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Floor supports/out riggers needed to be leveled then new supports fitted.
Lots of old rivet holes filled and cleaned up.
I ended up replacing a lot of the rear box section that supports the bird cage.
1985 CCX and 1795 like this.
a lot more work will go into these diff mounts, I will fill weld clean off then tig over.
As said above this is a tricky spot to get into to weld, waiting to put the frame into my rotisserie before I will finish these mounts.
Kevin or I will up date pictures when complete.
Thanks for all the comments .
Hey, I don't want to stir any crap or dis anybodies work. I've been welding both professionally and as a hobby for over 50 years since I was a teenager and have been known to be over critical. A point I might make is though that a weld-over unless the old weld is gone is only as good as the original. With thin section tubing you will find that multiple pass MIG will harden the steel and even a wash out with a TIG overlay could cause stress cracks any place the weld changes direction. You might want to add a little runout bead to redirect stress to a stronger area. Sorry, didn't mean to jack your thread.
I'm starting to believe this was possibly a used frame at one time after seeing all the rivet holes and modifications to the frame. Was there and interior tub and/or footboxes installed at one time? I didn't notice it in the first few pics.
Okay, went back and saw it was more complete than I had originally thought. Was any of the original pieces- fender liners, tub, footboxes, trunk pieces, etc... reusable? At least the roll bars? Or is this pretty much starting from scratch.
This is starting to look an awful lot like my project. When I received my chassis, it was missing most of the birdcage, the square tubing, motor mounts, roll bar mounts, fuel tank supports, and a lot of the existing tubing had to be replaced or relocated. I can definitely appreciate all the work that is going into this project and the quality of the work and the difficulty of the locating process.
Do you have all of the control arms, uprights, shocks, and other items needed for the suspension set up? How about hood and trunk hinges?
Last edited by Three Peaks; 07-22-2016 at 11:32 PM..
No problem, thanks for the tip!
Kevin may know more on the cars history than I, but to the best of my knowledge this project had never been completed .
The only pieces to be reused will be the fiberglass foot boxes, they need a little work but will be just fine.
All the aluminum panels that were in the car are scrap, new panels will be made.
We do have all the suspension, how ever we are yet to tackle that job, I did see some issues when I disassembled the car, so these will need to be addressed.
New trunk hinges and frame will be made, I have not checked the hood yet, Kevin made the ally hood for the fiberglass body and I must say it looks great and we intend on using it in the build.
Roll bar setup is new, thanks to a good friend with an original 3k car and his generosity of allowing us to take some key measurements, the roll bar is made close to original spec.
The pedal box had to be moved, (mounted incorrectly) I made the pedal box removable as this helps down the road with mounting the ally body and foot box install.
Looking good. I think the hardest part of my project was making the birdcage for the rear of the body over the trunk and the frames for the doors, trunk lid, and hood. I think I lost a bit of hair during that process.
I also made up a jig to make up original style hood and trunk hinges I was able to copy from a 4000 hinge a buddy had. I sold about a dozen of them and still have the jig if you need some made up. Also made up some reclining seat mounting pads for the seats. I think I have one left if you need it.
The removable pedal box is a great idea. I ended up doing the same thing for the same reasons- much easier to deal with the footboxes, body mounting, and access the foot pedals and adjustments if necessary. I installed a removable bottom plate so I could access and adjust the rods in the box without contorting myself in the footbox to reach them, not to mention pulling up the carpet and other items to get to the top cover. I've used it a couple times already to adjust my clutch rod and brake bias adjustment rods and it was easy as pie.
Kevin made the ally hood for the fiberglass body and I must say it looks great and we intend on using it in the build.
So, you're keeping the hood and building a new body around it?
You guys in Craig's area are fortunate to have such a resource around.
cobrakiwi and ScratchBuilder like this.
I also intend to use the ally trunk skin he made as well.
1985 CCX, cobrakiwi and ScratchBuilder like this.
West coast too. Craig will get it done n ship quality parts. I had to replace junk control arms from the same fabricator Kevin pulled his car from. Craig built up a set, powder coated, and sent them to me quickly.
On the front frame section I had to redo the sway bar mounts, twin pusher fan mounts and oil cooler mount.
Filled all the old rivet holes and squared up the radiator opening.
Just No chance of using these door hinge brackets .
CompClassics and ScratchBuilder like this.


text:
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Referències

variable

redpajama_set_name: RedPajamaWikipedia


text:
Los términos frazada, manta o cobija son nombres para una prenda textil de abrigo usada para proteger del frío, y en especial para arroparse mientras se duerme. Se diferencian de los edredones, colchas, sábanas y otros cobertores o cubrecamas por su grosor. Por lo general se fabrican con forma alargada y rectangular. Cualquier cosa rectangular cuya función sea proteger del frío y arroparse mientras se duerme puede ser llamado frazada como una sábana o cualquier otro tipo de tela.

También forma parte de diversos trajes regionales de distintos países. Su uso específico a lo largo de la historia en el comercio y la guerra la ha asociado como prenda complementaria en el oficio de los arrieros y aguadores y en la impedimenta de las caballerías.

Tipos y texturas
 de lana de oveja, el tipo más tradicional y cálido;

 de algodón en rama tejida con un baño de goma para mantener su consistencia;

 de mezclas sintéticas, fabricada con derivados del nylon y otros tejidos sintéticos

 de pared, o tapiz;

 manta eléctrica, hecha con dos capas de tejido envolviendo una resistencia eléctrica, y un cable de toma de corriente, por lo general provisto de un regulador de temperatura.

Galería

Véase también
 Poncho
 Top manta
 Frazada polar y frazada sherpa

Notas

Referencias

Enlaces externos

Mantas
Camas (mobiliario)
Indumentaria


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Q: Make sure saga is injected before actions are dispatched I'm having some bad time with saga injection in my app, sometimes saga is loaded before the action is dispatched and everything works, sometimes the action is fired and no saga effect is triggered.
I'm using pretty standard code, here's my route:
getComponent(nextState, cb) {
    const importModules = Promise.all([
        import ('containers/HostArea/reducer'),
        import ('containers/HostArea/ActivityRegistration/reducer'),
        import ('containers/HostArea/AccommodationRegistration/reducer'),
        import ('containers/HostArea/sagas'),
        import ('containers/HostArea/'),
    ]);

    const renderRoute = loadModule(cb);

    importModules.then(([hostAreaReducer, registerActivityReducer, registerAccommodationReducer, sagas, component]) => {
        injectReducer('hostArea', hostAreaReducer.default);
        injectReducer('registerActivity', registerActivityReducer.default);
        injectReducer('registerAccommodation', registerAccommodationReducer.default);
        injectSagas(sagas.default);
        renderRoute(component);
    });

    importModules.catch(errorLoading);
},

here's my saga (I removed getCurrentHost and getHostRegistrations but of course they are defined in the same file):
export function* currentHostWatcher() {
  yield takeLatest(GET_CURRENT_HOST, getCurrentHost);
}

export function* getHostRegistrationsWatcher() {
  console.log('getHostRegistrationsWatcher');
  yield takeLatest(GET_HOST_REGISTRATIONS, getHostRegistrations);
}

export default [
  currentHostWatcher,
  getHostRegistrationsWatcher,
];

and here's the relevant part of my component:
componentDidMount() {
    console.log('componentDidMount');
    this.props.dispatch(getCurrentHost({ resolve: ((host) => this.hostAuthenticated(host)), reject: () => this.unauthenticated() }));
  }

hostAuthenticated(host) {
    console.log('host is authenticated, get his registrations');
    this.props.dispatch(getHostRegistrations({
      host,
      resolve: this.onRegistrationsLoaded,
      reject: ((err) => console.log(err)),
    }));
}

Basically what I do is dispatching an action on componentDidMount, and on success dispatching a second action, both defined in the same saga.
What I see is that with the same code, just refreshing the page, sometimes the console log shows
componentWillMount
componentDidMount
getCurrentHost
getCurrentHostSuccess
getHostRegistrations

but no effect is invoked on getHostRegistrations. Other times, it all works and I see in the log:
getHostRegistrationsWatcher
componentWillMount
componentDidMount
getCurrentHost
getCurrentHostSuccess
getHostRegistrations
host registrations loaded

As you can see, in this second case the watcher is executed before the components mount and the flow is correct.
So my question is: is there a way to make sure that saga is injected before component is mounted? Or any other workaround?
If you want to see the code in action, just signup here https://www.amavido.it/join (use random email/name and not facebook); once  logged in, refresh and you will see some times the rendere component, some times a loading indicator which hangs forever)

redpajama_set_name: RedPajamaStackExchange


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Keri Russell In Motion – A multimedia biography project
KERI RUSSELL IN MOTION
Felicity costars reunite for the first time (in bed) for EW
Keri Russell Receives Star on the Hollywood Walk of Fame
Categories Actress
Often asked: What Actress Played Blossom?
Author Polly Humble
1 What happened to the girl who played Blossom?
2 Who is the girl that played Blossom?
3 Who starred as Blossom?
4 How much is Mayim Bialik worth?
5 What is the IQ of Jim Parsons?
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Who is the girl that played Blossom?
Mayim Chaya Bialik (/ˈmaɪəm biˈɑːlɪk/ MY-əm bee-AH-lik; born December 12, 1975) is an American actress, neuroscientist, and author. From 1991 to 1995, she played the title character of the NBC sitcom Blossom.
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You might be interested: Question: What Does The Actress Precious Look Like Now?
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Who is the richest actor?
The 20 Richest Actors in the World
Amitabh Bachchan.
Adam Sandler. Net Worth: $420 million.
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Robert De Niro. Net Worth: $500 Million.
George Clooney. Net Worth: $500 Million.
Tom Cruise. Net Worth: $570 Million.
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Jami Gertz. Net Worth: $3 Billion.
What is Kaley Cuoco worth?
As of 2021, Kaley Cuoco's net worth is estimated to be roughly $100 million. Kaley Christine Cuoco is an American actress from Camarillo.
Born: November 30, 1985
Source of Wealth: Professional Actress
What is Wolowitz salary?
Considering Howard's education and the relatively young nature of his career, we can assume he makes the national average for an aerospace engineer, which is around $89,000. While his friends technically make a good deal more than him, Howard's income is still above the national average.
Polly Humble
Question: How To Become A Actress At 10?
Readers ask: Hannah Baker 13 Reasons Why Actress?
Often asked: How To Become A Disney Actress?

