-JH Volleyball at 2:30 & Football at 4:00 today at Wynot. Please dismiss the team at 1:35; team bus will leave at 1:40.
-Jr. Class CPR will be tomorrow down in the weight room. Boys will be in the morning with the girls in the afternoon. Boys - Please report to your first period class for attendance and lunch count.
-A reminder to students who are taking part in the John Baylor OnTo College ACT Test Prep. It begins tomorrow at 7 am and will be held in the high school library, not the Science lab as we previously had agreed.
-Attention any senior who is the son or daughter of a VFW Auxiliary member! See Mr. Kneifl if are interested in applying got the VFW Auxiliary scholarship. He will have eligibility information as well as the application. You may also visit Mr. Kneifl's link on the school's webpage for information.
-Attention juniors & seniors who have signed up for the "Big Cat/Little Cat Mentoring Program." There will be a meeting today in the commons during homeroom. Please check into your homeroom and then proceed to the commons. This meeting may take the majority of the homeroom.
-Picture Retake day is Tuesday, October 9, please let the office know if you would like to have picture retaken. Also all picture orders must be turned in by the 9th!
Please fill out the FCCLA form that was emailed to you. Also, officer applications are due on Wednesday, October 3 by the end of the day. The membership dues of $35 are due at the October 4 meeting as well.


Serve as a leader for project execution from start to finish.
Manage the project team (Construction, Cost management, Operations etc.) to support all efforts that go into building.
Liaise with legal team to review, and issue contracts and/or work-orders to external trade partners or subcontractors.
Achieve objectives and key results as determined by the client's specifications.


Our Gel Press® Brand Ambassadors are professional artist educators with a personal history of teaching Gel Press® workshops online and in person. These professionals have completed a six-hour intensive training focused on Gel Press monoprinting techniques. They work closely with our product development team and are the first to see new products. Our brand ambassadors love Gel Press, and want to share their inspired perspectives with you.


Scattering processes affect electron dynamics, transport and quantum confinement. Hence, understanding the mechanisms behind different scattering phenomena is of paramount importance both for fundamental knowledge and the design of novel electronic nanodevices. This is particularly crucial in recently discovered 2D materials such as graphene and topological insulators, where scattering is characterized by the entanglement between orbital momentum and pseudospin (in graphene) or spin (in topological insulators), resulting in exotic charge and spin transport properties. We investigate the scattering phenomena in 2D systems using quantum resonators with controlled geometry, such as nanoislands or atomic steps.
Based on the earliest analysis of STM interference patterns, steps and metallic adsorbates at (111)-oriented surfaces are frequently assumed as canonical hard-wall potential barriers, on which surface electron waves undergo substantial reflection and absorption but negligible transmission. In contrast, angle-resolved photoemission (ARPES) experiments, performed in the ordered step superlattices of vicinal (111) noble metal surfaces, have repeatedly shown dispersing bands with clear signatures of weak repulsive scattering at steps, namely small size effects and narrow gaps at the Brillouin zone boundary. This behavior is only compatible with a high transmission coefficient across the step barrier. But, why does the step barrier strength change that much when going from a defectlike, random step, to the staircase of the vicinal surface? Previous ARPES experiments on vicinals surfaces with different terrace-size suggested the existeance of a transition from dispersing superlattice states to strongly confined quantum well states as we increase the terrace size. However, different experiments pointed to disorder effects as responsible for the transition to strong confinement.
Order vs. disorder in the electron scattering of (111) noble metal surfaces. (a) Schematics and picture of a curved vicinal single crystal. b) Superlattice band dispersion of the surface state and STM image of a curved vicinal Au(111) surface. c) Left: The potential obtained for step superlattices on different noble metal surfaces by fitting the dispersing bands with the Kronig-Penney model. Right: STS spectra acquired across a pair of isolated steps on Ag(111) reveal the formation of confined states at energies that correspond to an infinite potential well (horizontal dashed lines). The wave function of each case is sketched at the centre.
In order to solve this puzzle, we have combined STM spectroscopic measurements in isolated terraces with ARPES experiments on a special type of vicinal surface, a Ag(111) curve surface [Phys. Rev. B 87, 115425 (2013)]. Here, a high quality superlattice periodicity smoothly varies from 10 up to 200 Å, allowing us to study electron scattering varying the terrace size over one order of magnitude. We observe dispersing superlattice Bloch states for the whole range of step periodicity, with energy shifts corresponding to a weak potential barrier of 0.6 eV Å. On the other hand, the energy of the non-dispersing resonant states measured by STM on isolated terraces can be compared to that of infinite quantum wells, indicating a negligible transmission across steps, and suggesting that disorder and decoherence rather than a terrace-size dependent transition is the responsible for the strong quantum confinement observed in some vicinal surfaces.


text:
HomeTagsPosts tagged with "pet names"
Hey darling! Pet names are actually really good for your relationship
We've all been there.
As a young, free singleton you promised yourself you'd never use pet names for your future partner – after all, no one wants to be that couple.
Just hearing your friends refer to their other halves as "babe", "sweetheart" or "honey" was cringey enough to make you swear off romance for the rest of your life, but then all of a sudden, life throws you a curveball and you end up with a "babe" all of your own.
Slowly but surely the inside jokes and doting nicknames will creep their way into the relationship, and bam – you're just like every loved-up couple you've ever rolled your eyes at.
So, why does romance turn us all into mushy, baby-talking, doe-eyed softies?
Well, according to science, it likely stems from our parents.
"Baby talk is used really extensively, including cross-culturally, by mothers around the world," Florida State University neuroanthropologist Professor Dean Falk told Broadly.
"It exists for language acquisition in infants, and it also expresses love and facilitates bonding between the mother and the infant."
She believes that couples use pet names for each other because it brings them back to their childhood memories and first love – their mum.
And while this all might sound a bit Freudian, it's actually one of the most natural ways to bond with a partner.
So, if you've got a "baby", "chicken" or even a "darling" in your life, chances are you're onto a winner.
Gardaí have asked the public to help name their new puppy
An Garda Síochána have welcomed a new member to their crew and he is simply adorable. Taking to Twitter, the Gardaí revealed an adorable cocker spaniel is their latest recruit.
We just can't handle how cute he is. The little puppy has already started his training but the team needs your help with something.
Their fluffy friend has no name. They are hoping the public can lend a hand by helping them name their newest (and fluffiest) recruit.
Alongside a series of photos of the sweet cocker spaniel, they wrote: "Our latest recruit in the Garda Dog Unit is a full cocker spaniel aged 11 wks, mischievious and likes the rough and tumble with Elsa (Lab) & Bailey."
Our latest recruit in the Garda Dog Unit is a full cocker spaniel aged 11 wks, mischievious and likes the rough and tumble with Elsa (Lab) & Bailey . He has started his training to qualify as a specialist detection dog with GDU. He remains nameless but we are open to suggestions pic.twitter.com/2ouM8ukxvp
— Garda Info (@gardainfo) June 17, 2019
"He has started his training to qualify as a specialist detection dog with GDU. He remains nameless but we are open to suggestions," they added.
People have already started recommending names on Twitter including Fionn, Jarvis, Charlie and Chase.
What do you think they should call him?

redpajama_set_name: RedPajamaCommonCrawl


The new Braselton Location is open for appointments.
When traveling north on I-85 take exit 126. Turn left onto GA-211. Continue approximately 1.9 miles on GA-211 to the 3rd traffic signal. Turn left onto Friendship Road. Turn right into Creekside Village. Our office is located in the lower level of building 1235. Once in the Creekside Village parking lot, continue straight and go down the ramp on the right side of building 1235 to suite 100 in the back of the building.
When traveling south on I-85 take exit 126. Turn right onto GA-211. Continue approximately 1.8 miles on GA-211 to the 3rd traffic signal. Turn left onto Friendship Road. Turn right into Creekside Village. Our office is located in the lower level of building 1235. Once in the Creekside Village parking lot, continue straight and go down the ramp on the right side of building 1235 to suite 100 in the back of the building.
When traveling north on I-985 take exit 8. Turn right onto Friendship Rd /GA-347 E. Continue approximately 8 miles. Turn left into Creekside Village. Our office is located in the lower level of building 1235. Once in the Creekside Village parking lot, continue straight and go down the ramp on the right side of building 1235 to suite 100 in the back of the building.
When traveling south on I-985 take exit 17. Turn left onto Mundy Mill Rd/GA-53E. Continue approximately 4.7 miles. Turn right onto Old Winder Hwy NE/GA-211. Continue approximately 3.5 miles. Turn right onto Friendship Road. Turn right into Creekside Village. Our office is located in the lower level of building 1235. Once in the Creekside Village parking lot, continue straight and go down the ramp on the right side of building 1235 to suite 100 in the back of the building.


