text:
Robotic implant aids the treatment of oesophageal atresia
Posted: 22 January 2018 | Dr Zara Kassam (European Pharmaceutical Review) | No comments yet
Engineers have created a robot that can be used to help treat babies with a rare birth defect that affects an infant's oesophagus…
Researchers have created a robot that can be fixed into the body to aid the treatment of oesophageal atresia, a rare birth defect that affects a baby's oesophagus.
Dr Dana Damian from the Department of Automatic Control and Systems Engineering at the University of Sheffield and her team from Boston Children's Hospital have created the revolutionary prototype robotic implant which encourages tissue growth in babies.
The robot is a small device which is attached to the oesophagus by two rings. An incorporated motor then stimulates the cells by gently pulling the tissue. Using two types of sensors – one to measure the tension in the tissue and another to measure tissue displacement – the robot monitors and applies tissue traction depending on the tissue properties.
The robot's function is inspired by the Foker technique of correcting the oesophageal atresia which involves manually pulling the tissue slowly using sutures over a period of time.
Dr Damian said: "Doctors have been performing the Foker procedure as they realised that tissue lengthening can be achieved by pulling on the tissue. However, it is unknown how much force should be applied to produce tissue lengthening. Although the technique is one of the best standards, sometimes the sutures surgeons attach to the oesophagus can tear which can result in repetitive surgeries or scar tissue can form that can cause problems for the patient in the future.
"The robot we developed addresses this issue because it measures the force being applied and can be adapted at any time throughout the treatment. With it being implanted in the patient, it means they have – in effect – a doctor by their side all the time, monitoring them and changing their treatment when needed."
The study suggests that with this robot, babies would be free to move around and be allowed to interact with their parents while undergoing treatment, taking away some of the stress from both parties.
The implant is powered by a control unit which remains outside of the body, attached to a vest. This means that doctors can monitor the patient without impacting on the baby's routine.
Dr Damian said: "The biggest challenge we faced was to design a robot that works in a technology-hostile environment and to develop a robust physiologically-relevant interaction with the tissue that promotes its growth when there are so many unknowns about the underlying mechanisms. The robot we designed had to be soft and durable, air and water impermeable, abrasion resistant, non-corrosive and be able to be implanted for long-term treatment.
"This is the first step in adaptive regenerative-based treatments of tissues. We have made a device that can provide long-term control of the tissue growth using onboard medical expertise. We further want to look at other tubular tissues, such as the intestine and the vascular system, to see if this sort of technology can be used to help with other conditions, such as Short Bowel Syndrome."
Tissue growth has been an issue in the bioengineering field for many years, however, this research is a stepping stone to understanding how mechanical stimulation at the tissue level helps the cells multiply and how doctors can stimulate cells to grow using intuitive tools.
The research has shown cells will multiply in response to being pulled rather than stretching out of shape or scarring. Using the robot's monitoring and control abilities, the treatment can be changed to suit the patient and to optimize the cells' growth.
Professor Sheila MacNeil, Professor of Tissue Engineering in the Department of Materials Science and Engineering at the University of Sheffield, said: "Increasing knowledge of how tissues respond to mechanical strain with the production of new tissue has been needed for a long while.
Doctors and researchers understand that tissues will normally grow in response to traction forces, for example, this occurs naturally during pregnancy as the growing baby increases the pressure inside the mother, the abdominal wall and skin increase in area to relieve the tension generated from stretching these tissues. Plastic-surgeons have copied this trick by placing an inflatable balloon under the skin and inflating it over a period of weeks to expand skin and they then use this "extra skin" for reconstructive surgery for the patient.
"The development of this robotic implant is a breakthrough in applying the knowledge that tissues respond to strain with the production of new tissue in a practical and clinically useful manner."
Boston's Children Hospital, Harvard Medical School, University of Sheffield
Dr Dana Damian, Professor Sheila MacNeil
Related diseases & conditions
oesophageal atresia
By Dr Zara Kassam (European Pharmaceutical Review)
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text:
Q: UITableViewCell shadow How to add a shadow to both sides, top and bottom, of UITableViewCell?
I have tried this:
cell.layer.shadowOpacity = 0.75f;
cell.layer.shadowRadius = 5.0;
cell.layer.shadowOffset = CGSizeMake(0, 0);
cell.layer.shadowColor = [UIColor blackColor].CGColor;

However, it only displays a shadow to the bottom of the cell.

A: The problem was in z position of UITableViewCell. Actually, it was displaying the top shadow too, but the upper cell had bigger z position so that top shadow was under it.
I have just changed the z position of cell layer like this:
selectedCell.layer.zPosition = 999;

redpajama_set_name: RedPajamaStackExchange


It was the highest-grossing film ever to come out of Japan, earning $355.2M worldwide when it was released last year. It held the top spot for 12 non-consecutive weeks in the country and also became the highest-grossing Japanese film ever to release in China with $85.6M. Now Paramount Pictures and Bad Robot have joined with Japan-based Toho Co. to bring Your Name to worldwide audiences as a live-action feature with Oscar-nominated screenwriter Eric Heisserer (Arrival) on board to script.
Your Name, which was a lower-budgeted anime phenom from filmmaker Makoto Shinkai, tells the story of a teenage boy and girl from different backgrounds who discover they can swap bodies. They become desperate to cross space and time to find a way to meet and stop an impending disaster. The film was a hit among teens who saw it multiple times and was as well received in Japan as Disney's Frozen which sat at the top of the box office chart for 16 weeks in row.
For the live-action adaptation, J.J. Abrams (Star Wars: The Force Awakens, Star Wars: Episode IX) and Lindsey Weber will produce for Bad Robot, along with Genki Kawamura, producer of the original film. Toho will handle distribution of the film in Japan.


text:
\section{Introduction}
\label{Introduction}

Over the last century major strides have been made in the characterization of effective constitutive laws relating average fluxes to average gradients inside random heterogeneous media  see for example \cite{Hash, Maxwell04, Willis, Milton, NNH, Rayleigh}. However much less is known about the point wise behavior of local fluxes and gradients fields inside random media. While it is true that efficient numerical methods capable of resolving local fields are available for prescribed microstructures, it is also true that for most applications only a partial statistical description of the microstructure is available.  Thus for these cases one must resort to bounds or approximations for the local fields that are based upon the available statistical descriptors of the microgeometry and the applied macroscopic loading.
Bounds are useful as they provide a means to quantitatively assess load transfer across length scales relating the excursions of the local fields to applied macroscopic loads. Moreover, they provide explicit criteria on the applied loads that are necessary for failure initiation inside statistically defined heterogeneous media \cite{AlaliLipton}. In this paper we develop lower bounds on local field properties for statistically defined two phase microstructures when only the volume fraction of each  phase is known.
Here the focus is on lower bounds since volume constraints alone do not preclude the existence of microstructures with rough interfaces for which the $L^p$ norms of local fields are divergent see \cite{SeminalMilton}, \cite{faraco}, and also \cite{leonetinesi}.

We present a methodology for bounding the  $L^p$  norms, $2\leq p\leq\infty$, of the local hydrostatic stress field inside random media made up of two thermoelastic materials. The method is used to obtain new optimal lower bounds that are given by explicit formulas expressed in terms of the applied thermal and mechanical loading, coefficients  of thermal expansion, elastic properties, and volume fractions. We show that these bounds are the best possible in that they are attained by the local fields inside the coated sphere assemblage originally introduced in \cite{hscoated}.
It has been  known since 1963 that the coated spheres microstructure exhibits extreme effective elastic properties \cite{hashin}. However it was discovered only recently in \cite{Lipstress}, \cite{Lipstrain} that this geometry supports extreme local fields that minimize the maximum local hydrostatic field over all two phase elastic mixtures in fixed volume fractions. More recently several scenarios are identified for which, in the absence of thermal stresses, these microstructures attain lower bounds on the total local stress field inside each material when the composite is subjected to mechanical loading see, \cite{AlaliLipton}.

In this paper we consider mixtures of two thermoelastic materials with shear and bulk moduli specified by $\mu_1$, $k_1$, $\mu_2$, $k_2$ and coefficients of thermal expansion given by $h_1$ and $h_2$. New lower bounds are presented for elastically well ordered phases for which $k_1>k_2$ and $\mu_1>\mu_2$ as well as for non well ordered phases such that $k_2>k_1$ and $\mu_1>\mu_2$. For each of these cases we consider both macroscopic mechanical and thermal loads and present bounds that hold for $h_1>h_2$ and $h_2>h_1$. The set of bounds and optimal microstructures for the well ordered case  are listed in Section 3 and optimal lower bounds for the non well ordered case are listed in Section 4.
The methodology for deriving the bounds is presented in Section 5.

The optimal bounds and the associated coated sphere microstructures given in Sections 3 and 4  show  that there are combinations of applied stress and imposed temperature change for which the local hydrostatic stress inside the connected phase of the coated sphere assemblage vanishes identically. Other loading combinations are seen to cause the stress inside the included phase of the coated sphere assemblage to vanish identically.
Thus for these cases the applied hydrostatic stress is converted into a pure local shear stress inside a preselected phase.

Recent related work provides optimal lower bounds on  local fields in the absence of thermal loads.
The work presented in \cite{AlaliLipton} provides new optimal lower bounds on both the local shear stress and the local hydrostatic component of stress for random media subjected to a series of progressively more general applied macroscopic stresses. These bounds are explicit and given in terms of volume fractions, elastic constants of each phase, and the applied macroscopic stress.
Earlier work considers random two phase elastic composites subject to imposed macroscopic hydrostatic stress and strain  see, \cite{Lipstrain} and \cite{Lipstress}, as well as dielectric composites subjected applied constant electric fields see, \cite{Lipelect}. Those efforts deliver optimal lower bounds on the $L^p$ norms for the hydrostatic components of local stress and strain fields as well as the magnitude of the local electric field for all $p$ in the range $2\leq p \leq \infty$. Other work examines the stress field around a single simply connected stiff elastic inclusion subjected to a remote constant stress at infinity \cite{Wheeler} and provides optimal lower bounds for the supremum of the
maximum principal stress. The work presented in \cite{GrabovskyandKohn} provides an optimal lower bound on the supremum of the maximum principal stress for two-dimensional periodic composites consisting of a single simply connected elastically stiff inclusion inside the period cell. The recent work of  \cite{He} builds on the earlier work of \cite{Lipstrain, Lipstress} and develops new lower bounds on the
$L^p$ norm of the local stress and strain fields inside statistically isotropic two-phase elastic composites. However to date those bounds have been shown to be optimal for $p=2$ see, \cite{He}. Their optimality for $p>2$ remains to be seen. Optimal upper and lower bounds on the $L^2$ norm of local gradient fields
are established using integral representation formulas in \cite{lipsiama}.

We conclude by providing the notation and summation conventions used in this article. Contractions of
stress or strain fields $\sigma$ and $\epsilon$ are defined by
$\sigma:\epsilon=\sigma_{ij}\epsilon_{ij}$ and $|\sigma|^2=\sigma:\sigma$, where
repeated indices indicate summation. Products of fourth order
tensors $C$ and strain tensors $\epsilon$ are written as
$C\epsilon$ and are given by $[C\epsilon]_{ij}=C_{ijkl}\epsilon_{kl}$; and
products of stresses $\sigma$ with vectors ${\bf v}$ are
given by $[\sigma{\bf v}]_i=\sigma_{ij}v_j$. The fourth order identity
map on the space of stresses or strains is denoted by $\mathbf I$
and ${\mathbf
I}_{ijkl}=1/2(\delta_{ik}\delta_{jl}+\delta_{il}\delta_{jk})$. The
projection onto the hydrostatic part of $\sigma(\textbf{x})$ is denoted by
$\mathbb{P}^H$ and is given explicitly by
\begin{eqnarray}
\mathbb{P}^H_{ijkl}=\frac{1}{d}\delta_{ij}\delta_{kl}&\,\hbox{and}\,&\mathbb{P}^H\psi(\textbf{x})=\frac{tr\,\sigma(\textbf{x})}{d}I.
\label{proj}
\end{eqnarray}
The projection onto the deviatoric part of $\sigma(\textbf{x})$ is denoted by
$\mathbb{P}^D$ and ${\mathbf I}=\mathbb{P}^H+\mathbb{P}^D$ with $\mathbb{P}^D\mathbb{P}^H=\mathbb{P}^H\mathbb{P}^D=0$. The tensor product between two vectors $\u$ and $\v$ is the matrix $\u\otimes\v$ with elements$[\u\otimes\v]_{ij}=u_i v_j$.
Last we denote the basis  for the space of constant $3\times 3$ symmetric strain tensors by $\bar{\epsilon}^{kl}$ where $\bar{\epsilon}_{mn}^{kl}=\delta_{mk}\delta_{nl}$.