redpajama_set_name: RedPajamaCommonCrawl


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Born to German Catholic parents who converted to Judaism, acclaimed actress Sara von Schwarze talks to 'Journeys' about her split identity, which she mines in a new work.
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Q: Joomla - Controller task that returns JSON data I have the task run in my controller. I want it to return JSON data. As it stands, I am getting my JSON data wrapped inside the template HTML. How do I tell Joomla to just return JSON data from the controller? This is the function I have:
public function run  ( ) {

    JFactory::getDocument()->setMimeEncoding( 'application/json' );

    JResponse::setHeader('Content-Disposition','attachment;filename="progress-report-results.json"');

    JRequest::setVar('tmpl','component');

    $data = array(
        'foo' => 'bar'
    );

    echo json_encode( $data );

}

And this returns:
<html xmlns="http://www.w3.org/1999/xhtml" xml:lang="en-gb" lang="en-gb" dir="ltr">
...
</head>
<body class="contentpane">

<div id="system-message-container">
</div>
    {"foo":"bar"}
</body>
</html>

I would like to get:
{"foo":"bar"}

A: Quick method in existing controller
You need to use jexit() to return json data without any Joomla output.
public function run  ( ) {

    $data = array(
        'foo' => 'bar'
    );

    echo json_encode( $data );
    jexit();

}

Joomla 3.x Method
The better alternative is to create JSON controller and use JResponseJson to output JSON. The file name should have JSON suffix. For example, if your controller is an item, then your file name can be item.json.php and you can add controller code something like below.
public function run  ( ) {
  $data = array(
    'foo' => 'bar'
  );
  echo new JResponseJson($data);
}

The output will be json like below.
{"success":true,"message":null,"messages":null,"data":["foo": "bar"]}

Your ajax URL should have json parameter to trigger this json controller.
index.php?option=com_mycomponent&task=item.run&format=json

Use JResponseJson to inform errors and messages as well. Read complete documentation at the below location.
https://docs.joomla.org/JSON_Responses_with_JResponseJson

A: Joomla 4
You have to add the parameter &format=json to your URL.
This tells the system that you are waiting for a json response. The system will render JsonDocument and will send correct browser headers as response.
index.php?option=com_foo&task=report.run&format=json

class Report extends BaseController {

   public function run() {
       $data = [
         'foo' => 'bar'
       ];

       $response = new ResponseJson($data);

       echo $response;
   }
}

There is no need for closing the application with $app->close(); because the architecture of Joomla handles that for you.
If you close the application you will miss lot of stuff during the process of rendering. Many of the events will not be triggered. Furthermore, you will have to send headers for content type manually.
Your code should look like this one. This approach is not recommend.
class Report extends BaseController {

   public function run() {

       $this->app->mimeType = 'application/json';
       $this->app->setHeader('Content-Type', $this->app->mimeType . '; charset=' . $this->app->charSet);
       $this->app->sendHeaders();

       $data = [
         'foo' => 'bar'
       ];

       $response = new ResponseJson($data);

       echo $response;

       $this->app->close();
   }
}

A: Got the answer.
I needed to make a new controller. In my case the original controller was called, progressreports.php - I made a new controller called progressreports.raw.php.
Then when calling the url, add format=raw. i.e.
index.php?option=com_foo&task=progressreports.run&format=raw

A: You don't need to build a special JSON view (view.json.php; or controller progressreports.json.php) to achieve that. The only thing you have to do is to echo the JSON string and close the application.
public function run( )
{
    JFactory::getDocument()->setMimeEncoding( 'application/json' );
    JResponse::setHeader('Content-Disposition','attachment;filename="progress-report-results.json"');

    $data = array(
        'foo' => 'bar'
    );
    echo json_encode( $data );
    JFactory::getApplication()->close(); // or jexit();
}

You only need a separate view (or controller), if you want to provide the same function with both HTML and JSON output (chosen by the caller).

A: Depending on what you are doing you may want to make a json document, whatever.json.php instead of whatever.html.php.

A: I checked the accepted answer, it did not work with joomla 3.4.3. If somebody has the same problem, here is the solution for lower joomla versions:
$data = array(
    'foo' => 'bar'
);
header('content-type: application/json; charset=utf-8');
echo json_encode($data);
JFactory::getApplication()->close();

The content-disposition header is needed only if you want to offer the file for download.
off:
I just want to end this project and drink somethink to forget it. Even starting from scratch and writing a new CMS would be less painful. :S

A: I do not like to much JResponseJson and also I like to enqueue messages for the next request, so I made the following method on the main controller of my component:
public function returnJson($data)
{
    $app = Factory::getApplication();

    // Persist messages if they exist. (Same as CMSApplication->redirect)
    $session = \JFactory::getSession();
    $session->set('application.queue', $app->getMessageQueue());

    // Send json mime type.
    $app->mimeType = 'application/json';
    $app->setHeader('Content-Type', $app->mimeType . '; charset=' . $app->charSet);
    $app->sendHeaders();

    echo json_encode($data);

    $app->close();
}

In any task of the controller or sub-controller you could now do the following:
public function sampleTask()
{
    $app = Factory::getApplication();
    $app->enqueueMessage("Done (for the next user's request)", 'success');
    $this->returnJson("json data");
}


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text:
\section{Introduction}
\label{secintro}
Experimental evidence suggests that the size of grains and subgrains in
plastically deformed solids is not random, but rather relates inversely
to the flow stress,
\[ \sigma\sim D^{-1/2}, \]
see \cite{CGG06, CGG06b}. The foundations of this heuristic law are a
long-standing open problem in materials science and solid mechanics.
The qualitative and quantitative prediction of $D$ is particularly
vexing in dynamic recrystallisation (DRX), where new grains essentially free
of dislocations nucleate out of a highly fatigued sample. The experimental
studies \cite{FG08} on DRX show that the recrystallized grain sizes
can be linked to the subgrain size although the dependency of dynamically
recrystallized grain size and subgrain size on flow stress is different.

Derby and Ashby \cite{DA87}, and Roberts et al., \cite{RA78}, addressed the
grain size by making assumptions on the relevant criteria like back stresses at
grain boundaries or imbalance of subgrain size across prior grain boundaries
but did not touch the issue of mechanical behavior. A survey on the effect of
diffusion on grain boundaries can be found in \cite{Atk88}.

Evidently, despite extensive research during the past decades, the
physical mecha\-nisms of grain formation are not yet understood. The subject is
not only of academic interest but is also of immense importance for industrial
processing, see e.g. \cite{Raabe1,Raabe2,CB00,Ungar01},
since treatments like hot rolling, cold rolling and annealing
require reliable predictions of the microstructure and the texture evolution.

In this article, without spurious assumptions or introducing an artificial
mechanism, we show in a mathematically rigorous way why patterning in
deformed solids may occur. To develop our argument we compute analytically in
special cases the state of a solid that is deformed along its boundary.
We formulate the problem within the finite-strain Cosserat model of plasticity.
The interesting feature of this model, unlike other established approaches in
visco-plasticity, see the research articles and surveys
\cite{Simo,Simo2,Miehe98,Hill98}, is that it is a {\it gradient model}, i.e. a
length scale is introduced. The results given here substantiate this property:
it is demonstrated how for a certain parameter range the analytic solutions
naturally lead to transition layers between areas of approximately constant
micro-rotations $\Re$, a parameter that specifies the local orientation
of the material.

This paper is organised in the following way. In Section~\ref{secmodel} we
revise the rate-independent finite-strain Cosserat model as needed later
and formulate an energy minimisation procedure that allows to obtain the
time-discrete solution. We then restrict the plastic deformations to a priori
given single-slip systems and adopt the formulation accordingly.
In Section~\ref{secspecial}, we apply the resulting model to a simple shear
problem in 2D. The two-dimensional setting is chosen as this permits the
representation of the rotations by one scalar parameter.
In the following section \ref{secsol} some exact solutions to this shear
problem are computed with focus on the properties of the micro-rotations $\Re$.
As main result, two non-trivial examples are discussed where $\Re$ is connected
with the solutions of a stationary Allen-Cahn equation. We end with a discussion
of the results.

\section{The rate-independent finite-$\!$strain Cosserat model of
visco-plasticity}
\label{secmodel}
Let $\Omega\subset\mathbb R^d$ be a bounded domain with Lipschitz boundary that
serves as a reference configuration. The deformation of the material is
controlled by a mapping $\phi(\cdot,t)$ that maps $\Omega$ diffeomorphically to
the deformed state $\Omega_t$ at time $t\ge0$. Because of $\phi(\cdot,0)=\mathrm{Id}$
it holds $\det(D\phi(t))>0$ for all $t\ge0$.

The gist of the Cosserat approach is to multiplicatively decompose the
deformation tensor $F:=D\phi$ into a plastic part $F_\mathrm{p}$ and an elastic part
$F_\mathrm{e}$ by virtue of
\begin{equation}
\label{decomp}
F=F_\mathrm{e}F_\mathrm{p},
\end{equation}
and to split $F_\mathrm{e}$ by
\begin{equation}
\label{decomp2}
F_\mathrm{e}=\ReU_\mathrm{e}
\end{equation}
into a stretching component $U_\mathrm{e}\in\mathrm{GL}(\mathbb R^d)$ and a rotation part
$\Re\in\mathrm{SO}(d)$, where
\[ \mathrm{SO}(d):=\{R\in\mathrm{GL}(\mathbb R^d)\;|\;\det(R)=1,\,R^tR=\mathrm{Id}\} \]
denotes the special orthogonal group. Equation~(\ref{decomp}) states
that the plastic deformation of the material precedes the elastic deformation.
In general, $U_\mathrm{e}$ need not be symmetric and positive definite, i.e.
(\ref{decomp2}) is \textit{not} the polar decomposition.