text:
Not content to have released one of 2020's best albums in Set My Heart on Fire Immediately, Perfume Genius (Mike Hadreas) has announced Immediately Remixes, a full-length rework of his acclaimed fifth album, out Feb. 19 on Matador.
The companion album features the LP's original sequencing, with remixes courtesy of an impressive cast: Jaakko Eino Kaleivi, A. G. Cook, Jim-E Stack, Planningtorock, Jenny Hval, Initial Talk, Boy Harsher, Nídia, Danny L Harle, Westerman, Actress, Koreless and Katie Dey each contribute, in that order.
"I'm very honored to have all these incredible musicians rework these songs," says Hadreas in a statement. "I felt personally remixed listening to their versions, hearing the spirit of my song completely transformed was very magical. Each one feels like a little portal to a fucked up shared world."
Our first taste of Immediately Remixes is also out today (Jan. 14) in the form of electronic duo Boy Harsher's version of "Your Body Changes Everything," which is accompanied by a Poltergeist-inspired video, directed by Boy Harsher vocalist Jae Matthews and Caitlin Driscoll, and starring model Teddy Quinlivan and Brandon Gray.
Matthews says of the video in a statement:
For the video, I wanted to create something that reflected my feelings of disconnect. Summer during Covid was complex—everyone was locked down, but so desperately wanted out. Screens and distance became the norm for casual interaction. Inspired by David Cronenberg's Videodrome (1983) and Tobe Hooper's Poltergeist (1982), I developed this idea where a man becomes haunted by a beautiful alien—who can only access him through his television set. Long live the new flesh! Luckily, Teddy Quinlivan was eager to participate from the very start and was a perfect cast for the flawless extraterrestrial. The desire within the video—the man wanting this cosmic babe so bad—matches the tone of the remix, especially during the sequences where she asks "Can you feel my love?" through the static on the TV.
Boy Harsher producer Augustus Muller adds of the remix itself, "This remix was a product of the darkest days of spring lockdown. The original, 'Your Body Changes Everything,' reminded me a lot of The Walker Brothers, and I focused on that vibe when picking sounds, while attempting to honor the initial feelings of lust and desire."
Listen to Boy Harsher's "Your Body Changes Everything" below and find the details of Immediately Remixes further down. You can preorder the album here.
Immediately Remixes Tracklist:
01. Whole Life (Jaakko Eino Kalevi Remix)
02. Describe (A.G Cook Remix)
03. Without You (Jim-E Stack Remix)
04. Jason (Planningtorock 'Jason there's no rush' Remix)
05. Leave (Jenny Hval Remix)
06. On the Floor (Initial Talk Remix)
07. Your Body Changes Everything (Boy Harsher Remix)
08. Moonbend (Nídia Remix)
09. Just A Touch (Danny L Harle Remix)
Immediately Remixes Album Art:
The Paste Happiest Hour: Nahko & American Aquarium's BJ Barham
Listen to the SongWriter Podcast Featuring Mike Veve & Johnny Leitera
The 20 Best Country Songs of 2020 (So Far)


Though it limits its vision in some conventional ways, this book is an excellent introduction to and summary of many of the key features of neoliberalism, a shift in social relations that has swept the globe since the 1970s. It is organized much as you might expect for a book with such a goal. It examines the theory underlying neoliberalism, moves on to looking at how neoliberal changes were instituted in different places, how they function in practice (and how that differs significantly from the theory), and the particular ways that they can change state relations. There is a more focused look at the neoliberal shift in China. Then there is an assessment of the actual impacts of neoliberalism as well as some brief attention to struggles against it in the past and opportunities for struggle in the future.
Perhaps the most important accomplishment of this book is its thorough demonstration of the utter disconnect between the legitimizing rhetoric of neoliberalism and its actual consequences. Neoliberal disciples wax rhapsodic about freedom, and about the unmatched capacity of unfettered markets to meet human needs. Harvey demonstrates, in contrast, that the actual consequences of social relations organized in neoliberal ways are misery and want for many. Even rates of that oh so capitalist measure, economic productivity, are poor overall under neoliberalism -- often high in a few places at any given moment, but consistently low globally. The most consistent outcome of neoliberalism -- so consistent that Harvey concludes it must be neoliberalism's actual point -- is the reconstitution of capitalist ruling-class power (measured principally through concentration of wealth, with predictable political consequences) or its constitution de novo in some places.
Now, just before I read this, I finished another book by Harvey, which I may or may not get around to reviewing. This other book is a far ranging exploration of geographical theory that was somewhat beyond me but that I found a wee bit mindblowing and plenty challenging, that was materialist yet engaged with theory far beyond marxism, and that felt like it could, perhaps, end up giving me some very useful-to-me inputs into my own thinking about things (though I'm not sure yet). Because of that, I was a bit surprised that A Brief History of Neoliberalism set its boundaries in some fairly conventionally marxist ways. I mean, it isn't hidebound about it, but it is clear that this is a book that is meant to explore one particular topic using existing, well-worn tools, rather than something that takes the tools apart to see if they really are best for the job.
This shows up in lots of ways -- insert your favourite limitation of standard academic marxist analysis here -- but there were two ways in which I particularly noticed.
The first was the book's uneven engagement with the idea of freedom. Towards the end of the book it tackles the question with a certain amount of sophistication, and a recognition that the neoliberal understanding of "freedom" is far from the only one, but earlier on the book is very dismissive of freedom as a focus of struggle in ways that do little or nothing to explore what it can actually mean. This is connected with some very brief, dismissive analysis about a number of the social movements that arose in the 1960s which included freedom among their goals. It even goes so far as to assert that freedom and social justice are inherently incompatible, sometimes tempering that by saying they "seem to be" but at other times just saying it blankly. Now, it is clear from later in the book that Harvey doesn't actually mean this, exactly -- he's not some old marxist crank yearning for the days when women and people of colour knew their place while industrial wage earners lead the proletariat -- but I think there is far, far more to be said about freedom, about class, and about the movements of the '60s and '70s, and it is potentially politically dangerous not to say that stuff because of how readers might take up what is said. I suspect even if Harvey did explore all of that stuff in some depth, I would disagree with some of what he said, but it is the easily misunderstandable shorthand that I object to the most.
The other concern has to do with unarticulated assumptions about what exactly a book looking at the history of neoliberalism should talk about. That is, this is primarily a book about the elements of social relations that get reified as "the economy" and "the state." Which are important. They may even be central when neoliberalism is your focus. But are they everything? Really? It just seems like a huge mistake to try and talk about as all-encompassing a shift in social relations as neoliberalism and then to limit what you talk about so narrowly. I can't point to any sources that do it in ways that completely satisfy me, but I've seen a small number of things that talk about neoliberal shifts in relations of white supremacy and patriarchal relations -- enough to convince me that changes have happened in these areas that can legitimately be understood as neoliberal in nature. Which isn't to say that Harvey completely ignores race and gender, but they enter the analysis more in the form of occasional attention to racialized and gendered consequences of neoliberalism rather than as social relations completely integral to state relations and relations of production.
I think there are lots of political reasons why it is important to take a broader view, but one reason is that the political economy approach assumes that the causal energy moves in one direction and one direction only -- that, sure, there might be differences in how patriarchy is experienced because of neoliberalism, but neoliberalism happened because of changes in relations of production, right? Well, maybe, but I don't feel like I've ever read anything that demonstrates that. Yes, the crisis in accumulation in the early '70s was important, but was it everything? What about analysis that builds on the sorts of ideas in the book reviewed here and talks about the role of shifting relations of reproduction and how that exists in constant dynamic tension with production? What about Sunera Thobani's analysis around the instability of white supremacy in the '50s and '60s, the role of official state multiculturalism in Canada in stabilizing white supremacy in new forms, and the connection between multiculturalism and new approaches to immigration resulting from the demands of accumulation in the '70s? Is it possible that the impulse to stabilize global relations of white supremacy after the success of decolonization struggles in the '50s and '60s played an important role in shaping the overall condition now known as "neoliberalism"? I have no idea, but it seems to me to be the sort of thing that requires investigation.
So. Very predictable reservations on my part, I suppose. And certainly no reason not to read the book. Even if it is only part of the story, it is a very important story in understanding where we are at today and what we need to be doing. It doesn't do everything, but no book ever does, and the things that it does do are important. So read it.