\bigskip
\section{Stress and strain fields inside heterogeneous thermoelastic\\ media with imposed macroscopic loading}
\label{Prestress Problem}

Several distinct physical processes can generate prestress within heterogeneous media.  In many cases it is generated  by a mismatch between the coefficients of thermal expansion of the component materials. To fix ideas we present the
physical model associated with this situation. The tensors of thermal expansion inside each phase are given by $\lambda_1=h_1 I$ and $\lambda_2=h_2 I$ where $I$ is the $3\times 3$ identity.  The elastic properties of each component are specified by the elasticity tensors $C_1$ and $C_2$ respectively. In this treatment we consider heterogeneous elastically isotropic materials and
the elasticity tensors of materials one and two are specified by
\begin{eqnarray}
C_i=3k_i\mathbb{P}^H+2\mu_i\mathbb{P}^D, \hbox{ $i=1,2.$}
\label{elastconst}
\end{eqnarray}
Without loss of generality we adopt the convention
\begin{eqnarray}
\mu_1>\mu_2.
\label{order}
\end{eqnarray}

The elastic displacement inside the composite is denoted by $\textbf{u}$ and the associated strain tensor is denoted by $\epsilon (\textbf{u})$. The position dependent elastic tensor and thermal expansion tensor for the heterogeneous medium are denoted by $C(\textbf{x})$ and $\lambda(\textbf{x})$ respectively where $\textbf{x}$ denotes a point inside the medium. The domain containing the composite is given by a cube $Q$ of unit side length. Here is supposed that $Q$ is the period cell for an infinite elastic medium. In what follows the integral of a quantity $q$ over the unit cube $Q$ is denoted by $\langle q \rangle$.

A constant macroscopic stress $\overline{\sigma}$ and uniform change in temperature $\Delta T$ is imposed upon the heterogeneous material. The local stress inside the heterogeneous medium is expressed as the sum of a periodic mean zero fluctuation $\hat{\sigma}$
and $\overline{\sigma}$, i.e., $\sigma(\textbf{x})=\overline{\sigma}+\hat\sigma(\textbf{x})$ with $\langle\hat{\sigma}\rangle=0$. Elastic equilibrium inside each phase is given by:
\begin{eqnarray}
div \sigma =0.
\label{equlib}
\end{eqnarray}
The local elastic strain $\epsilon(\u)$ is related to the local stress through the constitutive law
\begin{eqnarray}
 \sigma(\textbf{x})=C(\textbf{x})(\epsilon (\textbf{u}(\textbf{x}))-\lambda(\textbf{x})\Delta T),
 \label{constitutive}
\end{eqnarray}
and the local elastic field is written in the form
\begin{eqnarray}
\epsilon(\u)=\overline{\epsilon}+\epsilon(\u^{per})
\label{epsilon}
\end{eqnarray}
where $\u^{per}$ is $Q$ periodic taking the same values on opposite sides of the period cell
and $\langle\epsilon(\u^{per})\rangle=0$.
Perfect contact between the component materials is  assumed, thus
both the displacement ${\u}$ and  traction $\sigma\textbf{n}$ are
continuous across the two phase interface, i.e.,
\begin{eqnarray}
\label{equlibbdry1}
{\u}_{|_{\scriptscriptstyle{1}}}&=&{\u}_{|_{\scriptscriptstyle{2}}},\,\,\\
\label{equlibbdry2}
\sigma_{|_{\scriptscriptstyle{1}}} \textbf{n}&=&\sigma_{|_{\scriptscriptstyle{2}}} \textbf{n}.
\end{eqnarray}
Here the subscripts indicate the side of the interface
that the displacement and traction fields are evaluated on and  $\textbf{n}$ denotes the normal vector to the interface pointing from material one into material two.

The effective ``macroscopic''  constitutive law for the heterogeneous medium is given by the constant effective elasticity tensor $C^e$  and effective thermal stress tensor $H^e$ that provide the linear relation  between the imposed macroscopic stress $\bar{\sigma}$, uniform change in temperature $\Delta T$, and the average strain $\bar{\epsilon}$ given by \cite{Milton},
\begin{eqnarray}
\bar{\sigma}=C^e\bar{\epsilon}+H^e \Delta T.
\label{effelast}
\end{eqnarray}
Here the components of $C^e$ are given by
\begin{eqnarray}
C^e_{ijkl}=\langle C_{ijmn}(x)(\epsilon(\varphi^{kl})_{mn}+\bar{\epsilon}^{kl}_{mn})\rangle,
\label{effectelast}
\end{eqnarray}
where the fields $\varphi^{ij}$ are the periodic solutions of
 \begin{eqnarray}
div (C(x)(\epsilon(\varphi^{kl})+\bar{\epsilon}^{kl}))= 0  \quad\text{inside each phase },
 \label{basis}
 \end{eqnarray}
 with the appropriate traction and continuity conditions along the two phase interface given by
 \begin{eqnarray}
\label{equlibbdry1e}
{\varphi^{kl}}_{|_{\scriptscriptstyle{1}}}&=&{\varphi^{kl}}_{|_{\scriptscriptstyle{2}}},\,\,\\
\label{equlibbdry2e}
C_1\left(\epsilon(\varphi^{kl})+\bar{\epsilon}^{kl}\right)_{|_{\scriptscriptstyle{1}}} \textbf{n}&=&C_2\left(\epsilon(\varphi^{kl})+\bar{\epsilon}^{kl}\right)_{|_{\scriptscriptstyle{2}}} \textbf{n}.
\end{eqnarray}
The effective thermal stress tensor $H^e$ is given by
\begin{eqnarray}
H^e=\langle C(x)(\epsilon(\varphi^p)-\lambda(\textbf{x})) \rangle.
\label{effectethstress}
\end{eqnarray}
Where $\varphi^p$ is the periodic solution of
\begin{eqnarray}
div (C(x)(\epsilon({\varphi}^p)-\lambda(\textbf{x})))= 0  \quad\text{inside each phase  },
\label{prestressequlib}
\end{eqnarray}
with the traction and continuity conditions along the two phase interface given by
\begin{eqnarray}
\label{equlibbdry1p}
{\varphi^p}_{|_{\scriptscriptstyle{1}}}&=&{\varphi^p}_{|_{\scriptscriptstyle{2}}},\,\,\\
\label{equlibbdry2p}
C_1\left(\epsilon(\varphi^p)-\lambda_1\right)_{|_{\scriptscriptstyle{1}}} \textbf{n}&=&C_2\left(\epsilon(\varphi^p)-\lambda_2\right)_{|_{\scriptscriptstyle{2}}} \textbf{n}.
\end{eqnarray}
From linearity it follows that the local fluctuating strain field is
given by the sum
\begin{eqnarray}
\epsilon(\u^{per})=\epsilon(\varphi^{kl})\bar{\epsilon}^{kl}+\epsilon(\varphi^p)\Delta T.
\label{linear}
\end{eqnarray}
We write $\varphi^e=\varphi^{kl}\bar{\epsilon}^{kl}$ and from linearity one has the expression for $C^e\bar{\epsilon}$ given by
\begin{eqnarray}
\label{otherconstitut}
C^e\bar{\epsilon}=\langle C(\textbf{x})(\epsilon(\varphi^e)+\bar{\epsilon}\rangle.
\end{eqnarray}

In this article the imposed mechanical stress is given by a constant hydrostatic stress
\begin{eqnarray}
\bar{\sigma}=\sigma_0 I,
\label{imposedstress}
\end{eqnarray}
where $\sigma_0$ can assume any value in $-\infty<\sigma_0<\infty$.
We introduce a method for obtaining optimal lower bounds on the higher moments of the hydrostatic component
of the local stress inside the composite when it is subjected to an imposed hydrostatic load $\sigma_0 I$ and temperature change $\Delta T$. Here no restriction is placed on $\Delta T$.
The volume fractions of materials one and two are denoted by $\theta_1$ and $\theta_2$ and the average of a quantity $q$ over material one is denoted by $\langle q\rangle_1$ and over material two by $\langle q \rangle_2$.
In the following section we present optimal lower bounds on the following moments of the local hydrostatic stress $\mathbb{P}^H\sigma(\textbf{x})$ over the domain occupied by each material
given by
\begin{eqnarray}
\langle|\mathbb{P}^H\sigma(\textbf{x})|^p\rangle_1^{1/p} &\hbox{  and  }&\langle|\mathbb{P}^H\sigma(\textbf{x})|^p\rangle_2^{1/p},
\label{locstressmoment}
\end{eqnarray}
for $1< p\leq\infty$,
as well as for the maximum local hydrostatic stress over the whole composite domain
\begin{eqnarray}
\max_{\textbf{x} \hbox{\tiny in Q}}\left\{|\mathbb{P}^H\sigma(\textbf{x})|\right\}.
\label{locstressmaxeverything}
\end{eqnarray}

It is pointed out that the case corresponding to $p=\infty$ in (\ref{locstressmoment}) corresponds to
lower bounds on the maximum local stress over each phase
\begin{eqnarray}
\max_{\textbf{x}\hbox{ \tiny in material 1}}\left\{|\mathbb{P}^H\sigma(\textbf{x})|\right\}, && \max_{\textbf{x}\hbox{ \tiny in material 2}}\left\{|\mathbb{P}^H\sigma(\textbf{x})|\right\},
\label{locstressmaxphase}
\end{eqnarray}

The lower bounds are given in terms of the volume fractions $\theta_1$ and $\theta_2$, as well as the bulk and shear moduli $k_1$, $k_2$, $\mu_1$, $\mu_2$, and the coefficients of thermal expansion $h_1$ and $h_2$. The lower bounds are described by the following characteristic combinations of these parameters given by:
\begin{eqnarray}
L_1&=& \frac{k_1(k_2+\frac{4}{3}\mu_2)}{k_1k_2+(k_1\theta_1+k_2\theta_2)\frac{4}{3}\mu_2},\label{L1}\\
L_2&=& \frac{k_2(k_1+\frac{4}{3}\mu_1)}{k_1k_2+(k_1\theta_1+k_2\theta_2)\frac{4}{3}\mu_1},\label{L2}\\
M_1&=& \frac{k_1(k_2+\frac{4}{3}\mu_1)}{k_1k_2+(k_1\theta_1+k_2\theta_2)\frac{4}{3}\mu_1},\label{M1}\\
M_2&=& \frac{k_2(k_1+\frac{4}{3}\mu_2)}{k_1k_2+(k_1\theta_1+k_2\theta_2)\frac{4}{3}\mu_2},\label{M2}
\end{eqnarray}
\begin{eqnarray}
D&=&\Delta T(\frac{3k_1k_2(h_2-h_1)}{k_2-k_1}),\label{D}
\end{eqnarray}
and
\begin{eqnarray}
F&=&D(1-\frac{1}{\frac{L_1+M_2}{2}}).
\label{F}
\end{eqnarray}

For elastically well--ordered materials, $k_1>k_2$
one has $L_1>1>L_2$, and $M_1>1>M_2$; for the non well--ordered case $k_2>k_1$, one has $L_2>1>L_1$ and $M_2>1>M_1$.

The lower bounds are shown to be obtained by the local fields inside the coated sphere assemblages introduced in \cite{hscoated}.
The lower bounds  presented here include the effects of thermal stresses due to thermal loads and reduce to the optimal bounds reported in  \cite{Lipstress} when $\Delta T=0$.

