the world, making up roughly 1/5 of the world's primary energy. After processing, it's still referred to as natural gas, but it's now a flexible energy currency and even after much of it has been turned into electricity, natural gas still makes up 15% of end use energy.
In its unprocessed state, natural gas is composed of varying quantities of methane, ethane, propane, butanes, and pentanes. Often impurities such as oxygen, hydrogen sulfide, nitrogen, water and carbon dioxide are also present. Once natural gas has been processed for consumption, it is primarily methane with trace amounts of other constituents.
Like all petroleum based products, natural gas is formed from the decomposing remains of animals and plants that lived millions of years ago. The high pressure and temperatures present deep underground facilitated the conversion of plant and animal matter to hydrocarbon fuels.
Almost every building (ranging from corporate offices to restaurants and even pools) in developed cities utilized natural gas during construction and rely on it for utility heating. Additionally there are industrial uses, for example in the Canadian province of Alberta, residential and commercial usage account for only 25% of Alberta's usage. The remaining 75% of natural gas used in Alberta is consumed by the industrial sector in applications like petroleum refining, food processing, metal, plastic and glass industries, and the pulp and paper industry.
A growing use for natural gas is the natural gas vehicle (NGV), which has lower emissions than diesel engines or gasoline engines.
As the demand for natural gas rises around the world, so does the need to transport it overseas. One method of transporting natural gas is in it's liquefied form, or LNG, and this is done using large ships.
According to CAPP, Canada has a natural gas resource of between 700 and 1,300 trillion cubic feet. While a little over 15% of that natural gas has been recovered, the rest is contained in four types of deposits: conventional, Shale gas deposit, Tight gas deposit, and coal bed methane.
Natural gas has a high energy density (for a fossil fuel) and flexible applications, which make it a popular fuel. People advocating for natural gas often point to it as the cleanest burning fossil fuels. Even as a cleaner fossil fuel, natural gas is still made up of hydrocarbons and burning it releases CO2 and other pollutants (NOx being a problem specifically). Natural gas use is often an improvement over coal, however, its combustion still contributes to air pollution and climate change.
Both natural gas extraction and electrical generation suffer from NIMBY (Not in my back yard syndrome) opposition. NIMBY syndrome is when people consent to an idea, as long as they will not be directly affected by it. Click here for data on Canadian support for natural gas as an energy source.
With advances in fracking techniques, natural gas reserves are expected to last a long time. See the interactive graph below to explore how much natural gas is used in countries around the world.
↑ Canaport LNG LP. (2008). "Canaport LNG FAQs," [Online]. Available: http://www.canaportlng.com/faqs.php. [Accessed 21 October 2013].
↑ 3.0 3.1 Natural Gas.org. (2011). "Background," [Online]. Available: http://www.naturalgas.org/overview/background.asp. [Accessed 20 October 2013].
↑ 4.0 4.1 4.2 4.3 Alberta Energy. (2013). "What is Natural Gas?" [Online]. Available: http://www.energy.alberta.ca/NaturalGas/723.asp. [Accessed 21 October 2013].


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Diversions Front Page Health U.S.
NFL: 1/4 of players will have brain problems
'Materially higher than those expected in general population'
(REUTERS) — About one in four National Football League players are likely to end up suffering dementia, Alzheimer's disease, Parkinson's disease or other cognitive impairments during their lifetime, according to a report filed in court by the league's lawyers.
The NFL submitted the summary of the findings of an actuarial study it had commissioned in the U.S. District Court for Eastern Pennsylvania on Friday as part of the ongoing litigation between former players and the league.
The study by the Segal Group, based in New York City, used a database of the medical history of retired players as part of its method.


One of the benefits of a data warehouse environment using both Amazon Redshift and Amazon RDS for PostgreSQL is that you can leverage the advantages of each service. Amazon Redshift is a high performance, petabyte-scale data warehouse service optimized for the online analytical processing (OLAP) queries typical of analytic reporting and business intelligence applications. On the other hand, a service like RDS excels at transactional OLTP workloads such as inserting, deleting, or updating rows.
In the recent JOIN Amazon Redshift AND Amazon RDS PostgreSQL WITH dblink post, we showed how you can deploy such an environment. Now, you can deploy a similar architecture using the Modern Data Warehouse on AWS Quick Start. The Quick Start is an automated deployment that uses AWS CloudFormation templates to launch, configure, and run the services required to deploy a data warehousing environment on AWS, based on Amazon Redshift and RDS for PostgreSQL.