text:
\section{Introduction}

Physical models often involve functionals that assign real values to the
solutions of partial differential equations (PDEs).
For instance, the compliance of a structure is a function of the solution
to the elasticity equations, and the drag of
a rigid obstacle immersed in a fluid is a function of the
solution to the Navier-Stokes equations.

This type of functional depends on the PDE parameters, and it is often
possible to compute the derivative of a functional with respect to a
chosen set of parameters.  This derivative can in turn be used to
perform sensitivity analysis and to run optimization algorithms with
respect to parameters in the PDE.

The shape of the physical domain that is part the PDE-model
(like the shape of the rigid obstacle mentioned above) is a parameter
that is not straightforward to handle. Although we can compute the
shape derivative of a functional following shape calculus rules \cite{DeZo11},
this differentiation exercise is often tedious and error prone.
In \cite{Sc18}, Schmidt introduces the open-source library FEMorph:
an automatic shape differentiation toolbox for the Unified Form Language
(UFL, \cite{AlLoOlRoWe14}). \textcolor{black}{The library }FEMorph is based on refactoring UFL expressions
and applying shape calculus differentiation rules recursively.
It can compute first- and second-order shape derivatives
(both in so-called weak and strong form), and it has been successfully employed
to solve shape optimization problems \cite{ScScWa18}.

This \textcolor{black}{article} presents an alternative approach to automated
shape differentiation. The key idea is to rely solely on pullbacks
and standard G\^ateaux derivatives. This approach is more generic and robust,
because it does not require handling of special cases.
In particular, it circumvents the implementation of shape
calculus rules, and required only a minor modification of UFL, because
UFL supports G\^ateaux derivatives with respect to functions.
As a result, UFL is now capable of shape differentiating any integral that can be
be expressed in it.

\textcolor{black}{This article is organized as follows.
In Section \ref{sec:theory},
we revisit shape calculus and describe how to shape differentiate using
standard finite element software. In Section \ref{sec:examples},
we consider three test cases and show how to compute shape derivatives using
Firedrake and UFL. In Section \ref{sec:implementation-validation},
we describe code validation of this new UFL feature.
In Section \ref{sec:shapeoptexample}, we solve a PDE-constrained shape optimization
test case with a descent algorithm implemented in Firedrake and UFL.
Finally, in Section \ref{sec:discussion},
we summarize the contribution of this article.}

\section{Shape differentiation on the reference element}
\label{sec:theory}

A \emph{shape functional} is a map
${\rm J}:{\Cu}\to\bbR$ defined on the collection of domains
${\Cu}$ in $\bbR^d$, where $d\in\bbN$ denotes the space dimension.
{We follow the perturbation of identity approach \cite{simon_differentiation_1980} and for} %
a vector field  ${\mathbf{V}}\in W^{1,\infty}({\bbR^d},\bbR^d)$,
we consider the family of transformations $\{{\mathbf{P}}_s\}_{s\geq0}$
defined by {${\mathbf{P}}_s({\mathbf{x}}) = {\mathbf{x}} + s\dT({\mathbf{x}})$ for every ${\mathbf{x}}\in\bbR^d$}. Note that
${\mathbf{P}}_s$ is a diffeomorphism for any sufficiently small $s\in\bbR^+$.

{For a domain $\Omega\in {\Cu}$}, let $\Omega_s\coloneqq {\mathbf{P}}_s(\Omega)$ and assume that $\Omega_s\in {\Cu}$ for $s$ sufficiently small.
The \emph{shape directional derivative}
of ${\rm J}$ at $\Omega$ in direction ${\mathbf{V}}$ is the derivative
\begin{equation*}
\mathrm{d\J}(\Omega)[{\mathbf{V}}]\coloneqq \lim_{s\searrow 0}\frac{{\rm J}(\Omega_s)-{\rm J}(\Omega)}{s}\,.
\end{equation*}

We say that  ${\rm J}$ is \emph{shape differentiable in $\Omega$} if the directional derivative $\mathrm{d\J}(\Omega)[{\mathbf{V}}]$ exists for every direction
${\mathbf{V}}\in W^{1,\infty}({\bbR^d},\bbR^d)$, and if
the \textcolor{black}{associated} map $\mathrm{d\J}(\Omega): W^{1,\infty}({\bbR^d},\bbR^d)\mapsto \bbR$ is linear and continuous.
In this case, the linear operator $\mathrm{d\J}(\Omega)$ is called the \emph{shape derivative} of ${\rm J}$ in $\Omega$.

To illustrate the shape differentiation of a shape functional, we consider
the prototypical example
\begin{equation}\label{eq:proto-j}
    {\rm J}(\Omega_s) = \int_{\Omega_s} u_{{\mathbf{P}}_s} \,\mathrm{d}\Bx\,,
\end{equation}
where $u_{{\mathbf{P}}_s}$ is a scalar function\footnote{Shape functionals that involve vector fields
or boundary integrals can be treated following the same steps and employing
suitable pullbacks.}.
The subscript ${\mathbf{P}}_s$ highlights the possible dependence of $u_{{\mathbf{P}}_s}$ on the domain $\Omega_s$.

The standard procedure to compute $\mathrm{d\J}$ is to employ
transformation techniques and rewrite
\begin{equation}\label{eq:JPs}
    {\rm J}(\Omega_s)= \int_{\Omega} (u_{{\mathbf{P}}_s}\circ{\mathbf{P}}_s) \det({\mathbf{D}}{\mathbf{P}}_s)\,\mathrm{d}\Bx\,,
\end{equation}
{where  ${\mathbf{D}}{\mathbf{P}}_s$ denotes the Jacobian matrix of ${\mathbf{P}}_s$,
and $u_{{\mathbf{P}}_s}\circ{\mathbf{P}}_s$ denotes the composition of $u_{{\mathbf{P}}_s}$
with ${\mathbf{P}}_s$, that is, $(u_{{\mathbf{P}}_s}\circ{\mathbf{P}}_s)({\mathbf{x}}) =u_{{\mathbf{P}}_s}({\mathbf{P}}_s({\mathbf{x}}))$ for every ${\mathbf{x}} \in \Omega$.}
Note that $\det({\mathbf{D}}{\mathbf{P}}_s)>0$ for $s$ sufficiently small.
Then, by linearity of the integral,
the shape derivative $\mathrm{d\J}$ is given by
\begin{align}
\nonumber
    \mathrm{d\J}(\Omega)[{\mathbf{V}}] &= \int_{\Omega}  \ders{(u_{{\mathbf{P}}_s}\circ{\mathbf{P}}_s)\det{\mathbf{D}}{\mathbf{P}}_s}\,\mathrm{d}\Bx \\
\label{eq:dJgen}
    &= \int_\Omega \ders{u_{{\mathbf{P}}_s}\circ {\mathbf{P}}_s} + u_{{\mathbf{P}}_0} \Div({\mathbf{V}})\,\mathrm{d}\Bx\,,
\end{align}
where $\ders{{}\cdot{}}$ denotes the derivative with respect to $s$ at $s=0$.
The term $\ders{u_{{\mathbf{P}}_s}\circ {\mathbf{P}}_s}$ is often called the \emph{material derivative} \cite{Be10}.
Its explicit formula depends on whether
the function $u_{{\mathbf{P}}_s}$ does or does not dependent on $\Omega_s$ (see Section \ref{sec:examples}).