\section{Lower bounds on local stress for elastically well-ordered thermoelastic composite media}
\label{sec-optstresshydrowell}
In this section  it is
assumed that the materials inside the heterogeneous medium are elastically well-ordered, i.e., $\mu_1>\mu_2$ and $\kappa_1>\kappa_2$.
We present lower bounds that are optimal for the full range of imposed hydrostatic stresses, i.e., $-\infty<\sigma_0<\infty$ as well as for unrestricted choices of $\Delta T$. The configurations that attain the bounds are given by the coated sphere assemblages \cite{hscoated}. To fix ideas we describe the coated sphere assemblage made from a core of material one with a coating of material two.
We first fill the cube $Q$ with an assemblage of spheres with sizes ranging down to the infinitesimal. Inside each sphere
one places a smaller concentric  sphere  filled with ``core'' material
one and the surrounding coating is filled with material two. The volume fractions of material one and two are taken to be the same for all of the coated spheres.

In what follows we list the lower bounds for the well ordered case. These bounds are derived in  Section 5.  Their optimality follows from explicit formulas for the moments of the local fields inside the coated sphere assemblage, these are discussed and presented  in Section 5.
The first set of bounds apply to all moments $\langle|\mathbb{P}^H\sigma|^p\rangle_2^{1/p}$ for $1< p\leq\infty$.
We suppose that $h_2>h_1$ fix $\Delta T$ and list the bounds as a function of the imposed macroscopic stress $\sigma_0$. The bounds are displayed in the following table where the optimal microstructures are given by the coated spheres construction. The coating and core phase of the optimal configuration is listed in the table below.

  $$
  \begin{array}{|l |l|p{1.35in}|}
   \hline
   Range & Lower Bound & Optimal microstructure\\ \hline
    -\infty<\sigma_0\leq D & \langle|\mathbb{P}^H\sigma|^p\rangle_2^{1/p}\geq
    \sqrt{3}[(D-\sigma_0)L_2-D] &  Core material 2 and  coating  material 1 \\ \hline
   D\leq \sigma_0\leq D(1-\frac{1}{M_2}) & \langle|\mathbb{P}^H\sigma|^p\rangle_2^{1/p}\geq \sqrt{3}[(D-\sigma_0)M_2-D]& Core material 1 and coating  material 2\\ \hline
   D(1-\frac{1}{M_2})< \sigma_0< D(1-\frac{1}{L_2}) & \langle|\mathbb{P}^H\sigma|^p\rangle_2^{1/p}\geq 0& Optimality undetermined \\ \hline
   D(1-\frac{1}{L_2})\leq \sigma_0<\infty & \langle|\mathbb{P}^H\sigma|^p\rangle_2^{1/p}\geq \sqrt{3}[(\sigma_0-D)L_2+D]& Core material 2 and coating material 1\\ \hline
   \end{array}
   $$

Next we suppose that $h_1>h_2$ and  present optimal lower bounds on $\langle|\mathbb{P}^H\sigma|^p\rangle_2^{1/p}$, for $1< p\leq\infty$. The bounds and associated optimal microstructures are given in the following table.
$$
\begin{array}{|l |l|p{1.35in}|}
   \hline
   Range & Lower Bound & Optimal microstructure\\ \hline
   -\infty<\sigma_0\leq D(1-\frac{1}{L_2})& \langle|\mathbb{P}^H\sigma|^p\rangle_2^{1/p}\geq \sqrt{3}[(D-\sigma_0)L_2-D] & Core material 2 and coating material 1 \\ \hline
   D(1-\frac{1}{L_2})< \sigma_0< D(1-\frac{1}{M_2}) & \langle|\mathbb{P}^H\sigma|^p\rangle_2^{1/p}\geq 0 & Optimality undetermined\\ \hline
   D(1-\frac{1}{M_2})\leq\sigma_0\leq D &\langle|\mathbb{P}^H\sigma|^p\rangle_2^{1/p}\geq \sqrt{3}[(\sigma_0-D)M_2+D]& Core material 1 and coating material 2\\ \hline
   D\leq \sigma_0 <\infty& \langle|\mathbb{P}^H\sigma|^p\rangle_2^{1/p}\geq \sqrt{3}[(\sigma_0-D)L_2+D]& Core material 2 and coating material 1\\ \hline
\end{array}
$$

Lower bounds and the associated optimal microstructures for all moments $\langle|\mathbb{P}^H\sigma|^p\rangle_1^{1/p}$ for $1< p\leq\infty$ for the case $h_2>h_1$ is given in the following table.
$$
\begin{array}{|l |l|p{1.35in}|}
   \hline
   Range & Lower Bound & Optimal microstructure\\ \hline
   -\infty<\sigma_0\leq D & \langle|\mathbb{P}^H\sigma|^p\rangle_1^{1/p}\geq\sqrt{3}[(D-\sigma_0)L_1-D] & Core material 1 and coating material 2 \\ \hline
   D\leq \sigma_0\leq D(1-\frac{1}{M_1}) & \langle|\mathbb{P}^H\sigma|^p\rangle_1^{1/p}\geq\sqrt{3}[(D-\sigma_0)M_1-D]& Core material 2 and coating material 1\\ \hline
   D(1-\frac{1}{M_1})< \sigma_0< D(1-\frac{1}{L_1}) & \langle|\mathbb{P}^H\sigma|^p\rangle_1^{1/p}\geq 0& Optimality undetermined\\ \hline
   D(1-\frac{1}{L_1})\leq \sigma_0<\infty & \langle|\mathbb{P}^H\sigma|^p\rangle_1^{1/p}\geq\sqrt{3}[(\sigma_0-D)L_1+D]& Core material 1 and coating material 2\\ \hline

  \end{array}
  $$
Lower bounds and the associated optimal microstructures for all moments $\langle|\mathbb{P}^H\sigma|^p\rangle_1^{1/p}$ for $1< p\leq \infty$ for the case $h_1>h_2$ is given in the following table.

$$
\begin{array}{|l |l|p{1.35in}|}
   \hline
   Range & Lower Bound & Optimal microstructure\\ \hline
   -\infty<\sigma_0\leq D(1-\frac{1}{L_1}) & \langle|\mathbb{P}^H\sigma|^p\rangle_1^{1/p}\geq\sqrt{3}[(D-\sigma_0)L_1-D] & Core material 1 and coating material 2 \\ \hline
   D(1-\frac{1}{L_1})< \sigma_0< D(1-\frac{1}{M_1}) & \langle|\mathbb{P}^H\sigma|^p\rangle_1^{1/p}\geq 0 & Optimality undetermined\\ \hline
   D(1-\frac{1}{M_1})\leq\sigma_0\leq D & \langle|\mathbb{P}^H\sigma|^p\rangle_1^{1/p}\geq\sqrt{3}[(\sigma_0-D)M_1+D]& Core material 2 and coating material 1\\ \hline
   D\leq \sigma_0<\infty & \langle|\mathbb{P}^H\sigma|^p\rangle_1^{1/p}\geq\sqrt{3}[(\sigma_0-D)L_1+D]& Core  material 1 and coating  material 2\\ \hline
\end{array}
$$

Next we display lower bounds on $\max_{\textbf{x} \hbox{\tiny in Q}}\left\{|\mathbb{P}^H\sigma(\textbf{x})|\right\}$.
We start with the case $h_2>h_1$ and the lower bounds and optimal geometries are given in the following table.
The phase in which the maximum is attained is denoted with an asterisk.
$$
\begin{array}{|l |l|p{1.35in}|}
   \hline
   Range & Lower Bound & Optimal microstructure\\ \hline
   -\infty<\sigma_0\leq D & \max_{\textbf{x} \hbox{\tiny in Q}}\left\{|\mathbb{P}^H\sigma(\textbf{x})|\right\}\geq\sqrt{3}[(D-\sigma_0)L_1-D] & Core material $1^*$ and coating  material 2 \\ \hline
   D\leq \sigma_0\leq F & \max_{\textbf{x} \hbox{\tiny in Q}}\left\{|\mathbb{P}^H\sigma(\textbf{x})|\right\}\geq\sqrt{3}[(D-\sigma_0)M_2-D]& Core material 1 and coating material $2^*$\\ \hline
   F\leq \sigma_0<\infty & \max_{\textbf{x} \hbox{\tiny in Q}}\left\{|\mathbb{P}^H\sigma(\textbf{x})|\right\}\geq\sqrt{3}[(\sigma_0-D)L_1+D]& Core material $1^*$ and coating material 2\\ \hline
  \end{array}
$$
Lower bounds for and optimal microgepmetries for the case $h_1>h_2$ are given in the following table.
The phase in which the maximum is attained is denoted with an asterisk.
$$
\begin{array}{|l|l|p{1.35in}|}
   \hline
   Range & Lower Bound & Optimal microstructure\\ \hline
   -\infty<\sigma_0\leq F & \max_{\textbf{x} \hbox{\tiny in Q}}\left\{|\mathbb{P}^H\sigma(\textbf{x})|\right\}\geq\sqrt{3}[(D-\sigma_0)L_1-D] & Core material $1^*$ and coating material 2 \\ \hline
   F\leq \sigma_0\leq D & \max_{\textbf{x} \hbox{\tiny in Q}}\left\{|\mathbb{P}^H\sigma(\textbf{x})|\right\}\geq\sqrt{3}[(\sigma_0-D)M_2+D]& Core  material 1 and coating material $2^*$\\ \hline
   D\leq \sigma_0 <\infty & \max_{\textbf{x} \hbox{\tiny in Q}}\left\{|\mathbb{P}^H\sigma(\textbf{x})|\right\}\geq\sqrt{3}[(\sigma_0-D)L_1+D]& Core material $1^*$ and coating material 2\\ \hline
\end{array}
$$

\section{Lower bounds on local stress for non well-ordered thermoelastic composite media}
\label{sec-optstresshydrononwell}

In this section  it is
assumed that the materials inside the heterogeneous medium are elastically non well-ordered, i.e., $\mu_1>\mu_2$ and $\kappa_2>\kappa_1$.
We fix $\Delta T$ and present lower bounds that are optimal for the full range of imposed hydrostatic stresses, i.e., $-\infty<\sigma_0<\infty$. The configurations that attain the bounds for the non well-ordered case are also given by the coated sphere assemblages \cite{hscoated}.