Introducing the dislocation density $\kappa$, frame indifference (which
amounts here to the invariance of the energy under rigid body motions)
implies that the mechanical energy density is the sum of three functionals,
\begin{equation}
\label{split}
W(F_\mathrm{e},\kappa)=W_{\mathrm{st}}(U_\mathrm{e})+W_{\mathrm{c}}(K_\mathrm{e})+V(\kappa),
\end{equation}
with the stretching part $W_{\mathrm{st}}$, the curvature part $W_{\mathrm{c}}$, and the energy due
to immobilised dislocations $V$.
With $K_\mathrm{e}:=\Re^tD_x\Re=(\Re^t\partial_{x_l}\Re)_{1\le l\le d}$ we
designate the third-order (right) curvature tensor. Eqn.~(\ref{split}) tacitly
assumes that the mechanical energy depends on the elastic energy $F_\mathrm{e}$ only.
For arbitrary materials, this need not be the case.

Following the ideas in \cite{OR99}, we now derive a time-discrete formulation
that allows to compute the evolution of the material by minimising the
mechanical energy. For known values $(F_{\mathrm{p}_0},\kappa_0)$ of the previous time step
and discrete time step $h>0$, the values of $(\phi,\Re,F_\mathrm{p},\kappa)$ at time
$t+h$ are calculated.

With $P:=F_\mathrm{p}^{-1}$, $P_0:=F_{\mathrm{p}_0}^{-1}$ we choose the discretisations
\[ d_t^h(F_\mathrm{p}):=\frac{\mathrm{Id}-P^{-1}P_0}{h},\qquad
\partial_t^h\kappa:=\frac{\kappa-\kappa_0}{h}. \]
By $f_\mathrm{ext}(t)$ we denote external volume forces applied to the crystal body,
$M_\mathrm{ext}(t)$ are external volume couples. Let $\Gamma_D\subset\partial\Omega$ be
the Dirichlet boundary (for simplicity postulated invariant in time)
which we assume to be a smooth curve with positive $(d\!-\!1)$-dimensional
Hausdorff measure. On $\Gamma_D$ we prescribe the Dirichlet boundary conditions
\begin{equation}
\label{BC} \phi_{|\Gamma_D}=g_D,\qquad {\Re}_{|\Gamma_D}=R_D.
\end{equation}
Since we are only interested in the traction-free case, we henceforth set
$\Gamma_D:=\partial\Omega$.
The time-discrete mechanical energy functional for given $(F_{\mathrm{p}_0},\kappa_0)$ then
reads
\begin{eqnarray}
E(\phi,\Re,F_\mathrm{p},\kappa)(t) \!\!\!&:=&\!\!\! \int\limits_\Omega\Big[W_{\mathrm{st}}(U_\mathrm{e})+W_{\mathrm{c}}(K_\mathrm{e})+V(\kappa)
-f_\mathrm{ext}(t)\!\cdot\!\phi-M_\mathrm{ext}(t)\!:\!\Re\nonumber\\
\label{Edef}
&& \hspace*{25pt} +hQ^*(d_t^h(F_\mathrm{p}),\partial_t^h\kappa)\Big]\,\mathrm{d}x.
\end{eqnarray}
The term $hQ^*(d_t^h(F_\mathrm{p}),\partial_t^h\kappa)$ in (\ref{Edef}) represents
the dissipated mechanical energy in a discrete time interval of length $h$,
defined by the Legendre-Fenchel dual
\begin{equation}
\label{Qstardef}
Q^*(F_\mathrm{p},\kappa):=\sup_{(X,\pi)}\{X\!:\!F_\mathrm{p}+\pi\kappa-Q(X,\pi)\}
\end{equation}
of the plastic potential
\[ Q(X,\pi):=\left\{\begin{array}{r@{,\quad}l} 0 & \mbox{for }
Y(X,\pi)\le0,\\ \infty & \mbox{else} \end{array}\right. \]
and $Y$ is the yield function
\begin{equation}
\label{Ydef}
Y(\sigma,\pi):=\|\mathrm{dev}\,\mathrm{sym}\,\sigma\|-\sigma_Y-\pi\le0.
\end{equation}
This is the von Mises approach,
$\mathrm{dev}\,\sigma:=\sigma-\frac1d\mathrm{tr}(\sigma)\mathrm{Id}$ designates the
deviatoric part of a tensor $\sigma$, $\mathrm{sym}\,\sigma:=0.5(\sigma+\sigma^t)$,
and $\sigma_Y>0$ is the yield stress.

The solution of the minimisation problem
\begin{equation}
\label{Emin}
E(\phi,\Re,F_\mathrm{p},\kappa)\to\min
\end{equation}
subject to the boundary conditions (\ref{BC}) yields $(\phi,\Re,F_\mathrm{p},\kappa)$ at
time $t+h$. The first variation of $E$ w.r.t. the (implicit dual) variables
$(X,\pi)$ leads to the time-discrete plastic flow rule (see \cite{Simo}
for details)
\begin{equation}
\label{flowrule}
(F_{\mathrm{p}_0} d_t^h(F_\mathrm{p}),\partial_t^h\kappa)\in\partial^\mathrm{sub}Q(X,\pi).
\end{equation}
The variation of $E$ w.r.t. $(\phi,\Re)$ gives back the field equations.
The variation w.r.t. $(F_\mathrm{p},\kappa)$ returns the definition of the back stress
$X$ and the hardening modulus $\pi$,
\[ X=-\frac{\partialW_{\mathrm{st}}(U_\mathrm{e})}{\partialF_\mathrm{p}},\qquad\pi=-V'(\kappa). \]

\section{Single-slip systems}
\label{secss}
We specialise the minimisation problem (\ref{Emin}), (\ref{Edef}) to
single-slip plasticity. In \cite{CO06}, it had been shown that the relaxed
behavior of crystals restricted to single-slip under the infinite latent
hardening constraint is identical to the dynamics of materials with general
multislip plasticity.

Let $m_a\in\mathbb R^d$ be given slip vectors, $n_a\in\mathbb R^d$ be
given slip normals with $|m_a|=|n_a|=1$, $m_a\!\cdot\! n_a=0$ for
$1\le a\le I$, $I$ the number of slip systems present. Let
\[ Y(\sigma,\pi):=\max_{1\le a\le I}\Big\{|m_a\!\cdot\!\sigma n_a|\Big\}
-\sigma_Y-\pi \]
be the corresponding yield function. For single-slip systems,
\[ F_\mathrm{p}=F_\mathrm{p}(\gamma):=\mathrm{Id}+\sum_{a=1}^I\gamma_am_a\!\otimes\!n_a, \]
with the parametrisation $\gamma=(\gamma_a)_{1\le a\le I}\in\mathbb R^I$.

As can be checked, the dissipated energy satisfies the identity
\[ Q^*(\dot{A},\dot{k})=\left\{\!\!
\begin{array}{l@{\quad}l}\sigma_Y\sum_{a=1}^I|\dot{\gamma}_a|,
& \!\mbox{if }\dot{A}\!=\!\sum_{a=1}^I\dot{\gamma}_a\,m_a\!\otimes\!n_a\mbox{ and }
\sum_{a=1}^I|\dot{\gamma}_a|+\dot{k}\le0,\\
\infty, & \!\mbox{else.} \end{array}\right. \]
Therefore (\ref{Emin}) becomes
\begin{eqnarray}
E(\phi,\Re,\gamma,\kappa) &=& \int\limits_\Omega\Big[W_{\mathrm{st}}(\Re^tD\phiF_\mathrm{p}(\gamma)^{-1})+W_{\mathrm{c}}(K_\mathrm{e})
+V(\kappa)-f_\mathrm{ext}\!\cdot\!\phi\nonumber\\
\label{Emin2}
&& \hspace*{25pt} -M_\mathrm{ext}\!:\!\Re+\sigma_Y\sum_{a=1}^I
|\gamma_a-\gamma_a^0|\Big]\,\mathrm{d}x\to\min
\end{eqnarray}
subject to
$f_1(\gamma,\kappa):=\sum_{a=1}^I|\gamma_a-\gamma_a^0|+\kappa-\kappa_0\le0$
and (\ref{BC}).

From now on, we set $M_\mathrm{ext}=\mathbf{0}$, $f_\mathrm{ext}=0$.

\section{The shear problem in $2D$}
\label{secspecial}
In general, even in two space dimensions the minimisation problem (\ref{Emin2})
is too complex to be solved analytically and numerical computations are
required. In order to proceed, we make two simplifying assumptions. The first
assumption is that there is only one active slip system, $I=1$, such that
\begin{equation}
\label{Fpdef}
F_\mathrm{p}(\gamma)=\mathrm{Id}+\gamma\,m\!\otimes\!n,\qquad
P(\gamma)=\mathrm{Id}-\gamma\,m\!\otimes\!n.
\end{equation}
The analysis can be carried out without this assumption, but the formulas
become very lengthy. Secondly, we assume that the total deformation is a shear
of the material along this slip system,
\begin{equation}
\label{shear}
D\phi(t)=\mathrm{Id}+\beta(t)m\!\otimes\!n\qquad\mbox{in }\overline{\Omega}
\end{equation}
for a given scalar function $\beta(t)$. On $\partial\Omega$, this identity must
be imposed by choosing in (\ref{BC}) the appropriate boundary conditions on
$\phi$. Eqn.~(\ref{shear}) states that the deformation at every point in
$\Omega$ follows this prescribed deformation at $\partial\Omega$, i.e.
postulates the validity of the Cauchy-Born rule.