Next, we repeat the derivation of \eqref{eq:dJgen} in the context of finite elements
and derive an alternative formula for $\mathrm{d\J}$.
Let $\{K_i\}_{i\in \Ci}$ be a partition of $\Omega$
such that $\dot\cup_i \overline K_i = \overline{\Omega}$ and such that
the elements $K_i$ are non-overlapping. Additionally, let
$\{{\mathbf{F}}_i\}_{i\in \Ci}$ be a family of diffeomorphisms such that
${\mathbf{F}}_i(\myref{K}) = K_i$ for every $i\in\Ci$,
where $\myref{K}$ denotes a reference element.
This induces a partition $\{{\mathbf{P}}_s(K_i)\}_{i\in \Ci}$ of $\Omega_s$.
To evaluate \eqref{eq:proto-j}, standard finite element software
rewrites it as
\begin{align}
\nonumber
{\rm J}(\Omega_s)
&= \sum_{i \in \Ci}\int_{{\mathbf{P}}_s(K_i)}   u_{{\mathbf{P}}_s} \,\mathrm{d}\Bx \\
\label{eq:JOsFEM}
&= \sum_{i \in \Ci}\int_{\myref{K}}  (u_{{\mathbf{P}}_s} \circ {\mathbf{P}}_s\circ {\mathbf{F}}_i)  \vert\det({\mathbf{D}} ({\mathbf{P}}_s\circ {\mathbf{F}}_i))\vert\,\mathrm{d}\xref\,.
\end{align}
{Let ${\mathbf{F}}_i^{-1}$ denote the inverse of ${\mathbf{F}}_i$, that is, ${\mathbf{F}}_i^{-1}({\mathbf{F}}_i({\mathbf{x}}))= {\mathbf{x}}$
for every ${\mathbf{x}}\in\myref{K}$, and ${\mathbf{F}}_i({\mathbf{F}}_i^{-1}({\mathbf{x}}))= {\mathbf{x}}$ for every ${\mathbf{x}}\in K_i$.}
Since ${\mathbf{P}}_s = ({\mathbf{P}}_s\circ{\mathbf{F}}_i)\circ{\mathbf{F}}_i^{-1}$ and ${\mathbf{P}}_s\circ{\mathbf{F}}_i = {\mathbf{F}}_i + s{\mathbf{V}}\circ{\mathbf{F}}_i$,
we can rewrite equation \eqref{eq:JOsFEM} as follows
\begin{multline}\label{eq:JOsFEMequi}
    {\rm J}(\Omega_s) %
     = \sum_{i \in \Ci}\int_{\myref{K}}  \left(u_{({\mathbf{F}}_i + s{\mathbf{V}} \circ {\mathbf{F}}_i)\circ{\mathbf{F}}_i^{-1}} \circ ({\mathbf{F}}_i + s{\mathbf{V}} \circ {\mathbf{F}}_i)\right) \\
      \vert\det({\mathbf{D}} ({\mathbf{F}}_i + s{\mathbf{V}} \circ {\mathbf{F}}_i))\vert\,\mathrm{d}\xref\,.
\end{multline}
{Let $\{g_i\}_{i\in\Ci}$ be the collection of maps defined by
\begin{equation*}
g_i({\mathbf{T}}) \coloneqq (u_{{\mathbf{T}}\circ{\mathbf{F}}_i^{-1}}\circ{\mathbf{T}})\vert\det({\mathbf{D}}{\mathbf{T}})\vert\,.
\end{equation*}
Then, formula \eqref{eq:JOsFEMequi} can be rewritten as
\begin{equation*}
{\rm J}(\Omega_s) =  \sum_{i \in \Ci}\int_{\myref{K}}  g_i({\mathbf{F}}_i + s{\mathbf{V}} \circ {\mathbf{F}}_i)\,\mathrm{d}\xref\,,
\end{equation*}
and}
taking the derivative of \eqref{eq:JOsFEMequi} with respect to $s$ implies
\begin{multline} \label{eq:dJgen-ufl}
\mathrm{d\J}(\Omega)[{\mathbf{V}}] = \sum_{i \in \Ci}\int_{\myref{K}} \ders{g_i({\mathbf{F}}_i + s{\mathbf{V}} \circ {\mathbf{F}}_i)}\,\mathrm{d}\xref\,.
\end{multline}
Equation \eqref{eq:dJgen-ufl} gives an alternative {and equivalent} expression
for the shape derivative \eqref{eq:dJgen}.
{However, to derive formula \eqref{eq:dJgen} it is necessary
to follow shape calculus rules by hand, which is often a tedious and error prone
exercise. Equation \eqref{eq:dJgen-ufl}, by contrast,
can be derived automatically with finite element software.
Indeed,
to evaluate ${\rm J}(\Omega)$, standard finite element software rewrites it as
\begin{equation*}
{\rm J}(\Omega) = \sum_{i \in \Ci}\int_{\myref{K}} g_i({\mathbf{F}}_i)\,.
\end{equation*}
{In UFL the maps $\{g_i\}_{i\in \Ci}$ are constructed symbolically and in an automated fashion.}
Therefore, it is possible to evaluate $\mathrm{d\J}(\Omega)[{\mathbf{V}}]$ by performing the
steps necessary for the assembly of ${\rm J}(\Omega)$ and, at the appropriate time,
differentiating the maps $\{g_i\}_{i\in\Ci}$. To be precise, this differentiation
corresponds to a standard G\^{a}teaux directional derivative, because
the integrand in \eqref{eq:dJgen-ufl} corresponds to the following limit
\begin{equation*}
\ders{g_i({\mathbf{F}}_i + s{\mathbf{V}} \circ {\mathbf{F}}_i)}=\lim_{s\searrow 0}\frac{g_i({\mathbf{F}}_i + s{\mathbf{V}} \circ {\mathbf{F}}_i)-g_i({\mathbf{F}}_i)}{s}\,,
\end{equation*}
which can be interpreted as the G\^{a}teaux directional derivative of $g_i$
at  ${\mathbf{T}}={\mathbf{F}}_i$ in the direction ${\mathbf{V}}\circ{\mathbf{F}}_i$ \cite[Def. 1.29]{HiPiUlUl09}.
This viewpoint is important to correctly implement this differentiation step in the existing pipeline in UFL
(see Figure \ref{fig:UFLworkflow}).}
We emphasize that this also enables computing higher-order shape
derivatives by simply taking higher-order G\^{a}teaux derivatives
in \eqref{eq:dJgen-ufl}.
\begin{figure}[htbp]
    \begin{center}
        \tikzstyle{block} = [rectangle, draw,
        text centered, minimum height=1em,
        node distance=0.5cm]
        \begin{tikzpicture}
            \node[block] (function-deriv) {Input: integrand in physical space};
            \node[block, below=of function-deriv] (degree) {Estimate quadrature degree};
            \node[block, below=of degree] (pullback) {Pullback to reference element};
            \node[block, below=of pullback] (coord-deriv) {New: calculate derivatives with respect to coordinates};
            \node[block, below=of coord-deriv] (assemble) {Output:
              integrand in reference space};
            \draw[-stealth] (function-deriv) -- (degree);
            \draw[-stealth] (degree) -- (pullback);
            \draw[-stealth] (pullback) -- (coord-deriv);
            \draw[-stealth] (coord-deriv) -- (assemble);
        \end{tikzpicture}
        \caption{Symbolic workflow in UFL to transform integrals from
          physical to reference space.}
          \label{fig:UFLworkflow}
    \end{center}
\end{figure}