In what follows we list the lower bounds for the non well-ordered case. These bounds are derived in  Section 5.  Their optimality follows from explicit formulas for the moments of the local fields inside the coated sphere assemblage, these are discussed and presented  in Section 5.
The first set of bounds apply to all moments $\langle|\mathbb{P}^H\sigma|^p\rangle_2^{1/p}$ for $1<p\leq\infty$.
We suppose that $h_2>h_1$ and list the bounds as a function of the imposed macroscopic stress $\sigma_0$. The bounds are displayed in the following table where the optimal microstructures are given by the coated spheres construction. The coating and core phase of the optimal coated sphere configuration is listed in the table below.

  $$
  \begin{array}{|l |l|p{1.35in}|}
   \hline
   Range & Lower Bound & Optimal microstructure\\ \hline
    -\infty<\sigma_0\leq D(1-\frac{1}{M_2}) & \langle|\mathbb{P}^H\sigma|^p\rangle_2^{1/p}\geq
    \sqrt{3}[(D-\sigma_0)M_2-D] &  Core material 1 and  coating  material 2 \\ \hline
   D(1-\frac{1}{M_2})\leq \sigma_0\leq D(1-\frac{1}{L_2}) & \langle|\mathbb{P}^H\sigma|^p\rangle_2^{1/p}\geq 0 & Optimality undetermined\\ \hline
   D(1-\frac{1}{L_2})< \sigma_0< D & \langle|\mathbb{P}^H\sigma|^p\rangle_2^{1/p}\geq \sqrt{3}[(\sigma_0-D)L_2+D]& Core material 2 and coating  material 1 \\ \hline
   D\leq \sigma_0<\infty & \langle|\mathbb{P}^H\sigma|^p\rangle_2^{1/p}\geq \sqrt{3}[(\sigma_0-D)M_2+D]& Core material 1 and coating material 2\\ \hline
   \end{array}
   $$

Next we suppose that $h_1>h_2$ and  present optimal lower bounds on $\langle|\mathbb{P}^H\sigma|^p\rangle_2^{1/p}$, for $1< p\leq\infty$. The bounds and associated optimal microstructures are given in the following table.
$$
\begin{array}{|l |l|p{1.35in}|}
   \hline
   Range & Lower Bound & Optimal microstructure\\ \hline
   -\infty<\sigma_0\leq D& \langle|\mathbb{P}^H\sigma|^p\rangle_2^{1/p}\geq \sqrt{3}[(D-\sigma_0)M_2-D] & Core material 1 and coating material 2 \\ \hline
   D< \sigma_0< D(1-\frac{1}{L_2}) & \langle|\mathbb{P}^H\sigma|^p\rangle_2^{1/p}\geq \sqrt{3}[(D-\sigma_0)L_2-D] & Core material 2 and coating material 1\\ \hline
   D(1-\frac{1}{L_2})\leq\sigma_0\leq D(1-\frac{1}{M_2}) &\langle|\mathbb{P}^H\sigma|^p\rangle_2^{1/p}\geq 0& Optimality undetermined\\ \hline
   D(1-\frac{1}{M_2})\leq \sigma_0 <\infty& \langle|\mathbb{P}^H\sigma|^p\rangle_2^{1/p}\geq \sqrt{3}[(\sigma_0-D)M_2+D]& Core material 1 and coating material 2\\ \hline
\end{array}
$$

Lower bounds and the associated optimal microstructures for all moments $\langle|\mathbb{P}^H\sigma|^p\rangle_1^{1/p}$ for $1< p\leq\infty$ for the case $h_2>h_1$ is given in the following table.
$$
\begin{array}{|l |l|p{1.35in}|}
   \hline
   Range & Lower Bound & Optimal microstructure\\ \hline
   -\infty<\sigma_0\leq D(1-\frac{1}{M_1}) & \langle|\mathbb{P}^H\sigma|^p\rangle_1^{1/p}\geq\sqrt{3}[(D-\sigma_0)M_1-D] & Core material 2 and coating material 1 \\ \hline
   D(1-\frac{1}{M_1})\leq \sigma_0\leq D(1-\frac{1}{L_1}) & \langle|\mathbb{P}^H\sigma|^p\rangle_1^{1/p}\geq 0& Optimality undetermined\\ \hline
   D(1-\frac{1}{L_1})< \sigma_0< D & \langle|\mathbb{P}^H\sigma|^p\rangle_1^{1/p}\geq \sqrt{3}[(\sigma_0-D)L_1+D]& Core material 1 and coating material 2\\ \hline
   D\leq \sigma_0<\infty & \langle|\mathbb{P}^H\sigma|^p\rangle_1^{1/p}\geq\sqrt{3}[(\sigma_0-D)M_1+D]& Core material 2 and coating material 1\\ \hline

  \end{array}
  $$
Lower bounds and the associated optimal microstructures for all moments $\langle|\mathbb{P}^H\sigma|^p\rangle_1^{1/p}$ for $1< p\leq \infty$ for the case $h_1>h_2$ is given in the following table.

$$
\begin{array}{|l |l|p{1.35in}|}
   \hline
   Range & Lower Bound & Optimal microstructure\\ \hline
   -\infty<\sigma_0\leq D & \langle|\mathbb{P}^H\sigma|^p\rangle_1^{1/p}\geq\sqrt{3}[(D-\sigma_0)M_1-D] & Core material 2 and coating material 1 \\ \hline
   D< \sigma_0< D(1-\frac{1}{L_1}) & \langle|\mathbb{P}^H\sigma|^p\rangle_1^{1/p}\geq \sqrt{3}[(D-\sigma_0)L_1-D] & Core material 1 and coating material 2\\ \hline
   D(1-\frac{1}{L_1})\leq\sigma_0\leq D(1-\frac{1}{M_1}) & \langle|\mathbb{P}^H\sigma|^p\rangle_1^{1/p}\geq 0& Optimality undetermined\\ \hline
   D(1-\frac{1}{M_1})\leq \sigma_0<\infty & \langle|\mathbb{P}^H\sigma|^p\rangle_1^{1/p}\geq\sqrt{3}[(\sigma_0-D)M_1+D]& Core  material 2 and coating  material 1\\ \hline
\end{array}
$$

Next we display lower bounds on $\max_{\textbf{x} \hbox{\tiny in Q}}\left\{|\mathbb{P}^H\sigma(\textbf{x})|\right\}$.
We start with the case $h_2>h_1$ and the lower bounds and optimal geometries are given in the following table.
The phase in which the maximum is attained is denoted by an asterisk.
$$
\begin{array}{|l |l|p{1.35in}|}
   \hline
   Range & Lower Bound & Optimal microstructure\\ \hline
   -\infty<\sigma_0\leq F & \max_{\textbf{x} \hbox{\tiny in Q}}\left\{|\mathbb{P}^H\sigma(\textbf{x})|\right\}\geq\sqrt{3}[(D-\sigma_0)M_2-D] & Core material 1 and coating  material $2^\ast$ \\ \hline
   F\leq \sigma_0\leq D & \max_{\textbf{x} \hbox{\tiny in Q}}\left\{|\mathbb{P}^H\sigma(\textbf{x})|\right\}\geq\sqrt{3}[(\sigma_0-D)L_1+D]& Core material $1^\ast$ and coating material 2\\ \hline
   D\leq \sigma_0<\infty & \max_{\textbf{x} \hbox{\tiny in Q}}\left\{|\mathbb{P}^H\sigma(\textbf{x})|\right\}\geq\sqrt{3}[(\sigma_0-D)M_2+D]& Core material 1 and coating material $2^\ast$\\ \hline
  \end{array}
$$
Lower bounds for and optimal microgepmetries for the case $h_1>h_2$ are given in the following table.
The phase in which the maximum is attained is denoted by an asterisk.
$$
\begin{array}{|l |l|p{1.35in}|}
   \hline
   Range & Lower Bound & Optimal microstructure\\ \hline
   -\infty<\sigma_0\leq D & \max_{\textbf{x} \hbox{\tiny in Q}}\left\{|\mathbb{P}^H\sigma(\textbf{x})|\right\}\geq\sqrt{3}[(D-\sigma_0)M_2-D] & Core material 1 and coating material $2^\ast$ \\ \hline
   D\leq \sigma_0\leq F & \max_{\textbf{x} \hbox{\tiny in Q}}\left\{|\mathbb{P}^H\sigma(\textbf{x})|\right\}\geq\sqrt{3}[(D-\sigma_0)L_1-D]& Core  material $1^\ast$ and coating material 2\\ \hline
   F\leq \sigma_0 <\infty & \max_{\textbf{x} \hbox{\tiny in Q}}\left\{|\mathbb{P}^H\sigma(\textbf{x})|\right\}\geq\sqrt{3}[(\sigma_0-D)M_2+D]& Core material 1 and coating material $2^\ast$\\ \hline
\end{array}
$$

\bigskip
\section{Derivation of the lower bounds on $<|\mathbb{P}_H\sigma|^p>_i^\frac{1}{p}$}
\label{lower bound 2}

In this section we outline the methodology for proving optimal lower bounds.
The bounds are derived using duality relations.  We use the following duality relation posed over the space of square integrable symmetric matrix fields $\eta$ that holds for $p>1$ given by
\begin{eqnarray}
\frac{1}{p}\langle|\mathbb{P}^H\sigma|^p\rangle_i=\sup_{\eta}\left\{\langle\mathbb{P}^H\sigma: \eta\rangle_i-\frac{1}{p'}\langle|\eta|^{p'}\rangle_i \right\},\hbox{  for $i=1,2$,
\label{vec1}}
\end{eqnarray}
where $p'$ is the conjugate exponent to $p$ given by $p'=\frac{p}{p-1}$.
This relation follows immediately from standard duality relations see, \cite{Dacorogna}.
Restricting $\eta$ to the set of all constant matrices and taking the supremum delivers the basic bounds:
\begin{eqnarray}
\langle|\mathbb{P}^H\sigma|^p\rangle_i&\geq &|\langle\mathbb{P}^H\sigma\rangle_i|^p
,\hbox{ $p>1$ and for $i=1,2$}.
\label{vecbound2}
\end{eqnarray}
We point out that equality holds in \eqref{vecbound2} if and only if $\mathbb{P}^H\sigma$ is identically constant inside the  $i^{th}$ material.
In what follows we outline the method for obtaining bounds on the moments in material two noting that the identical procedure delivers bounds on the moments in  material one. We introduce the indicator function of material one $\chi_1$ taking the value 1 in material one and zero outside. The indicator function corresponding to material two is denoted by $\chi_2$ and $\chi_2=1-\chi_1$.
To proceed we rewrite the right hand side of \eqref{vecbound2} in terms of the effective elastic properties and thermal expansion coefficient.
To do this we use the following identity given by
\begin{align}\label{5.1}
 tr<\chi_2\sigma>=\frac{3k_2}{k_2-k_1}(\sigma_0-k_1\sigma_0(C^e)^{-1}I:I+k_1\Delta T (C^e)^{-1}H^e:I+k_1\Delta T<\lambda>:I).
\end{align}
\par
This identity is obtained in the following way.
Taking averages on both sides of  \eqref{constitutive}  gives $<\sigma>=\langle C(x)(\epsilon (\textbf{u}(x))-\Delta T\lambda(x))\rangle$. On writing $C(\textbf{x})=C_1+(C_2-C_1)\chi_2(\textbf{x})$ we see that
\begin{align}\label{5.2}
 <\sigma>=C_1(\bar{\epsilon}-<\lambda>)+(C_2-C_1)C_2^{-1}<\chi_2\sigma>.
\end{align}

From \eqref{effelast} we see that $\bar{\epsilon}=(C^e)^{-1}(<\sigma>-\Delta T H^e)$ and  for $\langle\sigma\rangle=\sigma_0 I$ we obtain
\begin{align}\label{5.3}
<\chi_2\sigma>=C_2(C_2-C_1)^{-1}(\sigma_0I-C_1((C^e)^{-1}\sigma_0 I-\Delta T (C^e)^{-1}H^e-\Delta T<\lambda>)).
\end{align}
The identity (\ref{5.1}) now follows by applying the hydrostatic projection $\mathbb{P}_H$ to both sides of (\ref{5.3}).
\par
We now derive the lower bound. Applying the basic bound \eqref{vecbound2} to $
\langle|\mathbb{P}_H\sigma|^p\rangle_2$ and (\ref{5.1}) gives
\begin{eqnarray}
&&\langle|\mathbb{P}_H\sigma|^p\rangle_2\nonumber\\
&&\geq |\langle\mathbb{P}_H\sigma \rangle_2|^p=\left(\frac{tr(\langle\chi_2\sigma\rangle)}{\sqrt{3}\theta_2}\right)^p\nonumber\\
&&=3^{p/2}\theta_2^{-p}|\frac{k_2}{k_2-k_1}|^p|k_1\sigma_0\left(\frac{1}{k_1}-(C^e)^{-1}I:I\right)+k_1\Delta T(C^e)^{-1}H^eI:I+k_1\Delta T \langle\lambda\rangle:I|^p.\label{5.4}
\end{eqnarray}
We note that equality holds in (\ref{5.4}) when $\mathbb{P}_H\sigma$ is constant inside material two.

We now employ an exact relation that relates  the contraction $(C^e)^{-1}H^e:I$ involving the effective thermal stress tensor $H^e$ to the quantity $(C^e)^{-1}I:I$. The exact relation used here is given by
\begin{eqnarray}
(C^e)^{-1}H^e:I&=&\frac{3(h_2-h_1)(C^e)^{-1}I:I+3(\frac{h_1}{k_2}-\frac{h_2}{k_1})}{\frac{1}{k_1}-\frac{1}{k_2}}.
\label{exact}
\end{eqnarray}
This exact relation is a direct consequence of the exact relation developed by  \cite{HashinRosen} for the effective thermal expansion tensor $\mathbf{\alpha}^e=-(C^e)^{-1}H^e$.