Assuming (\ref{shear}), the mapping $\gamma\mapstoW_{\mathrm{st}}(\!\Re^tD\phi P(\gamma))$
is convex (see Lemma~\ref{lem1} below). This implies that the constraint
$f_1(\gamma,\kappa)\le0$ is satisfied with equality,
\[ |\gamma-\gamma_0|+\kappa-\kappa_0=0. \]
Therefore we can resolve this condition
and (\ref{Emin2}) can be written as the unconstrained minimisation problem
\begin{eqnarray}
E_\beta(\Re,\gamma) &=& \int\limits_\Omega\Big[W_{\mathrm{st}}(\Re^t(\mathrm{Id}\!+\!(\beta\!-\!\gamma)
m\!\otimes\!n))+W_{\mathrm{c}}(K_\mathrm{e})+V\big(\kappa_0\!-\!|\gamma\!-\!\gamma^0|\big)\nonumber\\
\label{Emin3}
 && \hspace*{25pt} +\sigma_Y|\gamma-\gamma^0|\Big]\,\mathrm{d}x\to\min,\\
{\Re}|_{\partial\Omega} &=& R_D.\nonumber
\end{eqnarray}

To explicitly compute the solutions to (\ref{Emin3}), we pick
\begin{equation}
\label{Vdef}
V(\kappa):=\rho\kappa^2.
\end{equation}
For $W_{\mathrm{st}}$, $W_{\mathrm{c}}$ we make the general ansatz, cf. \cite{Neff06},
\begin{eqnarray}
\label{Wstdef}
W_{\mathrm{st}}(U_\mathrm{e}) &:=& \mu\|\mathrm{sym}U_\mathrm{e}-\mathrm{Id}\|^2+\mu_c\|\mathrm{skw}U_\mathrm{e}\|^2+\frac\lambda2
|\mathrm{tr}(U_\mathrm{e}-\mathrm{Id})|^2,\\
W_{\mathrm{c}}(K_\mathrm{e}) &:=& \mu_2\frac{L_c^{1+p}}{2}(1+\alpha_4L_c^q\|K_\mathrm{e}\|^q)\nonumber\\
\label{Wcdef0}
&& \times(\alpha_5\|\mathrm{sym}K_\mathrm{e}\|^2+\alpha_6\|\mathrm{skw}K_\mathrm{e}\|^2
+\alpha_7|\mathrm{tr}(K_\mathrm{e})|^2)^\frac{1+p}{2},
\end{eqnarray}
for positive material parameters $\rho$, $\mu$, $\mu_2$, $\lambda$, $\mu_c$,
constants $L_c>0$, $\alpha_4\ge0$, $\alpha_5>0$, $\alpha_6,\alpha_7\ge0$, $p>0$,
$q\ge0$, and where $\mathrm{skw} A:=0.5(A-A^t)$,
\[ \|A\|:=\sqrt{\mathrm{tr}(A^tA)} \]
is the Frobenius matrix norm, and $\mathrm{tr}(A):=\sum_i A_{ii}$ the trace operator.
Setting $L_c:=\sqrt2$, $\alpha_5=\alpha_6:=1$, $\alpha_4=\alpha_7:=0$, $p:=1$,
the definition (\ref{Wcdef0}) simplifies to
\[ W_{\mathrm{c}}(K_\mathrm{e})=\mu_2\|K_\mathrm{e}\|^2. \]
Since
\begin{eqnarray*}
\|K_\mathrm{e}\|^2 &=& \sum_{l=1}^d\|\Re^t\partial_{x_l}\Re\|^2=\sum_{l=1}^d
\mathrm{tr}\big(\partial_{x_l}\Re^t\Re\Re^t\partial_{x_l}\Re\big)\\
&=& \sum_{l=1}^d\mathrm{tr}\big(\partial_{x_l}\Re^t\partial_{x_l}\Re\big)
=\sum_{l=1}^d\|\partial_{x_l}\Re\|^2,
\end{eqnarray*}
the definition of $W_{\mathrm{c}}$ simplifies further to
\begin{equation}
\label{Wcdef}
W_{\mathrm{c}}(\Re):=\mu_2\|\nabla\Re\|^2.
\end{equation}
In two space dimensions, we can benefit from the explicit representation
\begin{equation}
\label{alpha}
\Re=\Re(\alpha)=\left(\begin{array}{rr}\cos\alpha & -\sin\alpha\\ \sin\alpha &
\cos\alpha \end{array}\right),\qquad\alpha\in[0,2\pi).
\end{equation}
Finally, by direct computations,
\begin{eqnarray*}
\|\partial_{x_l}\Re\|^2 &=& \left\|\left(\begin{array}{rr} -\sin\alpha &
-\cos\alpha\\ \cos\alpha & -\sin\alpha \end{array}\right)\partial_{x_l}\alpha
\right\|^2=2|\partial_{x_l}\alpha|^2,\qquad l=1,2,\\
\|\mathrm{sym}U_\mathrm{e}\!-\!\mathrm{Id}\|^2 &=& \|\mathrm{sym}[\Re(-\alpha)(\mathrm{Id}+(\beta\!-\!\gamma)
m\!\otimes\!n)]-\mathrm{Id}\|^2\\
&=& 2(1-\cos\alpha)^2+2(\beta\!-\!\gamma)(1-\cos\alpha)\sin\alpha\\
&& +(\beta\!-\!\gamma)^2\Big(\sin^2\alpha+\frac{1}{2}\cos^2\alpha\Big),\\
\|\mathrm{skw}U_\mathrm{e}\|^2 &=& 2\sin^2\alpha+2(\beta\!-\!\gamma)\sin\alpha\cos\alpha
+(\beta\!-\!\gamma)^2\frac{\cos^2\alpha}{2},\\
|\mathrm{tr}(U_\mathrm{e}\!-\!\mathrm{Id})|^2 &=& 4(1\!-\!\cos\alpha)^2
+4(\beta\!-\!\gamma)(1\!-\!\cos\alpha)\sin\alpha
+(\beta\!-\!\gamma)^2\sin^2\alpha.
\end{eqnarray*}
In summary, using the definitions (\ref{Vdef}), (\ref{Wstdef}), (\ref{Wcdef})
and letting $\kappa_0=\gamma_0=0$ for simplicity, (\ref{Emin3}) becomes
(with $\Re(\alpha_D)=R_D$)
\begin{eqnarray}
E_\beta(\alpha,\gamma) &=& \int\limits_\Omega\!\Big[2\mu_2|\nabla\alpha|^2+\rho\gamma^2
+\sigma_Y|\gamma|+2(\lambda\!+\!\mu)(1\!-\!\cos\alpha)^2+2\mu_c\sin^2\alpha\nonumber\\
&& \hspace*{20pt} -2(\gamma\!-\!\beta)\big((\mu_c\!-\!\lambda\!-\!\mu)
\cos\alpha\!+\!\lambda\!+\!\mu\big)\sin\alpha\nonumber\\
\label{Emin4}
&& \hspace*{20pt} +\frac{(\gamma\!-\!\beta)^2}{2}\big(\mu+(\lambda\!+\!\mu)
\sin^2\alpha+\mu_c\cos^2\alpha\big)\Big]\,\mathrm{d}x\to\min,\\
\label{BC2}
\alpha|_{\partial\Omega} &=& \alpha_D.
\end{eqnarray}

\begin{Lemma}
\label{lem1}
The mappings $\gamma\mapsto E_\beta(\alpha,\gamma)$ and
$\gamma\mapstoW_{\mathrm{st}}(U_\mathrm{e}(\alpha,\gamma))$ are convex.
\end{Lemma}
\noindent{\bf Proof} From (\ref{Emin4}) we have
\[ \frac{\partial^2W_{\mathrm{st}}(U_\mathrm{e}(\alpha,\gamma))}{\partial\gamma^2}
=\mu+(\lambda+\mu)\sin^2\alpha+\mu_c\cos^2\alpha>0. \]
Since $V(\gamma)$ and $\gamma\mapsto\sigma_Y|\gamma|$ are convex, this implies
the convexity of $E_\beta(\alpha,\cdot)$.

\hfill $\Box$

\vspace*{5mm}
We study (\ref{Emin4}), (\ref{BC2}) for $\alpha\in H^{1,2}(\Omega;\,[0,2\pi))$
and $\beta(t)$, $\gamma\in L^2(\Omega;\,\mathbb R)$, where $\beta(t)$ is given and
controls the shear of $\Omega$.
From the direct method in the calculus of variations, since $E$ is coercive and
weakly lower semicontinuous, the existence of solutions $(\alpha,\gamma)$
follows.

\section{Analytic solutions of the 2D shear problem}
\label{secsol}
In this section we study properties of the solution $(\alpha,\gamma)$ of
(\ref{Emin4}) for several choices of the parameters and are especially
interested in cases where transition layers in $\Re$ occur.