\begin{remark}
  Lagrange finite element global basis functions are obtained by
  gluing local parametric basis functions, that is, basis functions
  $\{b_m^i\}_{m\in\Cm}$ defined only on $K_i$ and of the form
  $b_m = \myref{b_m}\circ {\mathbf{F}}_i^{-1}$, where $\{\myref{b_m}\}_{m\in\Cm}$
  is the set of reference local basis functions, which are defined
  only on the reference element $\myref{K}$.  If ${\mathbf{V}}$ lives in a Lagrange
  finite element space built on the partitioning $\{K_i\}_{i\in \Ci}$,
  it is possible to evaluate $\mathrm{d\J}({\mathbf{T}})[{\mathbf{V}}]$ by computing the
  G\^{a}teaux derivative in \eqref{eq:dJgen-ufl} in the direction of
  the reference local basis functions $\{\myref{b_m}\}_{m\in\Cm}$
  (instead of in the direction ${\mathbf{V}}\circ{\mathbf{F}}_i$) and summing these
  values. This allows us to fully rely on the symbolic
  differentiation capabilities of UFL.
\end{remark}
\begin{remark}
  The approach does not rely on the element being affinely mapped, but extends to elements that are mapped using a Piola transform such as the Raviart-Thomas or Nedelec elements.
  However, it does not work for elements such as the Hermite element that require different pullbacks for point evaluation and derivative degrees of freedom.
\end{remark}

\section{Examples}
\label{sec:examples}
In this section,
we consider three examples based on \eqref{eq:proto-j} that cover most applications.
For these examples, we give explicit expressions of $\mathrm{d\J}$ using
\eqref{eq:dJgen} and \eqref{eq:dJgen-ufl}
and show how to compute $\mathrm{d\J}$
with the finite element software
Firedrake\footnote{Examples using FEniCS \cite{Logg:2010,Logg:2012} will be almost identical,
modulo small differences in setting up initial conditions} \cite{Rathgeber:2016}.
To shorten the notation, we define ${\mathbf{V}}_i \coloneqq{\mathbf{V}}\circ{\mathbf{F}}_i$.
\begin{example}
  \label{example:1}
  Let the integrand be independent of $\Omega$, i.e. $u_{{\mathbf{P}}_s}= u$
  for some function $u$.  Then, the chain rule implies that
  $\ders{u_{{\mathbf{P}}_s}\circ{\mathbf{P}}_s}=\ders{u\circ{\mathbf{P}}_s}=\nabla u\cdot {\mathbf{V}}$.
  Recalling $\ders{\det{\mathbf{D}}{\mathbf{P}}_s} = \Div({\mathbf{V}})$, we conclude that
  equation \eqref{eq:dJgen} becomes
  \begin{equation}
    \label{eq:dJindep} \mathrm{d\J}(\Omega)[{\mathbf{V}}] = \int_{\Omega}  \nabla u \cdot {\mathbf{V}} +  u\Div({\mathbf{V}})\,\mathrm{d}\Bx\,.
  \end{equation}
  On the other hand, inserting $u_{{\mathbf{P}}_s}=u$ into
  \eqref{eq:dJgen-ufl}, we obtain the equivalent
  expression: %
  \begin{multline}\label{eq:dJindep-ufl}
    \mathrm{d\J}(\Omega)[{\mathbf{V}}] %
    = \sum_{i \in \Ci}\int_{\myref{K}}
    \big({\mathbf{V}}_i \cdot (\nabla u \circ {\mathbf{F}}_i) \\+ (u\circ {\mathbf{F}}_i) \Tr({\mathbf{D}} {\mathbf{V}}_i{\mathbf{D}} {\mathbf{F}}_i^{-1})\big)\vert\det({\mathbf{D}}{\mathbf{F}}_i)\vert \,\mathrm{d}\xref\,.
  \end{multline}
  Example code is shown in \textcolor{black}{Listing} \ref{lst:example1}.
  {
      Functionals with domain independent integrands are used in
      applications including image segmentation \cite{hintermuller_second_2004} or, when $u\equiv 1$, to enforce volume constraints in shape optimization.}

  \begin{mylisting}[htb!]
  \hspace{-1.52em}
\includegraphics[width=1.06\linewidth]{listing1.pdf}
  \caption{%
  \textcolor{black}{Firedrake code to compute $\mathrm{d\J}$ from Example \ref{example:1} when {$u(x,y) = x^2 + y^2 - 1$.}}}
  \label{lst:example1}
  \end{mylisting}

\end{example}

\begin{example}
  \label{example:2}
  Let $\{V_h(\Omega_s)\}_s$ be a family of scalar finite element
  spaces such that the global basis functions $\{B_s^i\}_i$ of
  $V_h(\Omega_s)$ are of the form $B_s^i = B^i\circ{\mathbf{P}}_s^{-1}$, where
  $\{B^i\}_i$ are basis functions of $V_h(\Omega)$ {and ${\mathbf{P}}_s^{-1}$
  is the inverse of ${\mathbf{P}}_s$, that is, ${\mathbf{P}}_s^{-1}({\mathbf{P}}_s({\mathbf{x}}))= {\mathbf{P}}_s({\mathbf{P}}_s^{-1}({\mathbf{x}}))={\mathbf{x}}$
  for every ${\mathbf{x}}\in \bbR^d$}.  Let
  $v_{{\mathbf{P}}_s}\in V_h(\Omega_s)$ and
  $u_{{\mathbf{P}}_s}=v_{{\mathbf{P}}_s}+\| \nabla v_{{\mathbf{P}}_s} \|^2$.  Since
  \begin{equation}
    v_{{\mathbf{P}}_s} \circ {\mathbf{P}}_s + \|(\nabla v_{{\mathbf{P}}_s})\circ {\mathbf{P}}_s\|^2 = v_{{\mathbf{P}}_0} + \|{\mathbf{D}}{\mathbf{P}}_s^{-T} \nabla v_{{\mathbf{P}}_0}\|^2\,,
  \end{equation}
  \textcolor{black}{equation} \eqref{eq:dJgen} becomes
  \begin{multline}
    \mathrm{d\J}(\Omega)[{\mathbf{V}}]
    = \int_\Omega (v_{{\mathbf{P}}_0} + \| \nabla v_{{\mathbf{P}}_0}\|^2) \Div({\mathbf{V}})
   \\ -2 \nabla v_{{\mathbf{P}}_0} \cdot ({\mathbf{D}}{\mathbf{V}}^{T} \nabla v_{{\mathbf{P}}_0})  \,\mathrm{d}\Bx\,.
  \end{multline}
  On the other hand, note that for any $\hat{\mathbf{x}}\in \hat K$ and for
  $i\in\Ci$, it holds $v_{{\mathbf{P}}_s}({\mathbf{P}}_s({\mathbf{F}}_i({\myref{\Bx}}))) = v_i({\myref{\Bx}})$,
  where $v_i$ is a linear combination of the local basis functions
  $\{\myref{b_m}\}_{m\in\Cm}$ defined on the reference element
  $\hat K$.  Therefore,
  \begin{multline}
    v_{{\mathbf{P}}_s} \circ {\mathbf{P}}_s \circ {\mathbf{F}}_i + \|(\nabla v_{{\mathbf{P}}_s})\circ {\mathbf{P}}_s \circ {\mathbf{F}}_i\|^2 \\
    = \hat v_i + \|{\mathbf{D}}({\mathbf{P}}_s \circ {\mathbf{F}}_i)^{-T} \nabla \hat v_i\|^2
    \quad \text{on } \hat K\,,
  \end{multline}
  and \eqref{eq:dJgen-ufl} becomes
  \begin{equation}
    \begin{aligned}
      \mathrm{d\J}(\Omega)[{\mathbf{V}}]
      = \sum_{i \in \Ci} \int_{\myref{K}} \big((\hat v_i + \|{\mathbf{D}}{\mathbf{F}}_i^{-T}
        \nabla v_i\|^2) \Tr({\mathbf{D}}{\mathbf{V}}_i {\mathbf{D}}{\mathbf{F}}_i^{-1}) \\
        - 2 \nabla \hat v_i
        \cdot {\mathbf{D}}{\mathbf{F}}_i^{-1}{\mathbf{D}}{\mathbf{V}}_i{\mathbf{D}}{\mathbf{F}}_i^{-1}{\mathbf{D}}{\mathbf{F}}_i^{-T}\nabla \hat
        v_i\big) \vert\det({\mathbf{D}}{\mathbf{F}}_i)\vert \,\mathrm{d}\xref.
    \end{aligned}
  \end{equation}
  \textcolor{black}{Listing} \ref{lst:example2} shows code for this case, using as $v_{{\mathbf{P}}_0}$
  the piecewise affine Lagrange interpolant of $\sin(x)\cos(y)$.
\begin{mylisting}[htb!]
\hspace{-1.52em} \includegraphics[width=1.06\linewidth]{listing2.pdf}
\caption{%
\textcolor{black}{Firedrake code to compute $\mathrm{d\J}$ from Example \ref{example:2}.}
Note that in this
case, $v$ does not depend explicitly on $x$ and $y$.}
\label{lst:example2}
\end{mylisting}
\end{example}