Substitution of \eqref{exact} into \eqref{5.4} and algebraic manipulation gives
\begin{eqnarray}
\langle|\mathbb{P}_H\sigma|^p\rangle_2^{1/p}\geq \sqrt{3}\left|(\sigma_0-D)X+ D\right|,
\label{finalbd}
\end{eqnarray}
where
\begin{eqnarray}
X=\frac{\theta_2^{-1}}{k_1^{-1}-k_2^{-1}}\left(\frac{1}{k_1}-(C^e)^{-1}I:I\right).
\label{x}
\end{eqnarray}
As before we point out that equality holds in (\ref{finalbd}) when $\mathbb{P}_H\sigma$ is identically constant inside material two.

Identical arguments deliver the lower bound on the moments over material two given by
\begin{eqnarray}
\langle|\mathbb{P}_H\sigma|^p\rangle_1^{1/p}\geq \sqrt{3}\left|(\sigma_0-D)Y+ D\right|,
\label{finalbd2}
\end{eqnarray}
where
\begin{eqnarray}
Y=\frac{\theta_1^{-1}}{k_2^{-1}-k_1^{-1}}\left(\frac{1}{k_2}-(C^e)^{-1}I:I\right),
\label{y}
\end{eqnarray}
where \eqref{finalbd2} holds with equality when $\mathbb{P}^H\sigma$ is a constant in material one.

The variables $X$ and $Y$ are constrained to lie within intervals set by bounds on the contraction
$(C^e)^{-1}I:I$. These bounds follow immediately from the work of Kantor and Bergman \cite{KB} and are given by
\begin{eqnarray}
(K_{HS}^+)^{-1}\leq (C^e)^{-1}I:I \leq (K_{HS}^-)^{-1},
\label{HS}
\end{eqnarray}
where $K_{HS}^-$ and $K_{HS}^+$ are the Hashin and Shtrikman  bulk modulus bounds \cite{hashin} given by
\begin{eqnarray}
K_{HS}^+=k_1\theta_1+k_2\theta_2-(\frac{\theta_1\theta_2(k_2-k_1)^2}{k_1\theta_2+k_2\theta_1+\frac{4}{3}\mu_1})
\label{hs+}
\end{eqnarray}
and
\begin{eqnarray} K_{HS}^-=k_1\theta_1+k_2\theta_2-(\frac{\theta_1\theta_2(k_2-k_1)^2}{k_1\theta_2+k_2\theta_1+\frac{4}{3}\mu_2}).
\label{hs-}
\end{eqnarray}
These bounds hold both for elastically well-ordered materials and elastically non well-ordered materials.
When the materials are well--ordered \eqref{HS} implies that $X$ and $Y$ lie in the intervals
\begin{eqnarray}
L_2\leq & X&\leq  M_2,\label{intervalwell1}\\
L_1\leq & Y& \leq  M_1.
\label{intervalwell2}
\end{eqnarray}
while for non well--ordered materials
\begin{eqnarray}
M_2\leq & X&\leq L_2,\label{intervalnonwell1}\\
M_1\leq & Y& \leq  L_1.
\label{intervalnonwell2}
\end{eqnarray}

A straightforward calculation in Section \ref{Newsolutions} shows that the hydrostatic component of the local stress is constant inside each phase of the coated sphere construction.  Hence  \eqref{finalbd} and \eqref{finalbd2} hold with equality for the coated spheres construction and we obtain explicit formulas for the moments of the hydrostatic component of the local stresses for these composites. For coated spheres with core phase 1 and coating phase 2, $(C^e)^{-1}I:I=(K_{HS}^-)^{-1}$ and
substitution of  \eqref{hs-} into \eqref{x} and \eqref{y} together with  \eqref{finalbd} and  \eqref{finalbd2}  shows that the moments are given by
\begin{eqnarray}
\langle|\mathbb{P}_H\sigma|^p\rangle_2^{1/p}=\sqrt{3}\left|(\sigma_0-D)M_2+ D\right|,\hbox{ and}
\label{finalbdhs+}\\
\langle|\mathbb{P}_H\sigma|^p\rangle_1^{1/p}= \sqrt{3}\left|(\sigma_0-D)L_1+ D\right|.
\label{finalbd2hs+}
\end{eqnarray}
For coated spheres with core phase 2 and coating phase 1, $(C^e)^{-1}I:I=(K_{HS}^+)^{-1}$ and
substitution of  \eqref{hs+} into \eqref{x} and \eqref{y} together with \eqref{finalbd} and  \eqref{finalbd2} shows that the moments are given by
\begin{eqnarray}
\langle|\mathbb{P}_H\sigma|^p\rangle_2^{1/p}=\sqrt{3}\left|(\sigma_0-D)L_2+ D\right|,\hbox{ and}
\label{finalbdhs-}\\
\langle|\mathbb{P}_H\sigma|^p\rangle_1^{1/p}= \sqrt{3}\left|(\sigma_0-D)M_1+ D\right|.
\label{finalbd2hs-}
\end{eqnarray}

We collect results and state the lower bounds and indicate when they are optimal.

\begin{theorem}{\rm Bounds for well-ordered composites, $k_1>k_2$.}
\label{optlowerboundswell}
For $1< p \leq\infty$, any choice of $\Delta T$,  and $-\infty<\sigma_0<\infty$ the lower bounds are given by the following formulas.
\begin{eqnarray}
\langle|\mathbb{P}_H\sigma|^p\rangle_2^{1/p}\geq \min_{L_2\leq X\leq  M_2}\left\{\sqrt{3}\left|(\sigma_0-D)X+ D\right|\right\},
\label{finalbdmin2well}
\end{eqnarray}
and when the minimum is realized for $X=L_2$ the bound is attained by the fields inside the core phase of a coated sphere construction with core material 2 and coating 1;  when the minimum is realized for $X=M_2$ the bound is attained by the fields inside the coating phase of a coated sphere construction with core material 1 and coating 2.

\begin{eqnarray}
\langle|\mathbb{P}_H\sigma|^p\rangle_1^{1/p}\geq \min_{L_1\leq Y\leq  M_1}\left\{\sqrt{3}\left|(\sigma_0-D)Y+ D\right|\right\},
\label{finalbdmin1well}
\end{eqnarray}
and when the minimum is realized for $Y=L_1$ the bound is attained by the fields inside the core phase of a coated sphere construction with core material 1 and coating 2 and  when the minimum is realized for $Y=M_1$ the bound is attained by the fields inside the coating phase of a coated sphere construction with core material 2 and coating 1.
\end{theorem}

\begin{theorem}{\rm Bounds for non well-ordered composites, $k_2>k_1$.}
\label{optlowerboundsnonwell}
For $1< p \leq\infty$, any choice of $\Delta T$, and $-\infty<\sigma_0<\infty$ the lower bounds are given by the following formulas.
\begin{eqnarray}
\langle|\mathbb{P}_H\sigma|^p\rangle_2^{1/p}\geq \min_{M_2\leq X\leq  L_2}\left\{\sqrt{3}\left|(\sigma_0-D)X+ D\right|\right\},
\label{finalbdmin2nonwell}
\end{eqnarray}
and when the minimum is realized for $X=L_2$ the bound is attained by the fields inside the core phase of a coated sphere construction with core material 2 and coating 1;  when the minimum is realized for $X=M_2$ the bound is attained by the fields inside the coating phase of a coated sphere construction with core material 1 and coating 2.

\begin{eqnarray}
\langle|\mathbb{P}_H\sigma|^p\rangle_1^{1/p}\geq \min_{M_1\leq Y\leq  L_1}\left\{\sqrt{3}\left|(\sigma_0-D)Y+ D\right|\right\},
\label{finalbdmin1nonwell}
\end{eqnarray}
and when the minimum is realized for $Y=L_1$ the bound is attained by the fields inside the core phase of a coated sphere construction with core material 1 and coating 2 and  when the minimum is realized for $Y=M_1$ the bound is attained by the fields inside the coating phase of a coated sphere construction with core material 2 and coating 1.
\end{theorem}

These bounds are stated explicitly in the first four tables of Sections 3 and 4.

We conclude by outlining the steps behind the derivation of the lower bounds on the maximum values of the local fields inside thermally stressed composites. For the well--ordered case we use the simple lower bound given by
\begin{eqnarray}
\max_{ \textbf{x}\hbox{ \tiny in $Q$}}\left\{\right|\mathbb{P}^H\sigma(\textbf{x})\}\geq\max\left\{A,B\right\}.
\label{linftyab}
\end{eqnarray}
where
\begin{eqnarray}
A&=&\min_{L_2\leq X\leq  M_2}\left\{\sqrt{3}\left|(\sigma_0-D)X+ D\right|\right\},\nonumber\\
B&=&\min_{L_1\leq Y\leq  M_1}\left\{\sqrt{3}\left|(\sigma_0-D)Y+ D\right|\right\}.
\label{ab}
\end{eqnarray}For the non well--ordered case we use
\begin{eqnarray}
\max_{\textbf{x}\hbox{ \tiny  in $Q$}}\left\{\right|\mathbb{P}^H\sigma(\textbf{x})\}\geq\max\left\{C,D\right\}.
\label{linftycd}
\end{eqnarray}
where
\begin{eqnarray}
C&=&\min_{M_2\leq X\leq  L_2}\left\{\sqrt{3}\left|(\sigma_0-D)X+ D\right|\right\},\nonumber\\
D&=&\min_{M_1\leq Y\leq  L_1}\left\{\sqrt{3}\left|(\sigma_0-D)Y+ D\right|\right\}.
\label{cd}
\end{eqnarray}

The bounds given in the last two tables presented in Sections 3 and 4 follow from  straight forward but tedious calculation of the explicit formulas corresponding to \eqref{linftyab} and \eqref{linftycd}.
A delicate but straight forward computation shows that these lower bounds are attained by the fields inside the coated sphere assemblage.

\bigskip
\bigskip
\section{Local stress and strain fields inside  thermally stressed  coated sphere geometries}
\label{Newsolutions}

In this section we summarize the properties of local fields inside the coated sphere assemblage in the presence of thermal stress due to a mismatch in the coefficients of thermal expansion. From linearity the local stress can be split into the sum of two components; one component arising from imposed mechanical stress and a second component associated with thermal stress. It is known that the local stress due to an imposed hydrostatic stress has constant hydrostatic part inside each phase, this follows from explicit solution see for example \cite{Milton}.
Here we display the  explicit solution for the local stress due to mismatch in the coefficients of thermal expansion and show that it has a constant hydrostatic component inside each phase. From this we conclude that the total local stress inside the coated sphere assemblage has a constant hydrostatic component inside each phase.