The Quick Start also includes an instance of Tableau Server, running on Amazon EC2. This gives you the ability to host and serve analytic dashboards, workbooks and visualizations, supported by a trial license. You can play with the sample data source and dashboard, or create your own analyses by uploading your own data sets.
Learn more about the Quick Start.
Read the JOIN Amazon Redshift AND Amazon RDS PostgreSQL WITH dblink blog post.
You can also join us for the webinar Unlock Insights and Reduce Costs by Modernizing Your Data Warehouse on AWS on Tuesday, August 22, 2017. Pearson, the education and publishing company, will present best practices and lessons learned during their journey to Amazon Redshift and Tableau.


This classic pink playpen with a black baby figurine is the perfect cake topper or centerpiece for your baby shower. Use it for your baby's birthday, pregnancy party, gender reveal party, pregnancy reveal party, or baby shower. The playpen and baby are not attached so they can be used separately for the most versatility. Great for your crafting diy project or for your crafting supplies.
The playpen is 3.5 inches x 3.5 inches.
The baby is 1.25 inches tall x 1.5 inches wide, the baby is holding a baby bottle.


Emmequattro drive gearboxes are suitable for self-propelled machines with combustion engine, hydromotor or electric motor.
The range of products, recently expanded with new products, includes rigid and steering differential drive axles (also with hypoid bevel gears), integrated differential gearboxes, fitted for hydraulic and electric motors, differentials with epicycloidal gear reduction and multiple oil-bath brake disks, 1- or 2-speed transfer reduction units.
Our products can equip trucks as well as light commercial vehicles (2 or 4 wheel drive), special vehicles used in city maintenance (street sweepers, municipal waste collectors), minibus or GSE Ground Support Equipment (passengers conveyors belts, conveyors and tow tractors) and, more generally, self-propelled farming machines (fruit harvesters and crop sprayers) and building industry machines (dumpers, concrete mixers, mini-shovels).
A wide range of electric motors is available to drive the axle.


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Failing the Future: A Dean Looks at Higher Education in the Twenty-first Century
by Annette KolodnyAnnette Kolodny
English 082239670X
Both revealing and compelling, Annette Kolodny's Failing the Future: A Dean Looks at Higher Education in the Twenty-first Century is drawn from the author's experience as a distinguished teacher, a prize-winning scholar of American literature, a feminist thinker, and an innovative administrator at a major public university. In chapters that range from the changing structure of the American family and its impact on both curriculum and university benefits policies to recommendations for overhauling the culture of decision making on campus, this former Dean of the College of Humanities at the University of Arizona explores the present state of higher education and offers a sobering view of what lies ahead.
In this volume Kolodny explains the reasons for the financial crisis in higher education today and boldly addresses the challenges that remain ignored, including rising birthrates, changing demographics both on campus and across the country, the accelerating globalization of higher education and advanced research, and the necessity for greater interdisciplinarity in undergraduate education. Moreover, while sensitive to the complex burdens placed on faculty today, Kolodny nonetheless reveals how the professoriate has allowed itself to become vulnerable to public misperceptions and to lampooning by the media.
Not simply a book about current problems and future challenges, Failing the Future is rich with practical solutions and workable programs for change. Among her many insights, Kolodny offers a thorough defense of the role of tenure and outlines a new set of procedures to ensure its effective implementation; she proposes a structure for an "Antifeminist Intellectual Harassment Policy"; and she provides a checklist of family-sensitive policies universities can offer their staff, faculty, and administrators. Kolodny calls on union leaders, campus communities, policymakers, and the general public to work together in unprecedented partnerships. Her goal, as she states in a closing coda, is to initiate a revitalized conversation about public education.
This book should be required reading for all those concerned with the future of higher education in this country—from college trustees to graduate students entering the professoriate, from faculty to university administrators, from officers of campus-based unions to education policymakers.
Lexile:
1530L (what's this?)
Annette Kolodny is the College of Humanities Professor Emerita of American Literature and Culture at The University of Arizona. She is the author The Land Before Her: Fantasy and Experience of the American Frontiers, 1630–1860 and The Lay of the Land: Metaphor as Experience and History in American Life and Letters. She is the editor of Joseph Nicolar's The Life and Traditions of the Red Man, also published by Duke University Press.