\begin{example}
  \label{example:3}
  Let $u_{{\mathbf{P}}_s}$ be the finite element solution to the boundary value
  problem
  \begin{equation}\label{eq:PDEconstr}
    -\Delta u_{{\mathbf{P}}_s} + u_{{\mathbf{P}}_s} = f \quad \text{in } \Omega_s\,,
    \quad\nabla u_{{\mathbf{P}}_s} \cdot{\mathbf{n}} = 0\quad \text{on } \partial \Omega_s\,.
  \end{equation}
  In this case, the functional \eqref{eq:proto-j} is said to be
  PDE-constrained, and computing its shape derivative is less
  straightforward. The standard procedure is to introduce an
  appropriate Lagrangian functional \cite[Ch.~10, Sect.~5]{DeZo11}.
  For this example, the Lagrangian is
  \begin{equation}\label{eq:Lagrangian}
    \mathrm{L}_s(u_{{\mathbf{P}}_s},v_s) \coloneqq {\rm J}(\Omega_s) + \mathrm{e}_s(u_{{\mathbf{P}}_s},v_s),
  \end{equation}
  where
  \begin{equation}\label{eq:state}
    \mathrm{e}_s(u_{{\mathbf{P}}_s}, v_s) \coloneqq
    \int_{\Omega_s}\nabla u_{{\mathbf{P}}_s}\cdot \nabla v_s + u_{{\mathbf{P}}_s}v_s - fv_s\,\mathrm{d}\Bx\,%
  \end{equation}
  stems from the weak formulation of the PDE constraint
  \eqref{eq:PDEconstr}.  The shape derivative $\mathrm{d\J}$ is equal to the
  shape derivative of
  $\mathrm{L}_s(u\circ{\mathbf{P}}_s^{-1},p\circ{\mathbf{P}}_s^{-1})$, where $u$ is the
  solution to \eqref{eq:state} for $s=0$ and $p\in V_h(\Omega)$ is the
  solution to an adjoint boundary value problem.  The shape derivative
  of $\mathrm{L}_s(u\circ{\mathbf{P}}_s^{-1},p\circ{\mathbf{P}}_s^{-1})$ can be computed
  as in \textcolor{black}{Example} \ref{example:2}.  The result is
  \begin{multline}\label{eq:dJconstr}
    \mathrm{d\J}(\Omega)[{\mathbf{V}}] = \int_{\Omega} (u + \nabla u\cdot \nabla p + up - fp)\Div({\mathbf{V}})\\
    - p\nabla f\cdot{\mathbf{V}}
    -  \nabla u\cdot ({\mathbf{D}}{\mathbf{V}}+{\mathbf{D}}{\mathbf{V}}^{T})\nabla p\,\mathrm{d}\Bx\,.
  \end{multline}
  For this example, we omit the equivalent formula on the reference
  element because of its length.  However, as \textcolor{black}{Listing} \ref{lst:example3}
  shows, UFL removes the tedium of deriving the shape derivative, and
  we can easily compute $\mathrm{d\J}$.
\begin{mylisting}[htb!]
\hspace{-1.52em} \includegraphics[width=1.06\linewidth]{listing3.pdf}
\caption{%
\textcolor{black}{Firedrake code to compute $\mathrm{d\J}$ from Example \ref{example:3} when $f(x,y) = xy$ in \eqref{eq:state}.}}
\label{lst:example3}
\end{mylisting}
\end{example}
\begin{remark}
  With appropriate modifications, the same code can be use for
  functionals constrained to boundary value problems with Neumann or
  Dirichlet boundary conditions.  For the Neumann case, it is
  sufficient to add the Neumann forcing term in line 6 of
  \textcolor{black}{Listing }\ref{lst:example3}. For the Dirichlet case, one needs to replace
  \texttt{u} with \texttt{u+g} in lines 6 and 7 (where \texttt{g} is
  the function defined in terms of \texttt{X} that describes the
  Dirichlet boundary condition) and impose homogeneous Dirichlet
  boundary conditions in lines 8 and 9.
\end{remark}
\begin{remark}
  To evaluate the action of the shape Hessian of a PDE-constrained
  functional, one can follow the instructions given in
  \cite[p. 65]{HiPiUlUl09}.  Note that by computing shape derivatives
  as in \eqref{eq:dJgen-ufl}, it is straightforward to combine shape
  derivatives of $\mathrm{L}_s(u\circ{\mathbf{P}}_s^{-1},p\circ{\mathbf{P}}_s^{-1})$
  with standard G\^{a}teaux derivatives with respect to
  $u\circ{\mathbf{P}}_s^{-1}$.
\end{remark}

\section{Code validation}
\label{sec:implementation-validation}
We validate our implementation by testing
that the Taylor expansions truncated to first and second
order satisfy the asymptotic conditions
\begin{equation}\label{eq:Taylor}
\rm\delta_1({\rm J}, s) = O(s^2) \quad \text{and} \quad \rm\delta_2({\rm J}, s) = O(s^3)\,,
\end{equation}
where
\begin{equation*}
\rm\delta_1({\rm J}, s) \coloneqq \|{\rm J}({\Omega_s}) - {\rm J}(\Omega) - s \mathrm{d\J}(\Omega)[{\mathbf{V}}]\|
\end{equation*}
and
\begin{multline*}
\rm\delta_2({\rm J}, s) \coloneqq \|{\rm J}({\Omega_s}) - {\rm J}(\Omega)\\
- s \mathrm{d\J}(\Omega)[{\mathbf{V}}] - \frac{1}{2} s^2 \mathrm{d^2\J}(\Omega)[{\mathbf{V}}, {\mathbf{V}}]\|\,.
\end{multline*}
In \textcolor{black}{Figure }\ref{fig:Taylor}, we plot the values of $\rm\delta_1$ and $\rm\delta_2$
for $s=2^{-1}, 2^{-2},$ $\dots, 2^{-10}$, and ${\rm J}$
as in \textcolor{black}{Examples 1 and 3} %
from the previous section (we
denote these functionals ${\rm J}_1$ and ${\rm J}_2$ respectively).
The vector field ${\mathbf{V}}$ is chosen randomly. This experiment clearly
displays the asymptotic rates predicted by \eqref{eq:Taylor}.
\begin{figure}[htb!]\label{fig:Taylor}
    \begin{center}
        \includegraphics{./taylortest.pdf}
        \caption{Taylor test for Examples 1 and 3. The convergence rates match the expected convergence.}
    \end{center}
\end{figure}
We have repeated this numerical experiment
for many other test cases, including functionals that are not linear
in $u$, {functionals given by integrals over $\partial\Omega$ involving the normal ${\mathbf{n}}$,}
and functionals that are constrained to linear and nonlinear
boundary value problems with nonconstant
right-hand sides and nonconstant Neumann and Dirichlet boundary conditions.
In every instance, we
have observed the asymptotic rates predicted by \eqref{eq:Taylor}.
The code for these numerical experiments is available at \cite{zenodoFiredrake20190402.0}.