\subsection{The limiting case $\mu_2\to\infty$}
\label{case1}
This limiting case corresponds to rigidity in bending. After rescaling,
only the curvature energy $W_{\mathrm{c}}$ contributes and (\ref{Emin4}) is equivalent to
\[ E(\alpha)=2\int\limits_\Omega|\nabla\alpha|^2\,\mathrm{d}x\to\min \]
subject to (\ref{BC2}). The minimiser $\alpha$ solves the classical harmonic
problem
\[ -\triangle\alpha=0\mbox{ in }\Omega,\qquad\alpha|_{\partial\Omega}=\alpha_D.
\]

\subsection{The limiting case $\rho$, $\sigma_Y\searrow0$}
\label{case2}
The limit $\rho\searrow0$, $\sigma_Y\searrow0$ corresponds to an ultra-soft
material where the dislocations do not contribute to the mechanical energy.
Here, Equation~(\ref{Emin4}) simplifies to
\begin{eqnarray}
E_\beta(\alpha,\gamma) \!\!\!&=&\!\!\! \int\limits_\Omega\!\Big[2\mu_2|\nabla\alpha|^2
+2(\lambda\!+\!\mu)(1\!-\!\cos\alpha)^2+2\mu_c\sin^2\alpha\nonumber\\
&& \hspace*{17pt} -2(\gamma\!-\!\beta)\big((\mu_c\!-\!\lambda\!-\!\mu)
\cos\alpha\!+\!\lambda\!+\!\mu\big)\sin\alpha\nonumber\\
\label{min2}
&& \hspace*{17pt} +\frac{(\gamma\!-\!\beta)^2}{2}\big(
\mu\!+\!(\lambda\!+\!\mu)\sin^2\alpha\!+\!\mu_c\cos^2\alpha\big)\Big)\Big]
\,\mathrm{d}x\to\min.
\end{eqnarray}
Clearly, due to convexity in $\gamma$,
the optimal $\gamma$ follows the given deformation $\beta(t)$,
\[ \gamma_\mathrm{opt}(t)=\beta(t). \]
Computing the Euler-Lagrange equation of (\ref{min2}), we need to find a bounded
solution $\alpha_\mathrm{opt}\in[0,2\pi)$ of the semi-linear elliptic partial
differential equation
\begin{equation}
\label{EL}
-\mu_2\triangle\alpha+[\lambda+\mu+(\mu_c-\lambda-\mu)\cos\alpha)]\sin\alpha=0
\mbox{ in }\Omega
\end{equation}
with boundary conditions (\ref{BC2}). This equation has been studied before in
\cite{PZ}. Based on a separation ansatz, special solutions have been found in
\cite{MR93}.

First consider the unphysical case $\mu_2=0$. Then evidently
\begin{equation}
\label{minW}
\alpha_\mathrm{opt}\in\{0,\pi\}\mbox{ in }\Omega,
\qquad{\alpha_\mathrm{opt}}|_{\partial\Omega}=\alpha_D.
\end{equation}
Since there is no regularising term $|\nabla\alpha|^2$ in $E$,
$\alpha_\mathrm{opt}\in\{0,\pi\}$ a.e. in $\Omega$ and $\alpha\in L^2(\Omega;\,[0,2\pi))$
has no additional regularity.

When $\mu_2>0$, the solutions to (\ref{EL}) are continuous and stationary
(in time) solutions of the Allen-Cahn equation
\begin{equation}
\label{AC}
\partial_t\alpha=\mu_2\triangle\alpha-J'(\alpha)
\end{equation}
with the nonlinearity
\begin{equation}
\label{Jdef}
J(\alpha):=-(\lambda+\mu)\cos\alpha+\frac{\mu_c-\lambda-\mu}2\sin^2\alpha.
\end{equation}
$J$ has a local minimum at $0$.
For
\begin{equation}
\label{mccond}
\mu_c>2(\lambda+\mu),
\end{equation}
there is exactly one other local minimum at $\alpha=\pi$
as illustrated in Fig.~\ref{fig1}.
\begin{figure}[hbt]
\unitlength1cm
\begin{picture}(10.0,4.0)
\put(0.2,0){\psfig{figure=fig1a.eps,height=40mm}}
\put(7.2,0.05){\psfig{figure=fig1b.eps,height=40mm}}
\end{picture}
\caption{Plots of $J$ for $\lambda=\mu=1$. Left: $\mu_c=12$.
$J$ has the two local minima $0$ and $\pi$. Right: $\mu_c=1$. $J$ has only one
minimum at $0$.}
\label{fig1}
\end{figure}

The properties of the solution to (\ref{AC}) when (\ref{mccond}) holds are
well known: $\alpha$ tends pointwise to one of the minimisers of $J$ (here
$0$ and $\pi$), but transition layers of width $\sqrt{\mu_2}$ and slope
$C/\sqrt{\mu_2}$ occur. For small $\mu_2$, the interface moves by its negative
mean curvature.
For $t\to\infty$, $\alpha$ becomes stationary and when periodic boundary
conditions are applied, $\alpha\equiv0$ or $\alpha\equiv\pi$ in $\Omega$.
If Dirichlet boundary conditions (\ref{BC2}) are imposed, a sufficient
condition for the presence of transition layers in the stationary limit
$t\to\infty$ is
\begin{equation}
\label{TL1}
\Big(0\!\le\!\alpha_D\!<\!\frac\pi2\Big)\mbox{ or }\Big(
\frac{3\pi}2\!<\!\alpha_D\!<\!2\pi\Big)\mbox{ in }D_1,\qquad
\frac\pi2\!<\!\alpha_D\!<\!\frac{3\pi}2 \mbox{ in }D_2,
\end{equation}
where $D_1$, $D_2\subset\partial\Omega$ are disjoint sets with positive
Hausdorff measure.

\subsection{The full problem in the elastic regime}
\label{case3}
Now we investigate a case complementary to the one previously studied
where the material is so hard that no plastic flow occurs. We assume again
$\gamma_0=\kappa_0=0$. Computing the first variation of
$E_\beta$ given by (\ref{Emin4}) w.r.t. $\gamma$, since
\[ \partial^\mathrm{sub}|\gamma|=\left\{\begin{array}{ll} +1, &\mbox{if }
\gamma>0,\\ -1, &\mbox{if } \gamma<0,\\
\;\![-1,+1], &\mbox{if }\gamma=0, \end{array}\right. \]
we obtain that no plastic flow occurs (i.e. $\gamma=\gamma_0$) if
\begin{equation}
\label{s1}
-2((\mu_c\!-\!\lambda\!-\!\mu)\cos\alpha\!+\!\lambda\!+\!\mu)\sin\alpha
-\beta(\mu\!+\!(\lambda\!+\!\mu)\sin^2\alpha\!+\!\mu_c\cos^2\alpha)\in
[-\sigma_Y,\sigma_Y].
\end{equation}
A sufficient condition independent of $\alpha$ for (\ref{s1}) is
\begin{equation}
\label{s2}
2\max\{2(\lambda+\mu)-\mu_c,\mu_c\}+|\beta(t)|\big(
\lambda+2\mu+\mu_c\big)\le\sigma_Y.
\end{equation}
For fixed $\lambda$, $\mu$ and $\mu_c$, Condition~(\ref{s2}) is satisfied if
the yield stress $\sigma_Y$ of the deformed material is large enough and then,
(\ref{s2}) turns into a smallness condition on $|\beta(t)|$.

The rotations $\Re$ are determined as solutions of the minimisation problem
\begin{eqnarray*}
E_\beta(\alpha) &:=& \int\limits_\Omega\Big[2\mu_2|\nabla\alpha|^2+2(\lambda\!+\!\mu)
(1\!-\!\cos\alpha)^2+2\mu_c\sin^2\alpha\\
&&\hspace*{25pt} +2\beta(t)\big((\mu_c\!-\!\lambda\!-\!\mu)\cos
\alpha\!+\!\lambda\!+\!\mu)\sin\alpha\\
&&\hspace*{25pt} +\frac{\beta(t)^2}{2}\big(\mu\!+\!(\lambda\!+\!\mu)\sin^2
\alpha\!+\!\mu_c\cos^2\alpha\big)\Big]\,\mathrm{d}x\to\min
\end{eqnarray*}
subject to (\ref{BC2}).

When computing the Euler-Lagrange equation, we thus need to
find $\alpha\in L^2(\Omega;\,[0,2\pi))$ which solves
\begin{eqnarray*}
-\mu_2\triangle\alpha \!\!\!&+&\!\!\! \Big[\lambda\!+\!\mu
+\Big(\mu_c\!-\!\lambda\!-\!\mu)
\Big(1\!-\!\frac{\beta(t)^2}{4}\Big)\!\cos\alpha\Big]\sin\alpha\\
&+& \frac{\beta(t)}{2}\Big((\lambda\!+\!\mu)\cos\alpha\!+\!\big(\mu_c
\!-\!\lambda\!-\!\mu\big)\big(\cos^2\alpha\!-\!\sin^2\alpha\big)\Big)=0\quad
\mbox{in }\Omega.
\end{eqnarray*}
(By standard elliptic regularity theory, then
$\alpha\in H^2(\Omega;\,[0,2\pi))\;$).

This time it remains to find stationary solutions to the Allen-Cahn equation
(\ref{AC}) with
\begin{eqnarray}
J_\beta(\alpha) &:=& -\Big(\lambda\!+\!\mu+\beta(t)
\frac{\lambda\!+\!\mu\!-\!\mu_c}{2}\sin\alpha\Big)\cos\alpha
+\frac{\beta(t)}{2}(\lambda\!+\!\mu)\sin\alpha\nonumber\\
\label{J2def}
&& +\, \frac{\mu_c\!-\!\lambda\!-\!\mu}{2}\Big(1\!-\!\frac{\beta(t)^2}{4}\Big)
\sin^2\alpha.
\end{eqnarray}
For $\beta=0$, $J_\beta$ is identical to (\ref{Jdef}) and the
partitioning of $\Omega$ into subsets with $\alpha\sim0$ and $\alpha\sim\pi$
takes place if (\ref{mccond}) holds as discussed in the previous subsection.
When $\beta\not=0$, the discussion is more elaborate as $J_\beta$ depends on
$2$ independent parameters and $\alpha$. Since $J_\beta(\alpha)$ is
particularly simple for $\beta=\pm2$, let $T>0$ be a stop time and $\beta(t)$
be any continuous curve with $\beta(0)=-2$, $\beta(T)=+2$
that fulfils (\ref{s2}) uniformly in $0\le t\le T$.