Failing the Future
A Dean Looks at Higher Education in the Twenty-first Century
By Annette Kolodny
Copyright © 1998 Duke University Press
Facing the Future: An Introduction
"The care of the public must oversway all private respects." —John Winthrop, "A Modell of Christian Charity," 1630.
This is a book about higher education, written for those who want to be part of its future. Most of my observations and recommendations will apply to public and private research universities, as well as to comprehensive (or nonresearch intensive) universities, because these are the institutions I have come to know best both as a student and as a professional educator. To a lesser degree, this book also reflects the current realities of four-year liberal arts colleges, public and private. But of the approximately 125 research universities in the United States—of which about forty are private and eighty-five are public—my major focus is on the public research university. These institutions are the focus of my concern because they are responsible for training most of the nation's Ph.D.s and other professionals, at the same time remaining accessible to large segments of the undergraduate population, providing superior education at relatively affordable tuition rates. Even so, despite their importance in undergraduate and professional education and their central place in the nation's research agenda, public research universities are now imperiled by budget cuts, by assaults on tenure, and by a general misunderstanding of what they do and how they do it.
That said, whether I am discussing colleges or universities—or even both at once—my remarks are informed by two carefully considered beliefs. To begin with, if we want our educational system to serve us as well in the future as it has in the past—or perhaps serve us even better—then it will require greater, and not reduced, investments of human and financial resources. An additional three million students are expected to enroll in the nation's colleges and universities between 1997 and 2,015, a 20 percent increase over current enrollment levels. These students will need more professors, more classrooms, more computers, more foreign language instruction, and better equipped science laboratories if they are to receive a quality education and fulfill the employment needs of the coming century. After all, in the next decade alone, in addition to the existing jobs that already require a college degree, approximately one-third of all new jobs created will require at least that.
Who these students are is also changing. At the moment, more than one-third of students in primary and secondary schools are minorities; and in Hawaii, California, New Mexico, Texas, Mississippi, and the District of Columbia more than half of the students are members of a racial minority. Those numbers continue to grow as the twentieth century's minorities become the twenty-first century's majority. As college and university enrollments increasingly draw upon this changing population, institutions of higher education will have to accommodate the fact that, disproportionately, these students will come from poor families and even poorer school districts. This means added costs in scholarship money and loans, counseling and academic tutoring facilities, and remedial programs for basic subjects like math and English.
But it is not only the investment in improved educational quality and updated facilities for growing numbers of students or even the costs of enrolling talented students with inadequate preparation that will account for the need for increased resources. It is also the fact that institutions of higher education will be called upon to play a variety of unprecedented roles in a transnational information age. The ease with which individuals will be able to access vast quantities of information whenever they want will be matched by a commensurate demand to learn how to analyze that information, recognize recurrent patterns or connections, and extract what is truly important. In effect, the new information technologies will make higher education both more necessary and ongoing, if only because learning to make connections and to reason rigorously across and between the disciplines is a lifelong process requiring sensitive tutelage. The twenty-first century, in other words, will be a century in which people are constantly "going back to school" in one form or another.
The second belief behind these chapters is that accelerating technological innovation will transform all aspects of teaching and learning in ways that cannot yet be predicted. What is certain, however, even from the current successes with self-paced computer learning programs and video transmission to off-campus learning sites, is that there is no substitute for the inspiration, rigor, and focus of direct human contact between a teacher and her students. Emily Weiner, a 1995 graduate of New York's Empire State College—a college that exists in cyberspace, providing instruction online and through email—made that clear when she assessed her own experience in a New York Times editorial. Despite her "excitement about new electronic educational opportunities" and the convenience of "on-line degrees," Weiner nonetheless came to depend on the professor at the other end for emotional and intellectual nurture (Weiner 42). In her view, the success of distance learning arrangements depends on "a person at the other end of the line who is watching to see that students are stretching themselves, choosing appropriate courses, struggling with new ideas, overcoming personal obstacles, getting smarter" (Weiner 42). But even when those ideal circumstances obtain, Weiner complained, "the fuller relationships that develop between students and teachers on a college campus will be missing" (Weiner 42). Clearly, then, the teacher as coach, as guide, and as immediately responsive presence—even beyond the teacher's disciplinary expertise—contributes to the learning process in a way that no computer program and no video, however well designed, can ever replicate.