\section{Shape optimization of a pipe}
\label{sec:shapeoptexample}
In this section, we show how to use Firedrake and the new UFL capability to code
a PDE-constrained shape optimization algorithm. As test case, we consider the
optimization of a pipe to minimize the dissipation of kinetic energy of the fluid into heat.
This example is taken from \cite[Sect. 6.2.3]{SchThesis}. To simplify the exposition,
we use a very simple optimization strategy. At the end of the section, we will comment
on possible improvements.

The initial design of the pipe is shown in Figure \ref{fig:pipe} (top).
The pipe contains viscous fluid (with viscosity $\mu$), which flows in from the left and is
modelled using the incompressible Navier-Stokes equations.
To be precise, let $\Omega$ be the shape of the pipe, $\Gamma\subset \partial\Omega$
be the outflow boundary of the pipe (that is, the end of the pipe on the right),
and ${\mathbf{u}}$ and $p$ be the velocity
and the pressure of the fluid, respectively. Then, ${\mathbf{u}}$ and $p$ satisfy
\begin{align*}
-\nu \Delta {\mathbf{u}} + {\mathbf{u}} \nabla {\mathbf{u}} + \nabla p &= 0 & \text{in } \Omega\,,\\
\Div {\mathbf{u}} &= 0& \text{in } \Omega\,,\\
{\mathbf{u}} &= {\mathbf{g}} &\text{on } \partial\Omega\setminus \Gamma\,,\\
p{\mathbf{n}} - \nu \nabla u\cdot {\mathbf{n}} & = 0 &\text{on } \Gamma\,.
\end{align*}
Here ${\mathbf{g}}$ is given by a Poiseuille flow at the inlet and is zero on the walls of the pipe

The goal is to modify the central region of the pipe
so that the shape functional
\begin{equation*}
{\rm J}(\Omega) = \int_\Omega \nu \nabla{\mathbf{u}} : \nabla{\mathbf{u}} \,\mathrm{d}\Bx
\end{equation*}
is minimized.
To solve this shape optimization problem,
we parametrize the initial design with a polygonal mesh and update
the node coordinates using a descent direction optimization algorithm
with fixed step size.
As descent directions, we use Riesz representatives of the shape gradient
with respect to the inner product induced by the Laplacian{, i.e. at each step the deformation is given by the solution to
\begin{equation}
    \begin{aligned}
        -\Delta {\mathbf{V}} &= -\mathrm{d\J}(\Omega) && \text{in } \Omega\\
        {\mathbf{V}} &= 0 && \text{on fixed boundaries.}
    \end{aligned}
\end{equation}
This approach is also known as Laplace smoothing.
}
To avoid degenerate results, we penalize changes
of the pipe volume.
The whole algorithm, comprising of state and adjoint equations and
shape derivatives, is contained in Listing \ref{lst:pipe} and described in
detail in the following paragraph. The optimized shape is displayed in Figure \ref{fig:pipe} (bottom),
the convergence history is in Figure \ref{fig:pipe-convergence}.
These results are compatible with those in \cite[Sect. 6.2.3]{SchThesis} and
clearly indicate the success of the shape optimization algorithm.

\paragraph{Description of Listing \ref{lst:pipe}}
In line 2-4, we load the finite element mesh \texttt{pipe.msh} and extract the vertex coordinates.
This mesh is generated with Gmsh \cite{geuzaine2009gmsh} and is available as part of \cite{zenodoFiredrake20190402.0}.
Lines 5-8 define the Gramian matrix of the inner product employed
to compute descent directions. In lines 9-14, we define the space of P2-P1
Taylor-Hood finite elements, which we use to discretize the weak formulation of
the Navier-Stokes equations, and set up the functions containing the solutions
to the state and adjoint equation as well as the test functions for the weak form.
In lines 15-22 we define the weak formulation of the Navier-Stokes equations and
certain parameters to prescribe the use of the MUMPS direct solver \cite{amestoy2000mumps} to solve
the linearized equations.  In lines 23-29, we define the shape functional
${\rm J}$, the functional describing the volume of the shape, as well as the
Lagrangian and its derivative. {In particular, note that
the shape derivative of the Lagrangian can be computed with
the simple command \verb!dL = derivative(L, X)! in line 28.
Without the new automatic shape differentiation capability in UFL,
line 28 would have to be replaced with the following formula
\begin{verbatim}
 dL = -inner(nu*grad(u)*grad(W), grad(v))*dx
      -inner(nu*grad(u), grad(v)*grad(W))*dx
      -inner(v, grad(u)*grad(W)*u)*dx
      +tr(grad(v)*grad(W))*p*dx
      -tr(grad(u)*grad(W))*q*dx
      +div(W)*inner(nu*grad(u), grad(v))*dx
      -div(W)*inner(div(v), p)*dx
      +div(W)*inner(div(u), q)*dx
      +div(W)*inner(v, grad(u)*u)*dx
      +nu*inner(grad(u), grad(u))*div(W)*dx
      -2*nu*inner(grad(u)*grad(W), grad(u))*dx
\end{verbatim}}
\noindent In lines 30-35 we set up a function that updates the solution to the state and
the adjoint equations.
{We emphasize that this shape optimization problem is not self-adjoint and that UFL derives the adjoint equation automatically.}
Note that, whenever the function
\texttt{solve\_state\_and\_adjoint} is called, the new values of the velocity ${\mathbf{u}}$
are stored in the file \texttt{u.pvd} (which can visualized using Paraview \cite{ahrens2005paraview}).
Finally, lines 36-46 contain the optimization algorithm: for 100 iterations we
compute the shape derivative and penalize volume changes (lines 38-40), compute the descent direction (lines 41-42),
update the domain (line 45), and
update the state and adjoint solutions (line 46).
\begin{figure}
  \includegraphics[width=\linewidth]{./pipe_initial.png}
  \includegraphics[width=\linewidth]{./pipe_final.png}
  \caption{Initial (top) and optimized (bottom) shape of a pipe connecting a given inflow and outflow.}
  \label{fig:pipe}
\end{figure}

\begin{figure}[htb!]
  \includegraphics{./pipe-convergence.pdf}
  \caption{The value of the objective (plotted in linear scale) is reduced from approximately $0.61298$ to $0.40506$.
  The $H^1$-norm of the gradient (plotted in logarithmic scale) is reduced from $0.487274$ to $0.000870$.}
  \label{fig:pipe-convergence}
\end{figure}

\begin{mylisting}[htb!]
\hspace{-1.52em} \includegraphics[width=1.06\linewidth]{listing4.pdf}
\caption{Firedrake code to optimize the shape of a pipe and minimize the dissipation of kinetic energy into heat. \textcolor{black}{Lines 26 and 28 use the newly developed automatic shape differentiation.}}
\label{lst:pipe}
\end{mylisting}

\begin{remark}
The optimization algorithm of Listing \ref{lst:pipe} is based on a simple optimization
strategy and can be improved in several ways, at the mere cost of adding lines of code.
For instance, instead of using a fixed step-size and a fixed number of iterations,
one could implement an adaptive step-size selection and stopping criteria.
Additionally, one could experiment with different inner products to define descent
directions \cite{IgStWe17}, as well as compute second order derivatives of
${\rm J}$ and implement (quasi-)Newton methods \cite{Sc18}. Despite the room for improvement,
we would like to stress that Listing \ref{lst:pipe} can be readily used for a 3D problem by simply passing a 3D mesh
and changing the inflow boundary condition in line 18.
\end{remark}

\section{Discussion}
\label{sec:discussion}
{We have presented a new and equivalent formulation of shape derivatives in the context of
finite elements as G\^ateaux-derivatives on the reference element.  While the
formulation applies to finite elements in general, we have implemented this
new approach in UFL due to its extensive support for symbolic calculations.
This new UFL capability allows computing shape derivatives of
functionals that are defined as volume or boundary integrals, and that are constrained to linear and non-linear PDEs.}
During shape differentiation, our code treats finite element functions
and global functions differently. This behavior is correct and
necessary to handle PDE-constraints properly.
In combination with a finite element software package, such as FEniCS
or Firedrake, that takes as input UFL, this enables the
entirely automated shape differentiation of functionals subject to boundary value problems.
\textcolor{black}{This notably simplifies tackling PDE-constrained shape optimization problems.}