Fig.~\ref{fig2} displays a typical plot of the two distinct local minima
$m_1$, $m_2$ of $J_\beta$ for $\beta\in[-2,2]$ computed with a one-dimensional
Newton method, here for the special choice $\mu_c=6\mu$, $\lambda=\mu$ which
satisfies (\ref{mccond}).

\begin{figure}[hbt]
\unitlength1cm
\begin{picture}(10.0,5.5)
\put(1.8,-0.5){\psfig{figure=fig2.eps,height=60mm}}
\put(4.0,3.5){\scriptsize$m_1$}
\put(8.1,2.3){\scriptsize$m_2$}
\end{picture}
\caption{The two local minima $m_1(\beta)$, $m_2(\beta)$ of $J_\beta$ as a
function of $\beta\in[-2,2]$ for $\mu_c=6\mu$, $\lambda=\mu$.}
\label{fig2}
\end{figure}
Like the condition (\ref{TL1}), we can derive sufficient conditions on
$\alpha_D$ for the formation of boundary layers. A strong time-independent
condition is
\begin{eqnarray}
\Big(0\!\le\!\alpha_D\!<\!M_1(2)\Big)\mbox{ or }
\Big(M_2(-2)\!<\alpha_D\!<\!2\pi\Big)\mbox{ in }D_1,\nonumber\\
\label{TL2}
M_1(-2)<\alpha_D<M_2(2)\mbox{ in }D_2.
\end{eqnarray}
where $D_1$, $D_2\subset\partial\Omega$ are disjoint sets with positive
Hausdorff measure; $M_1(t)<M_2(t)$ are the local maxima of $J_\beta$, and it
was used that $M_1(t)$ is strictly increasing,
$M_2(t)$ strictly decreasing in time.

\section{Discussion and concluding remarks}
\label{secdiscussion}
In this article we computed analytically solutions of a 2D shear problem
within the framework of finite-strain Cosserat plasticity.

As main result of our investigations, we considered two complementary cases of
shear in 2D, one of an ultra-soft material where plasticity occurs during the
entire deformation process, and another case of a hard material where the
applied loads are not large enough to initiate plastic flow.
In both examples it was shown that the micro-rotations $\Re$ are stationary
solutions of the Allen-Cahn equation (\ref{AC}) which may result in a
partitioning of the material into cells due to the occurrence of transition
layers in $\Re$. If $\sqrt{\mu_2}$ is small (compared to $|\Omega|$), the
transition layers are steep and $\Re$ is approximately constant in each cell
with a value determined by one of the local minimisers of a functional $J$ that
depends on the parameters $\lambda+\mu$, $(\mu_c-\lambda-\mu)/2$ and the
applied deformations $\beta(t)$, cf. Eqn.~(\ref{J2def}).

The simple example in Subsection~\ref{case1} demonstrates that this partitioning
is restricted to a certain parameter range of $\mu_2$ and does not always occur.
In addition, like the celebrated Cauchy-Born rule, the values of $\Re$
at $\partial\Omega$ determine the behaviour in the interior, especially
whether and where transition layers occur.

Yet, in many cases the analysis suggests a subdivision mechanism of $\Omega$
caused by deforming the solid that may lead to an explanation why grains and
subgrains form. Along this line, it is essential to work out the precise
relation between local orientation $\Re$ and orientation of the subgrain.
A first investigation in 3D using finite-element computations is
done in \cite{Forest00}. In this work, it was assumed that both coincide.

Since the analysed model relies on simplifying assumptions, it is natural to ask
whether the proposed mechanism carries over to the full three-dimensional
setup, to general deformations, and to more realistic
dislocation models. Another very important
question left to future work is the study of $\varepsilon$-minimisers, characterised by
\[ E(\phi_\varepsilon,{\Re}_\varepsilon,{F_\mathrm{p}}_\varepsilon,\kappa_\varepsilon)\le m+\varepsilon, \]
where $m$ is the absolute minimal value of $E$ and $\varepsilon>0$ a small number.
This notion goes along with the insight that most of the time, the solutions
observed in experiments do not reach a global minimum. If an almost optimal
micro-rotation ${\Re}_\varepsilon$ solves the time-dependent Allen-Cahn equation
(\ref{AC}) for large but finite time $t$, this may pave the way for quantitative
studies since the coarsening laws of the Allen-Cahn equation are well known.

\section*{Acknowledgements}
TB acknowledges the support by the Hausdorff institute of Mathematics, Bonn and
the support by the German Research Community (DFG) through grant BL 512 4/1.

\newpage

redpajama_set_name: RedPajamaArXiv


text:
Fort Ross Ventures is an international venture capital firm headquartered in Menlo Park, California. By 2022, it managed 4 funds focused on rounds from Seed to late-stage (Series D+).

History

Fort Ross Ventures was established in 2013 in Menlo Park by a former Sberbank tech executive, Victor Orlovski. The firm was named after a Northern Californian outpost set up by the Russian explorers in the 19th century. The bank was the firm's important LP in its early funds.

Fort Ross Ventures focused on startups in fintech, edtech, food tech, cloud computing, AI and machine learning, and business automation. Around 60% of its investments goes towards U.S. startups, and the other 40% are spread between the UK, Israel, and Europe.

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 SBT Ventures II $235-million fund had been raised by 2018 with participation of around 40 LPs, including corporations, family offices, and high-net-worth individuals.
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Portfolio

The firm's portfolio includes, but isn't limited to:

 eToro
 Rescale
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 Uber (IPO)
 Moven
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 Insurify
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References

Venture capital firms of the United States


When fish are hungry and feeding aggressively, they're easy to catch. Fishermen who are lucky enough to find a school of hunger feeding fish blitzing beneath screaming birds are certain to be successful, no matter what kind of lures they use. Unfortunately, it's not easy to find bigger fish feeding on the surface this time of year. I'm very envious of the few fishermen I know who have the time and money to chase blitzing rockfish all up and down the East Coast. Since most of us have to go fishing close to home in the limited time we have available, we have to look diligently for the few good stripers that might be around. When we're lucky enough to find them, we usually have to work hard to convince them to take our lures. Sometimes, they just don't want to bite.
The skeptics will tell you that the methods I recommend such as alternating colored lures, scented soft plastics, and good noise discipline don't matter. On good days, they're right. But when the fishing gets tough, it's the little extra steps that can turn your luck around and help you catch more and bigger fish. Since I prefer to let results do most of the talking, I'll share some things about a couple of successful trips I made last week when the strike triggers concepts were especially important.
Last week we had a blue moon – the second full moon in August. Full moons mean strong tides, and usually good light tackle fishing. Thursday evening Rich and I got out a couple of hours before dark. We launched Thunder Road at Kent Narrows and nosed out into the Chester River to look around. Just like usual, I cruised along the ledges and over the oyster bars looking for birds. Unfortunately, there were none to be found. Our window of daylight was closing and things were looking dim. Finally, just before dark, I brought the boat off plane to check the sonar over a seldom-fished oyster bar. A glance at the fish finder showed just a few small marks holding tight to the bottom. They weren't obvious, just a fish or two here and there. Good enough.
I took out a 6″ white BKD and dipped the tail in bright orange garlic dye. I threaded it on to a homemade three-quarter ounce chartreus and white jig head and pitched it out in the direction of the incoming current. First cast, nothing. Second cast, nothing. Third cast, still nothing. I dipped the lure again in the scented dye and readjusted the angle of my cast so that my lure was still moving with the current, but this time slightly at an angle to the flow. When fish are holding tight to the oysters, the lure has to pop the bottom (barely) as it sinks back down after every quick snap of the rod tip. Just throwing it out and jigging it back in won't work. It has to touch down every time. Snap, drop, pop the bottom – snap, drop, pop – snap, drop, BOOM! Fish on! I fought a healthy 28-inch striper to the side of the boat and released it while it was still in the water.
I repositioned the boat over the spot where I caught the fish. This time it was Rich's rod slashing through the air as he set the hook into another nice striper. The fish were holding in a very tight area relating to nothing more than a small hump that rose about 24 inches off the bottom. I started the engine again and moved the boat back up and slightly past the hump. This time, we both hooked up and I held up both fish as Rich shot a quick picture. By this time, the August Blue moon was well above the Eastern Shore horizon. We caught a few more fish but they stopped biting after it got dark. I think we could've given them another hour or so and they would've started biting again under the full moon, but we had accomplished our mission and turned what could have been a very bad evening into a successful fishing expedition.
Rich had plans the next night, but Jamie and Mark joined me on Thunder Road. I headed right back out to the same area where we'd found the fish the night before. The sonar pattern was the same. You could very easily miss those fish on the fish finder if you didn't know what to look for. The only thing apparent was a slight color change tight on the bottom. Like Rich the night before, Jamie and Mark are experienced light tackle fishermen and very good at figuring out the best direction for the cast. These fish simply would not hit a lure moving against the current. Since we had a slight breeze that pushed my boat along a little faster than the speed of the tide, I cut the motor hard right so we would drift a little slower and sideways with the current.
Jamie and Mark were casting Mann's Hard Head lures. These soft plastic baits are scented and salted in the bag. I stayed with BKD hot-rodded with chartreuse. After a half-dozen casts, Jamie set the hook into something solid. The fish lit out for deeper water so he pointed his rod tip toward the fish and let the drag on his baitcaster do the work. The fish eventually turned and Jamie fought it to the side of the boat. We pulled it onboard for a quick measurement – 33 inches – not bad.
On the next drift, both Mark and Jamie hooked up with mid-20 inchers. I hadn't had a strike so I was getting worried. I considered changing over to a Mann's lure, but decided just to reapply more color then bear down and concentrate as hard as I could on my jig: tune in – th ink down the line – snap, drop, pop the bottom. I could feel the jig head every time it touched the shells on the oyster bar. Get ready – stay alert – anticipate the strike – snap, drop, WHACK! Set the hook – tight line – good head shakes. I popped a nice one. In the world of rockfish, a 30-inch fish isn't all that big, but in August on the Chesapeake Bay, I'll certainly take them. Especially since I know from experience that the same technique will produce 40- and 45-inch fish later in the fall.
Just like before, the fish were holding very tight to a small area of underwater structure. It wasn't the same hump as last night, but it was in the same area. The full moon current was stronger than the night before, and the wind had picked up so we were over the fish for less than two minutes per drift. That didn't give us much time to get the lure into the strike zone. Every detail mattered. Strikes didn't come easy. On some drifts, most in fact, we didn't hook up at all.
Right at sunset, I moved a little farther south and turned the boat hard into the current. The blue moon was just coming up when Mark tied into a nice fish. I shot a picture of his rod bent with the moon in the background, then heard Jamie set the hook behind me, another drag screamer. With the setting sun over his left shoulder, I got as many pictures as I could of the action. Jamie brought the fish to the stern and lipped it over the side. This one went 35-inches. I'll take a fish like that anytime of year, but it's especially sweet to see them in August.
I have high hopes for a very good fall rockfish bite this year. Unless we get tropical storms or a hurricane like we did last year, conditions should continue to improve. As soon as we get a few cool nights, I'll start working the grass beds and shoreline structure with topwater plugs. I also think we'll see good light-tackle fishing in Eastern Bay and in the main Chesapeake channel near humps and ledges that are close to the mouths of major rivers. Water clarity is still very good, even in the Upper Bay.
So, polish up your strike triggers, sharpen your hooks and mash your barbs, then hang on for what could be one of the best fall seasons we've seen in a while. Hopefully, there will be a lot of hungry fish around, but I'm sure there will also be days when fish are hard to catch. When the going gets tough, take those extra steps. You might be surprised at how you can turn around the bad days and make the already good days great.
All I caught today was a crab cake and a Painkiller buzz at a dock bar in Rock Hall .
Great class of fish for August and hopefully and prelude to things to come!
Now those are summer rockfish. Are you sure you aren't in Maine right now?
Was a blast Shawn..nice fish for August or for anytime of year…was very surprised they were still biting after dark..thanks again for a couple of great trips..
You're right about the rough company..besides the hat matches my shirt…would wear a CLT hat but haven't seen any…you?
Mark thinks his shirt don't stink.
How far up the Chester?
Another great write. Well me an my buds under the tidal effect of a few adult style beverages have an opinion to be as consistant as you are, a horseshoe is hidden in some area where the sun don't shine. (not in the bildge either). But again enjoy your dicipline to the sport.
We have an offer for you to consider, I out bid you at the CCA auction fund raiser last year at the Baltimore event. We have room for you to stay at the Cape Cod house during the week of Oct 15-21 2012. at no fee we will have at least one Boston Whaler Montauk possibly two at our use and im trying to get Ron Arra World record distance casting champion to conduct a casting lesson and guide us on Cape Cod to the best fishing areas. We can work out the details. My home bus / cell is 410-419-9249.
Is this the same Jerry Hodnicky I knew from Western Electric Drafting dept. I hope it is, I would like to say hello!
On your way to Cape Cod, check out Captain Doubleday ("Doubles") Koch; Block Island, R.I. His boat; "Get the Godamn Net" is well known in the Northeast. He's a hellva fisherman, just ask him. Sells nice fishing apparel as well.
p.s. Superdink; stay in school son.
I believe I chartered a trip with you in Raritan Bay on a 30ft New England skiff about ten years ago and as I remember that same horseshoe must have been hidden somewhere near as we slammed the weakfish and bass jigging tigertails with a manns jellyworm as a trailer.That was one trip to remember I also recall you were the only guy around who did catch and release.
i KnowN dat cApt HaRry and tInay kOch too.
I've learned a lot from you Sean and because of your books, my 9 yr. old son and I hammered 13 flounder in about 3-4 hours per day of fishing over 5 days off of the rock jetty at the Indian River Inlet. Best of all, my son caught his first keeper flounder copying your light tackle jigging method! We did nothing but jig artificials using your methods.
Previously, I would have thrown squid or minnows hoping to catch using a flounder rig waiting for a bite.
We would have never caught these fish had I not read your books.
Best of all and you will get a kick out of this if you read this. We were giving out jig heads and gulps to anyone who was asking what we were doing and was fishing. At one time, I looked up and down the rock jetty only to see a bunch of men trying to imitate "Sean Kimbro light tackle jigging style!" It was hilarious. I was probably the worst with technique but it was a mountain of fun.
Most gave up after loosing a few jigs to the rocks and not catching.
Great post, thank you for everything you do for the fish, fisherman, oysters etc!
I am having a hard time catching quality fish on light tackle but I'm getting better.
Additionally in Thanks to you, my son knows to move off of the fish quickly if they are small in order not to kill them.
I hope this fall is the best fall fishing for you in all your years. You deserve it.
You don't even know me but you've taught me "much"and I've then passed what I've learned on to my son.