Of course, the understandable fear of many in the professoriate today is that universities will continue trimming their costs by replacing live teachers with computer programs or with videotapes of lectures that can be replayed semester after semester—what I call "the professor in a can." We learned, however, from the innovations introduced to basic language instruction in the College of Humanities' language learning laboratory at the University of Arizona that even the most sophisticated and creative computer programs proved successful only when combined with the give-and-take of the traditional classroom. Nothing substituted for spontaneous conversation between teachers and students in the targeted language.
The videotaped lecture series by "great professors" currently being marketed to schools and to the general public suffer from another significant liability. Because the knowledge base in any field of study is never static but, rather, dynamic and changing, these videos become obsolete almost as soon as they are canned. Although the lectures may be wonderful as performances, they will never replace professors who impart the very latest discoveries in their fields and make their students partners in the discovery process. Unlike the professor in the classroom or the laboratory, a video won't engage a student in dialogue about cutting-edge research or controversial new concepts.
The challenge facing the professoriate of the next century, therefore, is to become knowledgeable about the new technologies and their possibilities in order to adapt them both for enhanced on-campus instruction and for increased outreach to students not currently on campus. The challenge to our educational institutions is to provide incentives and continuous support to faculty willing to push the technology envelope. The challenge for policy-makers and the general public is to resist the impulse to force colleges and universities into substituting the kind of rote training that technology can cheaply supply for the more expensive education that teaches thinking and analytic skills, values and an understanding of complex relationships, which the learned professor in the classroom can facilitate. An exclusively cost-driven dependence on computers and telecourses may instruct students in a subject; but only the professor with passion and disciplinary expertise can help students understand why a subject is important to think about and how to think about it.
Having identified this as a book about higher education, I must add that it is consequently also a book about social responsibility. Despite all the trendy importations of corporate models into academe (like many others, my own campus embraced "total quality management"), the chapters that follow reject the notion that colleges and universities are merely training vendors, that students are end products or interim consumers, that the professoriate is a quantifiable human resource, or that prospective employers represent higher education's ultimate customers and most important constituency. In an open society, creative production and the making of new knowledge can never be reducible merely to commodities for market exchange. Markets may be excellent devices for increasing profits and personal wealth, but they are notoriously unreliable as protectors of the common good. Yet striving to define and enact the common good, since Plato, has been one of the major goals of advanced education. During my years as dean, when local business and community leaders asked whether universities should be training students to work effectively in an increasingly competitive international economy; or whether we needed to train more socially responsible participants for national and global citizenship; or whether we should concentrate on graduating individuals equipped for success in our own nation's complexly multicultural workplace, my answer was always the same: we need to be doing all three at once; we dare not separate or compartmentalize those missions; and we need to pursue each of them through high-quality curricular innovations.
What I now want to add to that answer is my profound belief that the quality of education reflects the quality of community that supports it. But at the end of the current millennium, any sense of community in this country is in short supply. Vicious corporate downsizing for the sake of short-term profits, a fraying social safety net, and widening inequalities in income distribution have turned the nation sour and cynical. Crime, violence, domestic terrorism, and smoldering racial tensions are regular features of the evening news. And, in a desperate act of scapegoating, too many citizens and politicians seem content to punish the poor as though, amid a myriad of better opportunities, the poor had stubbornly chosen their plight. It is a sad note on which to end the century.
If we have any hope of social harmony, it is a note we dare not carry over into the next century. My narrow focus on education in these pages, therefore, must be understood as grounded in the argument that the best educational system in the world is no substitute for—nor can it survive without—reinvestment in troubled communities, job creation, income redistribution, the reinstitution of a truly progressive tax system for individuals and corporations alike, and far more inclusive political and civic participation than is currently the norm. Unless we develop social programs to mitigate the economic displacements that impoverish entire neighborhoods, disrupt families, produce violence, and stunt young people's growth, educational reform will not stand proof against civil disorder.
Americans will have to get out of the habituated ruts of late-twentieth-century thinking. Social justice is not the enemy of economic growth, but rather its engine. Tax structures that continue to concentrate wealth among the few actually slow an economy's expansion by widening the income gap, depressing consumption, and depriving the dwindling middle and working classes of the opportunity to save and thereby spur investment. In fact, a truly progressive tax system is simultaneously a social good. Moreover, as the post-World War II pattern in East Asia demonstrates, "the most successful ... economies are also the most egalitarian," and there is a direct correlation between equitable "income distribution and a strong economy" (Passell 5).