We solve for the stress inside a prototypical coated sphere composed of a spherical core of material two with  radius $a$, surrounded by a concentric shell of material one with an outer radius $b$. The ratio $(a/b)^3$ is fixed and equal to the inclusion volume fraction $\theta_2$. Here the the coefficients of thermal expansion for the core and coating are given by $h_1$ and $h_2$ respectively. The local elastic displacement $\tilde{\varphi}$ satisfies the equations of elastic equilibrium are given by:

\begin{displaymath}
\left\{\begin{array}{ll} div(C_2(\epsilon (\tilde{\varphi})-h_2I))=0 & 0<r<a ,\\
div(C_1(\epsilon (\tilde{\varphi})-h_1I))=0 & a<r<b,\\
C_1(\epsilon (\tilde{\varphi})-h_1I) \textbf{n}|_1=C_2(\epsilon (\tilde{\varphi})-h_2I)\textbf{n}|_2 & \text{continuity of traction at } r=a,\\
\tilde{\varphi} \quad\text{is continuous}& \text{on $0<r<b$},\\
\tilde{\varphi}=0  &\text{on the boundary $r=b$}.\end{array}\right.
\end{displaymath}
\par
We assume a general form of the solution given by
\begin{equation*}
\tilde{\varphi} =
\begin{cases}
C\textbf{r} & 0<r<a,\\
A\textbf{r}+B\frac{\textbf{n}}{r^2} & a<r<b,\\
0 & r\geq b,
\end{cases}
\end{equation*}
where $r=|\textbf{r}|, \textbf{n}=\textbf{r}/r$ and $A, B, C$ are unknowns. The corresponding strain field $\epsilon(\tilde{\varphi})$ is given by
\begin{equation}
(\epsilon (\tilde{\varphi}))_{ij} =\frac{1}{2}(\tilde{\varphi}_{i,j}+\tilde{\varphi}_{j,i})=
\begin{cases}
C\delta_{ij} & 0<r<a,\\
A\delta_{ij}+\frac{B}{r^3}(\delta_{ij}-3n_in_j) & a<r<b,\\
0 & r\geq b.
\end{cases}
\label{hydroconst}
\end{equation}

On applying the continuity of displacement and the traction at the interface we find that
$$A=\frac{3\theta_2(k_1h_1-k_2h_2)}{3k_1\theta_2+4\mu_1+3k_2(1-\theta_2)} , $$
$$B=\frac{-3a^3(k_1h_1-k_2h_2)}{3k_1\theta_2+4\mu_1+3k_2(1-\theta_2)} , $$
$$C=\frac{-3(1-\theta_2)(k_1h_1-k_2h_2)}{3k_1\theta_2+4\mu_1+3k_2(1-\theta_2)}.$$
\\
\par
Computation of the radical component of the stress at $r=b$ gives
\begin{eqnarray}
C_1(\epsilon(\tilde{\varphi})-h_1I) \textbf{n}=H^\ast\textbf{n}
\label{normal}
\end{eqnarray}
where $H^\ast$
\begin{align}\label{2.3}
H^\ast=\frac{3\theta_2(3k_1+4\mu_1)(k_1h_1-k_2h_2)}{3k_1\theta_2+4\mu_1+3k_2(1-\theta_2)}I-3k_1h_1I.
\end{align}
\\
\par
In this way we have constructed a solution $\tilde{\varphi}$ for the elastic field inside  every coated sphere in the assemblage.
We now define $\varphi^p$ on the whole domain $Q$ to be given by $\tilde{\varphi}$ inside each coated sphere and zero outside. It easily follows on integrating by parts using
\eqref{normal} together with the fact that $\varphi^p$ vanishes on the boundary of each coated sphere that $\varphi^p$ is the weak  solution \cite{Gilbarg} of $div(C(\epsilon (\varphi^p-\lambda))=0 $ over the full domain $Q$, i.e.,$$\langle C(\epsilon (\varphi^p)-\lambda):\epsilon(\phi)\rangle=0$$ for every periodic test function $\phi$.
Equation \eqref{hydroconst} implies that hydrostatic component of stress is constant inside each phase.

Last we show that the effective thermal stress $H^e$ for the coated sphere assemblage is given by $H^\ast$. Inside each coated sphere $S_i$, $i=1,2,\ldots$ we consider $\sigma=C(\epsilon (\varphi^p)-\lambda)$ and integrate by parts and apply \eqref{normal} to find that
\begin{eqnarray}
\int_{S_i}\sigma d\textbf{x}&=&\int_{\partial S_i}(\sigma\textbf{n})\otimes\textbf{x} ds\\
&=&\int_{\partial S_i}(H^\ast\textbf{n})\otimes\textbf{x} ds=|S_i|H^\ast
\label{intbyparts}
\end{eqnarray}
where $ds$ is an element of surface area on the outer surface of the coated sphere $\partial S_i$
and $|S_i|$ is the volume of $S_i$.
Substitution of \eqref{intbyparts} into \eqref{effectethstress}
gives the required identity
\begin{eqnarray}
H^e=\langle\sigma\rangle=\sum_{i=1}^\infty \int_{S_i}\sigma d\textbf{x}=H^\ast.
\label{intbypartsandidentity}
\end{eqnarray}