We recently have been talking about nursing theories and theorists in class. It's interesting. Some good points are made by various people about what nursing is and should be.
There should probably be theories about most things we get involved in, whether work or play. I've been thinking about friendship a lot lately. As a kid I'd say I had a lot of friends. This extended through my time at college. Even the two and a half years following college I made and kept friends fairly well. However, in the last 3 years or so I've seen a distinct shift. I neither keep nor make new friends like I used to. I've asked myself what has changed about me? A lot, surely, but in terms of trying to make friends, not much. Same goes with trying to keep them. I am pretty loyal and dependable (though I admit I often am running a few - 15 minutes behind, always, since Kaia arrived). I am at least decent about calling, texting, emailing, or some other form of social media messaging friends, and yet . . . I am, largely unsuccessful. I have lost many friends.
So, what is it? I've asked my husband and my best friend (who thank God I have not lost) what gives? Is it something I am doing unwittingly? Am I coming across in a way I do not think I am? I haven't figured it out and it's both perplexing and painful.
One theory of friendship I just looked up states that friendship is dependent on: similarity, proximity, reciprocity, beauty, and competence (though not too much so). Well, according to this proximity is probably my biggest problem in losing friends, I'm no longer near them so no longer a priority and, I fear, some of those "friends" probably didn't have that much in common with me but liked me more because I was there to begin with. OK, so making them? What's my problem? I'm competent but definitely not too competent. I'm not too pretty but I'm not ugly so I think that's good enough. I treat people well. I smile and strike up conversation, heck I bring cookies! I'm here. They're here. So is it I'm just not similar enough? Perhaps but I dont feel like this is my answer either.
I promise Im not having a pity party. It's more of a think tank right now and you're here with me. I know that you've only met me through bloggy land (well, most of you), what do you think? Ideas? I promise my feelings wont get hurt if you're honest!
I'm sick. Blah! Thank goodness Kaia's being such a little sweetie and not too demanding right now. Oh, and I don't have to go to school today, yay!
So far, school's going well. I've completed two paper tests and one hands on one. The hands on one was giving a bed bath. Sandra, I'm sure you can appreciate that one, huh? I really am enjoying my classes and learning something new again. It's still overwhelming though, the sheer volume of reading to be done. Perhaps one of the best things about going to school is it forces me to get dressed every morning in something other than sweatpants. Plus the time until Todd comes home goes faster when I'm busy.
Want to know the worst class I'm in? Old Testament. Don't get me wrong, I'm as spiritual as the next girl, and, initially I was actually somewhat excited about this class for what it could teach me that, as a Christian, I should probably know better. But, the teacher and the environment is everything. And this class really just isn't working out for me. But, alas, 'tis a requirement so I must soldier on. What's the worst class you've ever taken? Pray, do tell. It will make me feel better.
What do you judge other Mothers for? Anything I left off the list?
Thank you all, again, sincerely, for your encouragement and support. You all, and this blog, have truly been a blessing to me.
I took my first test today. I am sure I got some wrong, but over all, I feel I did well. Fingers crossed. I am enjoying this new endeavour and knowledge - minus being away from my angel, but she is adjusting so well to the Nanny it makes it easier for me.
10. I would most certainly die, happily, defending the ones I love (such as my beautiful daughter) and many honorable, brave, and admirable men and women have done just that. And, in many ways, isn't that very Christian? Or like Christ? Sacrificing one's life for another? Or others?
So there are a few of my thoughts. I do have others and I am sure I will gain more as time goes on. But for now, I wish you all a very beautiful and blessed week!
Sorry I've been out of the loop for a few days. I think I've caught up on all of your lovely blogs now (even if I didn't leave comments on all your posts)! You all have been some busy ladies and I enjoyed reading everything, from accounts of your moves, to your school, work, weight loss, shopping, and big projects!
I survived my first week back to school and Kaia survived her first week separated from Mommy for an extended period of time. This semester is going to be HARD! Between the coursework, being away from Kaia, and not having hubby here to watch the little angel while I study, but I think with a little hard work, organization, prioritization, and a lot of prayers, I'll make it through. I'm sure this blog will suffer a bit so I apologize for that. I will likely only post a couple of times a week and I might end up trying to catch up on your lives on weekends and at random times throughout the week. Can you believe I already have my first test this coming week?! I think I'm going to take it on Monday.
Today's been a busy day. Little Miss wanted to wake up at 630 but she did go back to sleep eventually for a few more minutes. Then it was up, getting ready for the day, cleaning, making another batch of cupcakes, catching up on blogging, chatting with the hubs, reading videos, signing videos, and finally, a bit of homework. I really need to hit the books much harder tomorrow to study and get ahead for next week. It's so hard to get homework done when I get home during the week and Kaia needs things from me, whether food or just some dedicated attention to just her.
Well, we need to watch our Your Baby Can Read video one more time tonight before we hit the hay. Sweet dreams everyone!
p.s. How do you feel about pacifism? For or against? This is a post and question I've been thinking about for the past couple of days now.
Monday, January 10th, Day 1. I arrived late to my first class. I also, apparently, missed another class completely that was, initially, left off of my schedule. Whoops!
There are not many nursing students in my level. This is good in many ways. It is bad in others. There are three students that are older than me. They are, probably, in their 40s (I didn't ask) but just judging by the ages of their kids, they have to be at least late 30s. The others are all, pretty much straight out of HS and so are roughly between 19-20 yrs old. That puts me right in the middle. Neither early 20s or late 30s-40s. Everyone else also seemed to know at least two other students in the class that they'd palled up with if you will. Again, awesomeness. I think it will all be OK though. Even if I don't make super duper best friends forever, I'm really there to learn anyway so that's cool. I'm excited about getting started, though I must say, I'm not sure if I knew what I was getting into. The schedule is VERY confusing and the hours are a bit more in depth than I was prepared for. I just hope Kaia and I both make it through this first semester two happy girls. I know I'm even more ready for the summer with my little angel all to myself again!
Day 2: pretty much uneventful, minus the having to get up too early, boo!
We shall see how the remaining days of the week go.
P.S. Kaia is a superstar at going to sleep at night now! Knock on wood.
Kristen at eatdrinkloveandexercisedotcom tagged me for a survey so I thought it might be a fun and easy blog post for a busy Sunday. I've been cleaning and baking all day! And getting ready for class, or at least I hope I'm ready - I still want to puke whenever I think about it, and yes, I realize it totally is not that serious, but I can't help it!.
I'm supposed to pass this on to four ladies but I don't want anyone to feel obligated and I want anyone who wants to to join in the fun. So please, if it strikes your fancy, join in, I'd love to learn more about you too!
Sleep training has actually been going pretty well the past couple of nights. My angel always proves to be just that. That girl is good to her Mommy. I, on the other hand, am a fail at sleep training. I cannot fall asleep! Ahhhh! I lay there with her for hours and don't fall asleep. And I need to in the worst way. I start school on Monday and that means early mornings people! Very early. I cannot be up until midnight! I am not as young and crazy as I used to be. Wait, I was never young and crazy . . . I've always loved my sleep.
And, speaking of school, I am so nervous! I know everything will be fine. But I am worried that I will forget something I am supposed to bring. Or I won't find my classes and walk in all late whenever everyone else is already seated and the instructors already talking. Or what if I realize after I've gotten all the way there that I have baby spit up all over my shoulder? Or what if I forget to do something I was told to do? Or if everyone's already friends (you know most of my class will have been in classes together for 2 years already) and in cliques and I'm the odd, old lady out? And what if I'm late, well, because I'm often late to things and it's a long drive, and I'm not used to being away from the baby. And what if I miss her terribly? And, I know that I've talked about my nerves and worries about this already and you've all been so nice and generous and kind with your comments. And they have helped. And I hope that you are all right! But now that it is approaching with no turning back my fears, nerves, and worries are just amplified regardless. New is scary. At least new is scary to me. I am sure I will be keeping you all posted.