What this teaches us for the next century is that full employment at decent wages must be valued as a far greater social benefit than the lowest prices for consumers or the highest dividends for stockholders. And because the dignity and stability that well-paid employment brings to an individual translate into civic participation and political enfranchisement (not to mention social order), there need to be significant disincentives in place for employers who, as New York Times columnist Thomas L. Friedman phrases it, massacre their workers (Friedman 15). By any measure, after all, American workers "work longer and harder than workers in other industrialized nations, ... with less job security" (Meier 82), and they rank among the most productive in the world. The fact that stunning technological advances have allowed machines to replace hands and minds should mean shorter workweeks rather than fewer employees who put in overtime (as do most American workers today); and it should mean that those same hands and minds are now available to be educated to perform the tasks that technology, as yet, cannot.
A twenty-first century education can certainly make such transitions possible. But only if politicians and the general public first squarely face the consequences of current policies that protect profits before people.
I contemplate the profession that I am passing on to my graduate students with trepidation. Beyond the immediate question of whether there will be employment for these talented newcomers in a cost-cutting and downsizing academy is the larger question of how they will make a place for themselves within institutions that are already, in their view, obsolete. Often far more sophisticated than their teachers about the possibilities of technology for teaching and learning, they share with undergraduates the sense that the new technologies have the capacity to transform learning into play. Even more important, the students to whom I currently teach American literature and American studies see the university as a barrier rather than a bridge to the barrio, the reservation, and the 'hood. And they are determined to utilize the new technologies and to use their knowledge as a means of breaking down the barriers.
Perhaps as a consequence, today's Ph.D. candidates ask disturbing questions about how our society has organized itself, and they seem deeply committed to applying their studies to help solve problems like global poverty and environmental degradation. Because their intellectual ambitions have so wide a reach, these students chafe at disciplinary boundaries, pursuing dissertation topics that require professorial oversight committees made up of humanists, social scientists, and scientists in combinations that were unimaginable when I was going through my own Ph.D. training just thirty years ago. In terms of the way we have segmented disciplines and compartmentalized knowledge fields, these students are telling us, the organization of the American university in the late twentieth century cannot survive into the twenty-first century.
This is just one of many cues that major changes are upon us. As Donald Kennedy, the former president of Stanford University, wryly phrased it, "Another century's end, another revolution for higher education" (Kennedy 8). Kennedy's wearied humor notwithstanding, most colleges and universities are now expending considerable resources on strategic planning, the latest talisman for ensuring institutional survival into the next century. The trouble is that on most campuses strategic planning has been skewed into a search for strategies to deal with current fiscal problems while its potential to embolden creative thinking about the long-term future has been severely curtailed. As a result, the most important conversations about higher education in the twenty-first century have yet to begin in earnest. We have not generated paradigms for true interdisciplinarity; we have not planned for education's role in a society where the forty-hour week and a single career path have ceased to be the defining activities of adulthood; and we have not prepared for the internationalization of higher education.
(Continues...)
Excerpted from Failing the Future by Annette Kolodny. Copyright © 1998 Duke University Press. Excerpted by permission of Duke University Press.