redpajama_set_name: RedPajamaArXiv


text:
A life of magic chemistry : autobiographical reflections by George A. Olah, Thomas Mathew
By George A. Olah, Thomas Mathew
The autobiography of a Nobel Prize winner, this e-book tells us approximately George Olah's interesting study into super robust superacids and the way it yielded the typical time period "magic acids." Olah courses us via his lengthy and memorable trip, from Budapest to Cleveland to l. a., with a stopover in Stockholm. This up-to-date autobiography of a Nobel Prize winner George A. Olah:
Chronicles the celebrated profession of a chemist whose paintings in a vast diversity of chemistry parts, and such a lot significantly that during methane chemistry, resulted in applied sciences that impression the processing and software of other fuels
Is in keeping with Olah's paintings on super robust superacids and the way they yielded the typical time period, "magic acids"
Details occasions because the ebook of the 1st variation in 2000
Inspires readers with information on Dr. Olah's winning fresh examine on methanol, meant to aid supply an answer to "the oil problem"
Read Online or Download A life of magic chemistry : autobiographical reflections including post-Nobel Prize years and the methanol economy PDF
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Home » Europe » Turkish F-16 Shoots Down Syrian Plane, Caught On Live Video | Zero Hedge
Turkish F-16 Shoots Down Syrian Plane, Caught On Live Video | Zero Hedge
Turkish F-16 Shoots Down Syrian Plane, Caught On Live Video | Zero Hedge.
Remember this country, the place which about a year ago was supposed to be "Ukraine" in terms of geopolitical escalations:
Well, in the aftermath of what appears a tenuous detente over the Crimea while Putin plans his next step of how to "merge" with east Ukraine as he sets off to rebuild the USSR, Syria just may be set to regain its place at the top of the global geopolitical risk pyramid. Case in point, early this morning, the fragile ceasefire between Syria and Turkey was shatered after a Turkish F- 16 shot down a Syrian plane on Sunday after it crossed into Turkish air space in a border region where Syrian rebels have been battling President Bashar al-Assad's forces.
A photo of the falling plane was caught by twitter:
Anatolian Agency take the photos of Syrian jet down pic.twitter.com/xK59LUawvx
— Cüneyt Toros (@cuneyttoros) March 23, 2014
Reuters reports:
"A Syrian plane violated our airspace," Prime Minister Tayyip Erdogan told an election rally of his supporters in northwest Turkey. "Our F-16s took off and hit this plane. Why? Because if you violate my airspace, our slap after this will be hard,"
The rebels have been fighting for control of the Kasab crossing, the border region, since Friday, when they launched an offensive which Syrian authorities say was backed by Turkey's military.
Syria said Turkish air defenses shot down the jet while it was attacking rebel forces inside Syrian territory, calling the move a "blatant aggression".
State television quoted a military source as saying the pilot managed to eject from the plane. The Syrian Observatory for Human Rights monitoring group said initial reports from the area said the plane came down on the Syrian side of the border.
Al Manar, the television station of Assad's Lebanese ally Hezbollah, said two rockets had been fired from Turkish territory at the Syrian jet.
Amazingly, here is a clip of a live broadcast by HaberTurk which appears to have caught the moment of the plane's crash live on video.
Why did Turkey really engage? Simple: to distract from PM Erdogan's relentless political collapse when one after another political scandal is hitting the embattled premier who last week shut down access to Twitter, and it likely set to block YouTube as well, where a phone recording of his admitting graft and embezzlement can still be found. Naturally, it struck at the one country it knows will hardly fight back against the NATO member, although now that Russian foreign policy sentiment is once again shifting dramatically, and may call for far greater support for Syria, not to mention that suddenly Turkey is hardly in "democratic" Europe's good graces in the aftermath of the Twitter censorship scandal, Erdogan may just have miscalculated.
As for the next steps in Turkey, we repeat what we said on Friday: "We eagerly look forward to see which particular pro-Western agent is groomed to take Erdogan's place. After all remember: those Qatari gas pipelines that in a parallel universe, one without Putin, would have already been transporting nat gas under Syria, would enter Europe under Turkey."
Surely following yet another "chess" victory by Putin in the foreign relations arena, the urgency to find that Qatari natgas outlet to Europe is that much greater…
Tags: Erdogan, qatari syria pipelilne, Syria, syrian jet, syrian jet turkey, Turkey, turkey erdogan, turkey syria
By https://olduvai.ca in Europe, Geopolitical, Middle East on March 23, 2014 .
← Would America Go to War with Russia?	The Federal Reserve Seems Quite Serious About Tapering – So What Comes Next? →
hgfjklm says:
THE ROTHSCHILDS TAKE PART IN THE DANCE OF THE WAR AGAINST SYRIA
" Syria has been gripped by deadly violence since 2011.
Over 130,000 people have been killed and millions displaced due to the violence fueled by Western-backed militants.
The Western powers and their regional allies — especially Qatar, Saudi Arabia and Turkey — are reportedly supporting the militants operating inside Syria."
http://www.strategic-culture.org/news/2014/03/25/militants-seize-parts-of-northwestern-syria-town.html
1) ERDOGAN, PRIME MINISTER OF TURKEY, AGENT OF THE BRITISH ROYAL FAMILY FRONT OF THE ROTHSCHILDS.
" As we noted here, Turkish Prime Minister Erdogan had blocked Twitter access to his nation ahead of what was rumored to be a "spectacular" leak before this weekend's elections. Then this morning, amid a mad scramble, he reportedly (despite the nation's court ruling the bans illegal) blocked YouTube access. However, by the magic of the interwebs, we have the 'leaked' clip and it is clear why he wanted it blocked/banned. As the rough translation explains, it purports to be a conversation between key Turkish military and political leaders discussing what appears to be a false flag attack to launch war with Syria…."
http://www.zerohedge.com/news/2014-03-27/here-youtube-false-flag-attack-syria-clip-erdogan-wanted-banned
" Erdoğan couple meets with Britain's Queen Elizabeth in London
3 April 2011 /
Turkish Prime Minister Recep Tayyip Erdoğan and his wife, Emine, met with Britain's Queen Elizabeth II at Buckingham Palace on Thursday. Erdoğan, together with his wife, State Minister Zafer Çağlayan and Chief European Union Negotiator Egemen Bağış were on an official visit to London.
The visit came three years after the queen made her first visit to Turkey in 37 years in 2008, a trip designed to underscore the UK's support for Turkish membership in the European Union. During her four-day trip with her husband, Prince Philip, the queen toured the city of İstanbul, where she took in exhibitions and enjoyed a boat tour of the Bosporus. She held meetings with President Abdullah Gül and Erdoğan.
During his visit to London Erdoğan announced that he is contemplating whether Turkey should adopt the presidential system in a referendum following the general elections of June 12. Speaking to Bloomberg TV during his visit to London, Erdoğan said he has been a supporter of the presidential system for years and that he is willing to take a step to this effect with the approval of the public. When asked whether he will take the issue to a referendum, Erdoğan replied: "It could be presented to a referendum. It is not possible to take the issue to a referendum straightaway. This matter is not on our election agenda, either. We can discuss it after the general elections."
The Justice and Development Party (AK Party) government, which is expected to secure a third term in power following the general elections of June, wants to push ahead with the preparation of a new, civilian and pro-democratic Constitution. Erdoğan, who is a supporter of the presidential system, frequently brings the issue to the public's attention, and many say he intends to become Turkey's first president under a presidential system. "
http://www.todayszaman.com/newsDetail_getNewsById.action?load=detay&newsId=240011&link=240011
" Queen Elizabeth II and husband Prince Philip were in Turkey May 16, 2008 to watch a soccer match. The game began with a ceremony with the Queen presenting the match ball to the young player – in front of Turkey's Prime Minister Tayyip Erdogan his wife Emine Erdogan. "
http://www.everyjoe.com/2008/05/20/sports/queen-elizabeth-ii-attends-football-match-in-turkey/
http://www.zimbio.com/pictures/2sG70uzyZa8/Queen+Duke+Edinburgh+During+Their+State+Visit/qdxFjAPANkj/Recep+Tayyip+Erdogan
THE BRITISH ROYAL FAMILY IS CONNECTED WITH JACOB ROTHSCHILD, BENJAMIN DE ROTHSCHILD, ARIANE DE ROTHSCHILD AND EVELYN DE ROTHSCHILD.
JACOB ROTHSCHILD "is also a Member of the Council for the Duchy of Cornwall for HRH The Prince of Wales……", a "Trustee of the Prince of Wales' Prince's Charities Foundation. " and in " 2002 awarded the Order of Merit by Her Majesty the Queen. Members of the Order are limited in number to 24 and the order is given to those who have rendered exceptionally meritorious service in the field of the arts, learning, literature and science "
https://en.wikipedia.org/wiki/Jacob_Rothschild,_4th_Baron_Rothschild
" Prince Charles, Prince of Wales, President, Arts and Business awards The Prince of Wales Medal for Philanthropy 2013 to Lord Jacob Rothschild, one of the five recipients, during a ceremony on December 11, 2013 in London, England. " http://www.zimbio.com/photos/Prince+Charles/Jacob+Rothschild/Reception+Held+Prince+Charles+London/08Isgaq04Qa
https://en.wikipedia.org/wiki/Waddesdon http://www.waddesdon.org.uk/ https://wikispooks.com/ISGP/organisations/introduction/PEHI_Jacob_de_Rothschild_bio.htm
" Prince Charles already played polo with EVELYN DE ROTHSCHILD in his student years and later set up the Interfaith consultations with him. "
http://www.gnosticliberationfront.com/ people_with_the_endless_bios.htm
Evelyn de Rothschild " In 1989, he was knighted by Queen Elizabeth II,[2] for whom he serves as a financial adviser. " https://en.wikipedia.org/wiki/Evelyn_Robert_de_Rothschild – http://www.breathingenglishair.blogspot.fr/2012/04/ascott-house-buckinghamshire.html
EVELYN DE ROTHSCHILD IS ALSO A FRIEND OF PRINCE ANDREW. https://wikispooks.com/ISGP/organisations/introduction/PEHI_Evelyn_de_Rothschild_bio.htm
But the Royal Bank of Scotland, a bank controlled by the British Royal Family, is also connected with the bank Edmond De Rothschild controlled by BENJAMIN DE ROTHSCHILD and by his wife ARIANE DE ROTHSCHILD FOR EXAMPLE THROUGH THE PERSONS OF MARK PHILLIPS AND LAURA SCOLAN, ETC..
http://www.mirror.co.uk/news/uk-news/prince-charles-dumps-rbs-boss-372885 https://en.wikipedia.org/wiki/Benjamin_de_Rothschild https://en.wikipedia.org/wiki/Ariane_de_Rothschild
Mark Phillips, Current Vice President at Banque Privée Edmond de Rothschild, was Vice President at RBS Coutts Bank Ltd, Geneva from March 2003 to September 2011.
http://www.linkedin.com/pub/mark-phillips/4/5b9/772
Laura Scolan, current Executive Director of Royal Bank of Scotland, was Associate at LCF Edmond de Rothschild. http://www.linkedin.com/pub/laura-scolan/a/ba1/7b7
http://wikimapia.org/6825620/fr/Chateau-de-Pregny http://www.panoramio.com/photo/77169200
" Benjamin de Rothschild, only son of the late Edmond de Rothschild, was a classic case of great expectations gone astray. Despite being groomed for greatness from a young age, as a teenager he skipped university and instead headed for Los Angeles with dreams of being a film producer. In LA he started taking drugs, and ended up on heroin. Meanwhile, he failed to make it into Hollywood's charmed circle and bombed as a film-maker. "
http://www.independent.co.uk/arts-entertainment/poor-little-rich-boys-1097744.html
http://www.lejdd.fr/ Economie/Images/Les-plus-grosses-fortunes-de-France/Benjamin-de-Rothschild-206941
2) QATAR IS A PROTECTORATE OF THE BRITISH ROYAL FAMILY AND OF THE ROTHSCHILDS.
" Asked what role RBS intended to play in Qatar's development, he said, "Our relationship with Qatar began some 20 years ago: from the beginning of project finance in the energy industry. We greatly value our relationship. "And we will expand all our efforts to support the economy here through financing, through ideas of diversifying the wealth internationally, in both directions. And where we have advisory expertise, we will bring that here. Where we have expertise in financial and risk management, we will bring that as well. RBS will work in partnership with our good clients here."
The Edinburgh-based global bank opened its branch at the Qatar Financial Centre with a focus on investment banking, and private banking through RBS Coutts, the private banking arm. " http://www.ipfa.org/news/12957/rbs-pledges-its-expertise-to-support-long-term-qatar-growth
" The power behind the Royal Bank of Scotland (RBS), is the British monarchy. Among RBS's holdings is Coutts & Co., perhaps the premier private bank in the world. Coutts, whose logo consists of three crowns, provides discreet banking services for members of the British royal family, foreign royals, and many prominent imperial agents around the world." http://larouchepac.com/node/13516
"Qatar's leader visits Britain for talks with David Cameron, Queen Elizabeth II
According to the AP, "The Emir of Qatar, the ruler of a tiny, oil-rich nation in the Persian Gulf, is visiting Britain for talks with Queen Elizabeth II and Prime Minister David Cameron. Sheik Hamad bin Khalifa Al-Thani began his three-day visit Tuesday with Sheika Mozah bint Nasser al-Missned, the most high-profile of his three wives. …."
http://www.swfinstitute.org/other-swf-news/qatars-leader-visits-britain-for-talks-with-david-cameron-queen-elizabeth-ii/
3) ALSO THE SAUDI ROYAL FAMILY IS STRONGLY RELATED WITH THE BRITISH MONARCHY AND THE ROTHSCHILDS.
A) " BEIRUT, MARCH 25 – "Changing the balance of power on the ground" in Syria by providing more aid to rebels is necessary to get out of the crisis, Saudi heir prince, Salman bin Abdulaziz, said in Kuwait, where he opened the annual Arab League summit, al Arabiya reported Tuesday. The Saudi representative also called for the Syrian coalition of opposition forces to be offered the seat representing Damascus within the Arab League."
http://www.ansa.it/ansamed/en/news/nations/kuwait/2014/03/25/Syria-Saudi-Arabia-balance-of-power-must-change_85eb6eb3-20cf-4738-86fd-6866eab270a3.html
" Prince Salman was born on 31 December 1935.[1] He is reported to be the 25th son of King Abdulaziz." https://en.wikipedia.org/wiki/Salman_bin_Abdul_Aziz
https://en.wikipedia.org/wiki/King_Abdulaziz
" The Bush family has had a long and mutually profitable connection with the corrupt Saudi oil dictatorship. Prince Bandar, Saudi ambassador to the United States, has been an honored guest both at the Bush I summer home in Kennebunkport, Maine, and at Bush 11's getaway in Crawford, Texas (hence his nickname, "Bandar Bush"). Bandar expressed his gratitude to Bush I by donating $1 million to the Bush Presidential Library in Texas. And Bandar's prodding prompted Saudi King Fahd to send another $1 million to Barbara Bush's campaign against illiteracy.
Saudi Prince al-Walid contributed half a million petrodollars to help launch the George Herbert Walker Bush Scholarship Fund at Phillips Academy, the alma mater of both Bush presidents. The depth of these connections was highlighted when the former president visited the Saudis to "discuss U.S.-Saudi business relations" with Crown Prince Abdullah during his son's 2000 presidential campaign.
And then there is the bin Laden problem. The bin Laden family, a key Carlyle investor, stood to make millions of dollars from the war on terror-a war that has as its chief villain a member of their own family. The bin Ladens withdrew from the Carlyle Group in late October 200 1, but it's not just the bin Laden family proper that was problematic for the Bushes. It turns out that Prince Bandar's wife, Princess Haifa, had made charitable contributions that may have helped finance two of the 9/11 hijackers. "
http://www.thirdworldtraveler.com/Bush_Gang/CarlyleGroup_TETTR.html
( Did Saudi Prince Bandar Give Chemical Weapons to the Syrian Opposition? http://larouchepac.com/node/27965 )
( Bandar Threatens U.S. and Foreign Journalists Who Exposed Syrian Rebel Role in Chemical Attack http://larouchepac.com/node/28248 )
Prince Bandar is the son of Sultan bin Abdulaziz " the 12th son of King Abdulaziz" https://en.wikipedia.org/wiki/Sultan_bin_Abdul_Aziz
THE BUSH FAMILY IS CONNECTED WITH THE QUEEN OF ENGLAND.
" Ronald Reagan (who along with George Bush, was knighted by the Queen" http://www.despatch.cth.com.au/Despatch/Vol93_Charles_sustainable.htm
B) " …….Al-Massari is allied with the well-known Saudi expatriate Osama bin Laden, who, to this day, maintains a residence in the wealthy London suburb of Wembly. And London is the headquarters of bin Laden's Advise and Reform Commission, run by the London-based Khalid al-Fawwaz.
Bin Laden has been given regular access to BBC and a variety of major British newspapers, to spread his calls for jihad against the United States. Thus, in July 1996, bin Laden told the London Independent, "What happened in Khobar [the U.S. Army barracks that was bombed on June 25] is a clear proof of the enormous rage of the Saudi population against them. Resistance against America will spread in many places through Muslim lands……"
http://www.larouchepub.com/lar/2000/terror_memo_2703.html
( Threat of 9/11 US terror network still looms http://nypost.com/2014/03/23/threat-of-us-terror-network-still-looms/ )
THE BBC IS ALSO WELL CONTROLLED BY THE QUEEN ELIZABETH II.
" Christopher Francis Patten, Baron Patten of Barnes CH PC (born 12 May 1944) is a British public servant. He is chairman of the BBC Trust and Chancellor of the University of Oxford……. On 7 April 2011 the Queen approved Patten's appointment as the Chairman of the BBC Trust, the governing body of the British Broadcasting Corporation…….In 1998, Queen Elizabeth II appointed him a Companion of Honour (CH)." https://en.wikipedia.org/wiki/Lord_Patten_of_Barnes
C) PRINCE CHARLES AND THE ROTHSCHILDS TAKE PART TO THE DANCE OF THE WAR AGAINST SYRIA?
" 19 February 2014 …………
Prince Charles joined members of the Saudi royal family for the Ardah – or sword dance – in the capital Riyadh.
The prince wore a traditional ankle-length garment, known as a "thobe", for the all-male ceremony which is usually performed at events such as weddings.
He is touring the Middle East, where he is visiting Saudi Arabia and Qatar.
10th trip
It is HIS SECOND VISIT TO THE TWO NATIONS IN JUST UNDER A YEAR AND HIS 10th OFFICIAL TRIP TO SAUDI since he first toured the nation in 1986………..
The prince's host was Prince Muqrin bin Abdulaziz, the former head of the Saudi intelligence service who was named as the second deputy prime minister by King Abdullah last year.
The Associated Press news agency reported a Buckingham Palace statement that said the prince had also planned to meet the Saudi king before he heads to QATAR for a two-day visit. " http://www.bbc.co.uk/news/uk-26252091
" Muqrin bin Abdulaziz was born in Riyadh on 15 September 1945.[3][4] He is the 35th and the youngest surviving son of King Abdulaziz "
https://en.wikipedia.org/wiki/Muqrin_bin_Abdulaziz_Al_Saud
The King of Saudi Arabia " Abdullah was born on 1 August 1924. He is the tenth son of King Abdulaziz." https://en.wikipedia.org/wiki/Abdullah_of_Saudi_Arabia
4) WHAT IS GONE TO DO IN RIYADH THE INSIGNIFICANT PUPPET OF THE ROTHSCHILDS CALLED obama ?
" Over seven decades, the United States and Saudi Arabia forged a strategic alliance that became a linchpin of the regional order: a liberal democracy and an ultraconservative monarchy united by shared interests in the stability of the Middle East and the continued flow of oil.
But with President Obama arriving in Riyadh on Friday, the rulers of Saudi Arabia say they feel increasingly compelled to go their own way, pursuing starkly different strategies from Washington in dealing with Iran, Syria, Egypt and the role of the Muslim Brotherhood in the region……"
http://seeker401.wordpress.com/2014/03/31/obama-seeks-to-calm-saudis-as-paths-split/
( FIGHTING AL QAEDA BY SUPPORTING AL QAEDA IN SYRIA: THE OBAMA ADMINISTRATION IS A 'STATE SPONSOR OF TERRORISM' ) http://jimcraven10.wordpress.com/2013/06/23/4928/
" The Queen symbolises the "best of England" to the whole world, President Barack Obama has told the BBC.
Speaking ahead of his first state visit to the UK on Tuesday, he said the Queen and Duke of Edinburgh were "extraordinarily gracious people".
The president and First Lady Michelle Obama will be guests of the Queen at Buckingham Palace for three days……..
The president told the BBC's Andrew Marr: "I think what the Queen symbolises not just to Great Britain, but to the entire Commonwealth, and obviously the entire world, is the best of England. And we're very proud of her."
He also went on to highlight the Queen's kindness, praising how welcoming she had been when the first lady and their two daughters visited Buckingham Palace without him in June 2009.
"She could not have been more charming and gracious to the girls," said President Obama." http://www.bbc.co.uk/news/uk-13489879
http://www.theguardian.com/world/gallery/2011/may/24/barack-obama-uk-state-visit-in-pictures?picture=374933181
5) THE CORRUPT BIG DRUG TRAFFICKERS OF AFGHANISTAN
" Afghan H-bomb: Record opium harvest, billions burn in 'war on drugs'
Introduction — April 2, 2014
It cannot be overemphasised: drugs were the real reason Coalition forces invaded Afghanistan and toppled the Taliban.
Poppy fields in HELMAND Province. Click to enlarge
In 2000, the year before the U.S. led invasion the then ruling Taliban banned the cultivation of poppies as a sin against Islam. By spring of the following year Afghanistan's once thriving drugs trade was all but dead. In less than one growing season the edict brought to a close a narcotics industry that had formerly produced three-quarters of the world's opium.
Or so it seemed.
By the end of 2001, the U.S. led invasion also brought a revival of Afghanistan's drugs trade. From that point on Afghanistan' narcotics trade went from strength to strength. So that from having produced virtually no narcotics in the final year of the Taliban's rule, Afghanistan is now producing over 80% of the world's opium and heroin.
This is the real legacy of the U.S. led invasion. Not "freedom" or even the eradication of the Taliban, who will remain a potent threat for whoever sits in Kabul when Coalition forces finally withdraw at the end of the year.
Apart from the many thousands of wounded, maimed and dead, the real legacy of the U.S. led invasion is a revived drugs trade and millions of drug addicted Afghans. According to a recent U.N. estimate between 3% and 4% of Afghans are now addicted to drugs.
This is what the U.S. led invasion has really brought Afghanistan. Transforming it in little more than a decade from a nation that was well on the way to becoming free of narcotics to one of the most drug dependent nations on Earth.
So the invasion of Afghanistan wasn't just an exercise in futility. Above all else it helped revive Afghanistan's moribund narcotics trade.
The British Empire had done pretty much the same thing during the Opium War, when China prohibited the sale of opium imported from India. Britain had been trading the narcotic from its Indian Crown Colony for Chinese silk and tea. However, recognising the growing number of addicts it produced the Chinese had outlawed the trade and war followed.
Being the pre-eminent global power at the time assured Britain of victory and a continuation of the opium trade …." http://www.thetruthseeker.co.uk/?p=94277
" U.K. IMPLICATED IN AFGHANISTAN DRUG TRADE
Thu Dec 15, 2011 2:28AM GMT
http://www.presstv.ir/detail/215748.html
A senior Afghan official has accused Britain of involvement in illicit narcotics trade in Afghanistan, Press TV reports.
"There are documents and evidence that show that British forces in [Afghanistan's] HELMAND Province not only did nothing to prevent the illicit drug trade, but in some cases also took part in it," Yousef-Ali Vaezi, an advisor to Afghan President Hamid Karzai, told Press TV on Thursday.
"They cooperated in the cultivation, production, and trafficking of drugs," he added…." http://theunhivedmind.com/wordpress/?p=15655
WHO HAS CONCRETE INTERESTS IN THE CULTIVATION OF OPIUM POPPIES IN AFGHANISTAN ?
" PRINCE CHARLES INSPECTS HIS MOTHER'S POPPY FIELDS IN HELMAND
April 15, 2010 • 9:00AM
On March 25-26, Prince Charles visited British troops in Afghanistan, becoming the most senior royal to visit British troops there. He received a briefing from Gen. Stanley McChrystal, U.S. commander [editor confused whether it is "British" or "U.S." commander] of all foreign troops in the country. The Guardian reported that "during a two-day visit amid tight security, he was flown by Chinook helicopter to Lashkar Gar, capital of Helmand province, where he met local leaders, the Governor Gulab Mangal, and British soldiers at a patrol base surrounded by opium poppy and wheat fields (emphasis added)."
It was not reported where Prince Charles met McChrystal, for example, in a poppy field, a heroin laboratory, or on a carpet, where the Prince was sitting cross-legged socializing with the local governor. Associated Press reported that "the 61-year-old heir to the British throne said troops can keep themselves busy in the field, but for the relatives left behind, it's 'ghastly.'" However, the Prince did not identify what the troops were keeping themselves busy with.
The AP shamelessly, but ironically, reports: "Britain has lost 276 troops since the war began in 2001. British soldiers have mainly been tasked with battling the Taliban in Helmand, the center of Afghanistan's illegal narcotics trade that has financed the militant group."
AP added that "Prince Charles crisscrossed Helmand by helicopter, flying over the canals, poppy fields, and mud compounds that make up much of the district. He met with local leaders in the provincial capital of Lashkar Gah, sitting crossed-legged on a cushion as he talked about the situation in Helmand."
It further revealed the setting where the British troops are keeping themselves busy: "At Patrol Base Pimon, nestled among the blooming pink poppy fields of Nad Ali, he met some of the 140 British troops holding the front line and was told by commanding officer Maj. Ian Lindsay-German: 'It's a lot more quiet out there now, but it hasn't been cleared fully' of insurgents."
However, clearing the fields of opium poppy is not on the agenda.
With this visit, the British are probably making it clear that Helmand might become the capital of what would be left of Afghanistan, when the catastrophic Obama Administration policy comes to a crushing defeat, and Kabul is abandoned to its fate in a sectarian and ethnically divided Afghanistan. Therefore, Helmand Province is of more interest for the British to keep quiet and "economically thriving" with the help of such American dupes as President Obama and General McChrystal. Helmand, whose Governor Mangal is being groomed by the British royals as a great tribal leader (as the British royals are themselves, oligarchical tribe leaders), is being portrayed as the stable and well-governed region of Afghanistan, unlike the "corrupt" President Karzai's Kabul. " http://larouchepac.com/node/14178
" By the 19th century – British Queen Victoria was the biggest drug trafficker. Even Queen Victoria used Opium ( Laudanum ), and records exist in the Royal Apothecary at Balmoral, as to how many times Opium was passed on to the royal palace. A lot of British noblemen were Opium eaters………. ..
"Wherever in the world any type of corruption starts,
it ends in London." "
http://greatgameindia.wordpress.com/2013/04/14/the-rothschild-colonization-of-india/
"………Such "threats" worked for HSBC in 2012, the Crown Jewel of the British dope trade for centuries which continues to operate freely in the United States, despite having been caught red-handed laundering over $15 billion in drug cartel money into the U.S. (not to mention LAUNDERING AL QAEDA FUNDS), under Obama Attorney General Eric Holder's stated doctrine that systemic banks are "too big to jail. " http://larouchepac.com/node/28700
"..The short-lived marriage, which it is understood Annabelle ended, was turbulent from the outset, with reports that the pair moved with a fast crowd of heavy drinkers and drug users in New York and London.
Mrs Neilson also made it plain yesterday that neither she nor any memberof her family wanted to have anything to do with Nat Rothschild [SON OF JACOB ROTHSCHILD] or his family again." http://www.dailymail.co.uk/news/article-1080664/Nat-Rothschild-naughty-boy-says-mother-law.html