But for now, for now I really must try to sleep.
Hi everyone! This is a very important topic. Please stay, read, pass on the word, and donate if you can. Thank you!
Both the foundation (Crickett's Aswser for Cancer) and my favorite lymphedema sleeve maker (Lymphedivas) were founded in honor of thirty-something women (one a blogger!) who had breast cancer (and then died). I made an earnest plea to each of them, told them about the women that each other were honoring, and then held my breath and made the ask.
Would you, could you, please consider working with each other to provide lymphedema sleeves to women in need?
They agreed to talk to each other. They liked each other, and a few weeks later, box upon box of lymphedema sleeves and gauntlets (like a glove without fingers – you can see mine in Monday's post) arrived at the foundation. Sue's friend Carole, the foundation's VP, unpacked them, totaled it up, and found that she had received over $12,000 worth of lymphedema sleeves and gloves to give away.
Pretty amazing, no?! So, you may be asking, why does this matter to me?
Well, first, you are a woman too (probably because I don't think any men currently read my fancy blog) and you have or will, likely, be touched by breast cancer at some point in your life, whether you yourself, a family member, or friend.
If you are currently a breast cancer survivor in need, you can now go to Crickett's Answer for Cancer, and complete the forms requesting help by writing in "lymphedema sleeve and gauntlet" on page 2 of the application.
Or, if you want to help someone else, you can pass this message on. Either directly to a friend/family member in need, blog about it, email it out, or make a donation here.
And if you want to tell Susan how awesome and fabulous she is, go vist her at Toddler Planet.
Now get to work! Love ya ladies!
Kaia fell asleep a little after 8. The smart me knew I should probably wake her up. The idiot me said let's roll with it. So, roll with it we did.
Kaia was back up again by 10.
There was singing. There was staring at the illuminated mobile. There was more singing. There was cuddling. And some more singing. But there was definitely no sleeping again until well after midnight. And then she woke up for good just after 7. Awesome!
Idiot me may make a reappearance, or many, I don't doubt that. But, she will not make that mistake again!
Here's to hoping we all get some good sleep tonight!
Last night was the first night of Kaia and I's attempt at sleep training. So far, I don't have the heart for the cry it out method. So, we tried our own version of the no tears sleep training. I laid Kaia down at 1025 (25 minutes later than I meant to, darn dogs!) with our usual night time soothing sounds playing. I also added her projection mobile on the ceiling for her to gaze at. Then I laid down next to her ('cause we co-sleep) and closed my eyes (you know, show her what we were supposed to be doing and all). She entertained herself quite well for 15-20 minutes just cooing and talking to the pictures on the ceiling and sucking on her fingers. She then decided she didn't like this idea and started crying and fussing. I let her do this for about a minute, maybe two, at which point I got her attention to show her Mommy was still there and sang to her while letting her hold my finger if she wanted to; she liked this and stopped crying. I could tell she was definitely getting sleepy because of the yawning and heavy, droopy lids but then she decided she was too hungry to go to bed. So, I nursed her while we both stayed laying in bed and she fell asleep about 1115-1130. When I put her back in her little "bed" 20 minutes later or so, she opened her eyes and went right back to sleep. Not perfect, but I think it was a decent attempt for the first night. I figure consistency's going to be the key here. I hope it works. Then, if you're into the (semi-)attachment parenting thing, like me, maybe my method will work for you someday too :) Here's to hoping ladies!
Also, Kaia had her 6 month appointment yesterday. She's 26 1/4 inches long, head circumference at 16 3/4, and weight 14.4. She's a tiny little thing. Her head and height are in the 50th percentile, yay! But her weight . . . not so much. Munchkin's a little small, only 25th percentile :( So, Mommy's going to try and up her solid food intake and see if that helps with a reweigh-in in a few weeks. Good news is, Mommy and Daddy aren't big people, and Kaia's happy, peeing, and pooping so at least there's that! All that in mind, we started jarred baby food yesterday. Exciting! We started with sweet potatoes. Kaia's decided she's not a big fan but she's made a good effort. She ate all of them yesterday and most of them today. But the faces, precious city folks!
So, I start school next Monday. I know, gah! Old lady on campus people!
That means I finally have to bite the bullet and sleep train my angel, or at least try to. Otherwise I'm going to die on the road (worst case) or fail all my classes for sleeping in class(best case). I know, I know, I probably waited a little long to get started, but to be honest, I'm a pushover already and I sorta enjoyed the late nights with my baby. Plus, I was skyping with Todd late at night too so getting Kaia to bed late was good for Mommy sometimes too (selfish Mommy!).
Also, I know that my blog's kinda been on the sucky side the last couple of weeks. Minus maybe my Stepmonster post they've been lacking a bit in content and quality. I am going to work on getting better again, even if that means posting less frequently to not waste your time with poor quality writing or fluff.
I'm pretty sure that with starting school again, Kaia being at home with the Nanny, and homeworker I'll probably have a lot of material coming. That being said, please also excuse me if, starting next week, I seem a bit overwhelmed, I probably am.
Again, thank you all so much for following along on my bloggy journey and our little lives here. I am honored and humbled to have you.
P.S. I'm also sorry it's taking me a long time to respond to a lot of your comments lately! I'm going to try and catch up on that too!
Yay! I received my first blog award from Jhen, over at From Here To Eternity. Thank you so much for thinking of me! If you haven't already, please go check her blog out. She's a very real and inspiring blogger.
There it is, over on my sidebar, aren't I so trendy?!
Pass it along to 10 others.
And, leave a link to the Trendy Blog Button so they can grab it too!
Is there such a thing as a perfect mother? Or, better yet, is there ever a point at which you stop worrying if you are doing enough? Or the right things?
I know that I'm not a total mess. I mean Kaia's achieving her milestones. She's growing. She's healthy. She's eating well. She is, generally, happy and content. She has LOTS of things. Almost all the toys, clothes, furniture a baby could dream of.
Yet, I worry as far as doing goes. I'm not doing enough. Do I set her down too often? Should I be holding her more? Are there more games I should be playing with her? Should I be taking her to do more stimulating things? Scheduling and attending playgroups, play dates? Are my priorities right? Should they be different? What would she say? What would she tell me, if she could only talk? Should I be working harder to get her on a schedule?
Do all mothers have these thoughts? These worries? Is it with every baby? Or only the first? Do you become a better mother the more children you have? Is the youngest the luckiest? The oldest the least fortunate this way?
I feel when Kaia gets older I will be much better at this mothering thing. I look forward to trips to the library, the park, swim lessons, dance class, eventually school. But this, the infant stage, I'm finding exceedingly difficult. Don't get me wrong, I love every minute with Kaia. I love everything about my angel baby. But still, it is stressful. It is frustrating. It is full of worry. Am I doing this right? Or, am I doing at least, all right? OK? Passable?
Maybe my biggest resolution for this year should be, be the best mother I can be. Always try to do better. Because Kaia, Kaia is the perfect baby. I could not ask for better. I know I couldn't.


text:
Prince George loves one TV show so much a special episode was dedicated to the royal
She said: "Fireman Sam has taken an awful lot of interest." Kate also explained that George loves helicopters which appear in the show and in 2016 the duchess was spotted buying a Fireman Sam reading book for George at a charity shop.
Judi Love breaks down in tears after routine dedicated to late parents 'I miss them'
Anton agreed, admitting the dance was "beautiful" before saying: "I love this side of you. "This sensitive, this romantic, this quiet – I think that's gorgeous. Such a change from what we've had the past couple of weeks." Craig Revel Horwood, however,
Bravo! Dedicated Queen takes break from holiday to send Canada important message
In a message to the Canadian public, Her Majesty joined the country on its day of Truth and Reconciliation. Today is the first time the country will mark its National Day for Truth and Reconciliation. She said: "I join with all Canadians