Acknowledgments ix
A Personal Preface: Reflections on Five Years in a Dean's Office I
1. Facing the Future: An Introduction 33
2. "60 Minutes" at the University of Arizona: The Polemic against Tenure 53
3. Raising Standards While Lowering Anxieties: Rethinking the Promotion and Tenure Process 81
4. Paying the Price of Antifeminist Intellectual Harassment 98
5. Creating the Family-Friendly Campus 131
6. Teaching and Learning in a World of Cognitive Diversity 159
7. Setting an Agenda for Change 173
8. Failing the Future; or, How to Commit National Suicide at the End of the Twentieth Century 214
A Closing Refrain: Reflections at a Graduation 249
Appendix 1. University of Arizona College of Humanities Promotion and Tenure Procedures 257
Appendix 2. Summary Checklist of Selected Family-Friendly Initiatives and Programs 269
Works Cited 281
Annette Kolodny has turned her articulate mind and her marvelous imagination to the world of academic leadership. Failing the Future is personally moving, with a sharp and honest focus, and it should be read by all those who care about the future of higher education."—Barry Munitz, President and Chief Executive Officer of the J. Paul Getty Trust and former Chancellor of the California State University System
"This book should lead to an opening of the American mind. It is possibly the best book on higher education in the last decade. It is full of ideas that one needs to wrestle with, discuss, and chew over in faculty lounges, over e-mail, in journals, and in faculty senates. Failing the Future shows us not only what we must do, but explains HOW."—Emily Toth, author of Ms. Mentor's Impeccable Advice for Women in Academia
"This is a welcome and outstanding work. Particularly at this time, with the avalanche of right-wing and largely mindless criticism of universities, this book clearly sets forth the actual situation, the real problems, and suggests useful and possible solutions to the complex situation of higher education in our country today."—Carolyn Heilbrun, Avalon Professor in the Humanities Emerita, Columbia University
book by trevor schoonmaker
driftless photographs from iowa
book by annette kolodny
book by maciej baranowski
racism postrace by roopali mukherjee hardcover
book by lauren pond
AIDS TV: Identity, Community, and Alternative Video
Camcorder AIDS activism is a prime example of a new form of political expression—an outburst ...
Camcorder AIDS activism is a prime example of a new form of political expression—an outburst of committed, low-budget, community-produced, political video work made possible by new accessible technologies. As Alexandra Juhasz looks at this phenomenon—why and how video has become ...
Cherishing Men from Afar: Qing Guest Ritual and
In the late eighteenth century two expansive Eurasian empires met formally for the first time—the ...
In the late eighteenth century two expansive Eurasian empires met formally for the first time—the Manchu or Qing dynasty of China and the maritime empire of Great Britain. The occasion was the mission of Lord Macartney, sent by the British ...
Critically Sovereign: Indigenous Gender, Sexuality, and Feminist
Using a range of historical, literary, and legal texts, the contributors to Critically Sovereign trace ...
Using a range of historical, literary, and legal texts, the contributors to Critically Sovereign trace the ways in which gender is inextricably linked to Indigenous politics and U.S. and Canadian colonialism, showing how gender, sexuality, and feminism work as co-productive ...
Dalit Studies
The contributors to this major intervention into Indian historiography trace the strategies through which Dalits ...
The contributors to this major intervention into Indian historiography trace the strategies through which Dalits have been marginalized as well as the ways Dalit intellectuals and leaders have shaped emancipatory politics in modern India. Moving beyond the anticolonialism/nationalism binary that ...
Demanding Images: Democracy, Mediation, and the Image-Event in
The end of authoritarian rule in 1998 ushered in an exhilarating but unsettled period of ...
The end of authoritarian rule in 1998 ushered in an exhilarating but unsettled period of democratization in Indonesia. A more open political climate converged with a rapidly changing media landscape, yielding a vibrant and volatile public sphere within which Indonesians ...
Driftless: Photographs from Iowa
Winner of the third biennial Center for Documentary Studies/Honickman First Book PrizeRobert Frank, Prize JudgeIn ...
Winner of the third biennial Center for Documentary Studies/Honickman First Book PrizeRobert Frank, Prize JudgeIn Driftless, Danny Wilcox Frazier's dramatic black-and-white photographs portray a changing Midwest of vanishing towns and transformed landscapes. As rural economies fail, people, resources, and ...
Iraq Perspectives
Selected by William Eggleston as WinnerThe Center for Documentary Studies / Honickman First Book Prize ...
Selected by William Eggleston as WinnerThe Center for Documentary Studies / Honickman First Book Prize in PhotographyBenjamin Lowy's powerful and arresting color photographs, taken over a six-year period through Humvee windows and military-issue night vision goggles, capture the desolation of ...
Rubble: The Afterlife of Destruction
At the foot of the Argentine Andes, bulldozers are destroying forests and homes to create ...
At the foot of the Argentine Andes, bulldozers are destroying forests and homes to create soy fields in an area already strewn with rubble from previous waves of destruction and violence. Based on ethnographic research in this region where the ...


For Aries Ascendant people, Venus rules the 2nd house & 7th house of chart with its sign Taurus & Libra. So, let's look at 2nd house, 7th house, Taurus and Libra too.