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Instagram model Jade Ramey look like singer Demi Lovato twin
March 30, 2020 | Posted in Female Celebrities Who Look Alike, Instagram Models Who Look Alike | No comments
Jade Ramey is best known as a Instagram Star. Fitness model whose sportswear, swimwear and lingerie photos have earned her more than 700,000 followers on Instagram. She also helps others achieve their fitness goals with the workout programs sold on her personal website. Jade Ramey and Gage Bordeaux are both Instagram models who grew up in Portland. Born 29th November 1994 in Portland, Oregon Jade Ramey is well known in the social media world. Jade Ramey an instagram model appears in French Montana – Bad B*tch ft. Jeremih music video. She was seen next to French Montana brother Zack Kharbouch known on instagram zakaria_og. The music video for "Bad B!tch" was directed by Eif Rivera and released on February 23, 2015. It features cameo appearances by Travi$ Scott, Lil Durk and DJ Khaled. Jade Ramey was largely mistaken for Demo Lovato in the music video. Jade Ramey website can be found on : https://www.greatestphysiques.com/female-physiques/jade-ramey/
Demi Lovato was born on August 20, 1992 in Albuquerque, New Mexico to former Dallas Cowboys cheerleader Dianna De La Garza (née Dianna Lee Smith) and engineer and musician Patrick Martin Lovato. She has an older sister named Dallas; a younger maternal half-sister, actress Madison De La Garza; and an older paternal half-sister named Amber, whom she first spoke to when she was 20. Demi Lovato a pop, pop rock, and R&B artist singer, songwriter, actress, and television personality. She began her career in 2002 appearing on the children's television series Barney & Friends, before rising to prominence for portraying Mitchie Torres in the Disney Channel musical television film Camp Rock (2008) and its sequel Camp Rock 2: The Final Jam (2010). Demi Lovato has released six studio albums: Don't Forget (2008), Here We Go Again (2009), Unbroken (2011), Demi (2013), Confident (2015), and Tell Me You Love Me (2017); all of which debuted in the top five of the Billboard 200. She has earned nine top-20 tracks on the Billboard Hot 100 with "This Is Me", "Here We Go Again", "Send It On", "Skyscraper", "Give Your Heart a Break", "Heart Attack", "Cool for the Summer", "Sorry Not Sorry", and "I Love Me". In total, she has sold over two million albums and 20 million singles in the United States.[8] On television, Demi Lovato has starred as the titular character on Sonny with a Chance (2009–2011), served as a judge and mentor on The X Factor USA in its second and third seasons, and appeared as a recurring character on Glee. Her struggles with several personal issues received significant media attention in the 2010s; in response to which she published the book Staying Strong: 365 Days a Year (2013) and released a YouTube documentary about her life and career, titled Demi Lovato: Simply Complicated (2017). She has earned numerous awards and nominations, including an MTV Video Music Award, 14 Teen Choice Awards, five People's Choice Awards, and two Latin American Music Awards. She also holds one Guinness World Record and was included on the annual Time 100 list of the most influential people in the world in 2017. Outside the entertainment industry, Lovato is an activist for several social causes.
Instagram model Jade Ramey from French Montana – Bad B*tch music featuring Jeremih look like singer Demi Lovato twin. They are instagram models who look alike.


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Q: Inserting/Updating XMP in a PDF? How can I insert/update some XMP metadata into a PDF file preferably using java ?

A: Have a look at pdfmark from CrossRef.

A: I found that the PDFBox library can be used to insert or extract those data. See http://plindenbaum.blogspot.com/2010/07/pdfbox-insertextract-metadata-frominto.html


PENTECOSTAL, noun. A member of a Pentecostal church.
PENTECOSTAL, noun. (obsolete) An offering formerly made to the parish priest, or to the mother church, at Pentecost.
PENTECOSTAL, noun. Any member of a Pentecostal religious body.
PENTECOSTAL, adjective. Of or relating to or characteristic of any of various Pentecostal religious bodies or their members.
PENTECOSTAL, adjective. Of or relating to or occurring at Pentecost.