What will Venus do in Aspect? – Now, Venus can be sitting in any house of chart for an Aries Ascendant person.1st of all, Venus will take the energy of house of chart, it rules with Taurus & Libra sign, and take it to the house where it sits. Then from the house it sits, it will throw its aspect on the 7th house from its place. Now, as Venus basically represents Relations & Creativity, with Venus's aspect on a particular house, it shows that person wants to be creative with things related to that house or has natural love/relationship towards that house.
Now, let's see the meaning and impact of Venus's aspect through different houses for Aries Ascendant people.
Venus in 1st house – Venus will be in Aries here. Venus in Ascendant means person is all about relationship. May be they can't survive without being in relation. And that's what Venus is showing in aspect at 7th house. Person loves to create relationship. He wants to connect with other people through love or creativity. It also shows someone who is in Business of Finance or Creative Pursuits. It also shows that person wants to serve other people.
Venus in 2nd house – Here Venus is in own sign in Taurus. It shows that other people or spouse can bring lots of wealth in family. This person can gain a lot in Business. Marriage may bring positive transformation in family and wealth. Venus's aspect on 8th house also suggests that person has a loving relation with in-laws and wants to serve other people in needs. It shows person's love towards occult and mystic world.
Venus in 3rd house – Venus is in Gemini here. This again shows someone gaining wealth through creative skills or Business as 7th house and 3rd house both represents Business. But Venus's aspect on 9th house suggest a love towards higher learning which can help him in improving his Business. it also shows a natural love for travelling and reading about religion and philosophy. They may like to have relation with people of different ethnicity.
Venus in 4th house – Venus is in Cancer here. This shows love towards Mother and Home. This also shows that Wealth is coming from Mother or Home. They may be doing some creative work at home which may bring Wealth to them. Venus's aspect on 10th house shows that person wants to relate to people at their work through Creativity. That means they want to follow a creative career. They would love to stay at home or with mother.
Venus in 5th house – This is a real creative person. Planet/House/Sign of Creativity coming together. Another position for Love Marriage and Business related with Creative Pursuits. Venus's aspect on 11th house confirms the gains from creative pursuits. It also shows that they want to relate with friends and networking circle on the basis of their creativity, so that their gains can improve. It also shows that they want to serve humanity through their creative pursuits.
Venus in 6th house – Here, Venus will be debilitated and it is also Venus's marana karaka position. It shows that person can face obstacles in gaining wealth, connecting with people and relations. But it also shows someone who wants to heal or serve others, specially Animals. Venus's aspect on 12th house suggests that they want to serve people at hospitals. They want to relate with Foreign or Spiritual people.
Venus in 7th house – Venus is again in own sign Libra. It again shows wealth through Business and a person who is all about relationship. They can't survive without being in relation. It is through relationship with others, they find themselves. This is what Venus's aspect on 1st house shows. If they are in a relation and able to connect with other people, they will find beauty and love within themselves. They need that recognition from others through relation to survive.
Venus in 8th house –Venus is in Scorpio here. This shows a love life full of ups and downs. This also shows someone in secret love affair. Although, love life is not too good here but it shows a person completely passionate about Occult and Mystic World. They are in love with research. Venus's aspect on 2nd house of wealth also suggests that they want to serve people in Occult & Mysticism which can bring wealth to their family. They would like to relate with their family through occult, mysticism and service to other people.
Venus in 9th house – Venus is in Sagittarius here. A natural love for travelling, higher learning, religion and philosophy. They love to study more and have relation with people of different ethnicity. Venus's aspect on 3rd house shows that after gaining all knowledge, they want to have relationship with people through their communication and teaching. They have a very pleasant way of speaking. They love travelling too.
Venus in 10th house – Venus is in Capricorn here. A natural love towards Father. They may be in Business oriented Career or a Creative Career. Venus's aspect on 4th house also suggests that they want to serve people of home land through their career. So, here they try to relate with people of homeland. They also seek pleasant relation with their Mother and at home. They want to keep their home beautiful. They may have a relation at work place or marry a colleague. .
Venus in 12th house – Venus is exalted in Pisces here. This shows a really spiritual and devoted person. Venus's highest trait is Service and Devotion. In Pisces, it gets best environment. So, these people would dedicate themselves in service of people or God. Venus's aspect on 6th house shows that they serve people with devotion and heal/resolve their issues/disputes. They like to relate with people through their service and devotion.
So, this is a basic idea of how Venus's aspect will work in different houses for Aries Ascendant people. Love, Wealth and Relations will remain natural factors with Venus.