Compared to the existing shape differentiation toolbox FEMorph,
our code does not compute shape derivatives in strong form
because it neither relies on shape calculus differentiation rules
nor performs integration by parts.
However, in practice we do not consider this a limitation as it has been shown in
\cite{HiPaSa15,Be10,Zh18} that the weak form is superior when the state and
the adjoint equations are discretized by finite elements.

\begin{acknowledgements}
DAH is supported by the Natural Environment Research Council [grant number
NE/K008951/1]. LM is supported by the Engineering and Physical Sciences
Research Council [grant number EP/L000407/1].  FW is supported by the EPSRC
Centre For Doctoral Training in Industrially Focused Mathematical Modelling
[grant number EP/L015803/1].\\~\\
\textbf{Contributions}
This work originated in a discussion between the four authors at the FEniCS 18 conference, where AP and DAH suggested to calculate shape derivates as in Section \ref{sec:theory}.
FW implemented this idea in UFL with help from LM.
The manuscript was written by AP and FW, with feedback from LM and DAH.
\\~\\
\textbf{Conflict of interest statement}
 On behalf of all authors, the corresponding author states that there is no conflict of interest.
 \\~\\
\textbf{Replication of results}
The code for the numerical experiments is available at \cite{zenodoFiredrake20190402.0}.
\end{acknowledgements}

\bibliographystyle{plainurl}

redpajama_set_name: RedPajamaArXiv


The Comedy Button. Podcasts And Stuff!
Justin Moorhouse is an English stand-up comedian and radio DJ from Manchester. Comedy Carnival, Leicester Sq., offers the experiences on Thursday, Friday and Saturday nights all through out the yr and can solely settle for group bookings of not more than six individuals. Please note at the Comedy Loft venues (Studying, Watford, Leicester, Nottingham, Camden Lock and Birmingham) bookings are restricted one voucher per occasion. Whether you are planning an evening out with associates, a date night time, or you might be trying to find native group events, The Comedy Zone is the place to be. Then, together with your new abilities, make your debut on the Comedy Gong Show, where our celebrity comedians will judge your performance.
In case you suppose you've gotten what it takes to take the stage, attempt a Comedy Workshop where our execs provides you with inside suggestions. The very best part about these films is that they are going to at all times be funny, no matter what generation watches them. Join us for Weekend Brunch at Lucy Restaurant, positioned on the second ground of Comedy Works South.
John Robins – probably the most exciting and distinctive voices in comedy – returns reflecting on love, loss and lamenting the actual fact he cannot break up with himself. We welcome you chill out and revel in specialty drinks and eats when you take heed to live music as a part of our 12 months-round music sequence, Acoustic Dwell at Lila B.
Stephen Bailey's pleasant, open brand of gossipy humour has made him one of the vital fulfilling acts on the UK comedy circuit at present. Holding just over 100 folks, Zanies/Chicago is probably the most intimate venue through which to experience the artwork of standup comedy. You could watch them with an open mind, as a result of regardless that they are pretty old, they are still a few of the funniest motion pictures round. But as Killam points out, there was doubtlessly some clever, self-aware comedy to be mined from such a robust reversal on Trump. He'll headline the upcoming collection of BBC2's Dwell from the BBC and is a regular face on TV, with recent appearances together with BBC2's Mock The Week, Dave's Alan Davies: As But Untitled and BBC3's Russell Howard's Good News.


text:
Peterborough set to be awarded massive £22m grant for major regeneration
The investment comes as part of the Government's scheme to 'level up' Britain
The old Guildhall in Peterborough (Image: Cambridge News)
Sign up to our dedicated Peterborough newsletter for the latest news direct to your inbox each day
The Cambridgeshire city of Peterborough has been offered a deal through the Government's Towns Fund to help boost the economy, build more homes, and support local businesses.
Communities Secretary Robert Jenrick made the announcement on Tuesday, October 27, in which it revealed Peterborough had been offered a Town Deal worth up to £22 million.
It is one of the first of seven towns across the country to have a funding offer made as part of the landmark £3.6 billion Conservative Government scheme, aimed at levelling up local economies and creating jobs by investing in transport, infrastructure, and skills.
In Peterborough the funding will be used to make the town fit for the future, and achieve the long term vision put forward by the council and local businesses for the next 30 years.
This includes plans to make Peterborough more sustainable, encouraging low carbon living through cutting emissions and being kinder to the environment.
Latest Cambridgeshire coronavirus cases and lockdown restrictions in full - October 28
The plans will also help residents maintain healthy and active lifestyles with the development of a new Activity Centre in town, and improvements to pedestrian areas and walkways to encourage people to get outdoors.
A new Enterprise Hub will also be created in the city to encourage inward investment and help local businesses and budding entrepreneurs to success, by giving them access to the tools and space they need.
Work is currently underway to confirm the final funding amount and get deals in place, and once it is the much needed regeneration projects can begin.
Alongside the plans to help level Peterborough up and bring it closer in line with other areas, the Towns Fund will play a huge role in helping the city recover from the impacts of the pandemic.
This CGI image of what Fletton Quays, one of Peterborough's biggest new developments, could look like once completed (Image: Peterborough Investment Partnership & NORR)
This is in addition to the Government's package of coronavirus support, which included £18.67m for Peterborough.
Councillor John Holdich, leader of Peterborough CIty Council, said: "We want to build a Peterborough for the future, one that our children and grandchildren can be proud to live in.
"Our city has a rich heritage and a diverse, yet unified population. With Government funding support we can make our community even stronger and create a city of growth, prosperity and opportunity."
Peterborough City Council is now waiting to find out the details about which of the following key areas have been approved as part of the funding.
Riverside development and connections
This involves creating a masterplan for the Embankment, the new University campus and Middleholme, that protects the open green space.
Thereare also hopes to design and build an additional bridge across the River Nene for pedestrians and cyclists to connect the north and south of the city.
New and improved visitor and cultural attractions
The council hopes to create new library and cultural facilities for the city, and improve visitor attractions such as a Bronze Age themed extension to the Town Museum and a lakeside activity centre at Ferry Meadows.
Opening up Station Quarter
The redevelopment will include the creation of the 'Station Quarter'
One of the biggest planned developments for Peterborough is the work around the train station - known as Station Quarter.
This will hopefully create a welcoming route from the station into the city centre to make the journey easier for visitors to navigate by foot or bike, as well as creating space for developing new homes and offices.
Enterprise and skills infrastructure
To support new city businesses and start ups, the city council hope to create a new enterprise training and business incubation hub, as well as a training centre for green technology skills - aimed toward the construction and automotive sectors.
Future green city
Peterborough has been trying to build the country's environment capital for years, and hope to use the funds to create safer, easily accessible routes for pedestrians and cyclists to the train station and city centre from key points in the city.
They also hope to improve public spaces to support the wellbeing of residents, and to help the city move toward its goal of becoming carbon neutral.
Ministers will remain in conversation with local leaders over the appropriate coronavirus alert levels for their areas, including any further support that might be required.
Busy Bridge Street in Peterborough
Matthew Bradbury, independent chair of the Peterborough Towns Board, said: "This positive indication from the Government that it is willing to invest in our city has shown the time really is now for Peterborough.
"Our economy has begun to bounce back, from the lockdown. Investment in Peterborough continues to be strong with a lot of new development planned, or already underway.
"The Towns Fund offers an opportunity to develop the infrastructure the city will need to support its growth, promote the wellbeing of residents, encourage further business investment and move the city closer to its goal of becoming carbon neutral."
Enter your postcode below to find out the latest job postings in your area:
Luke Hall, Minister for Regional Growth and Local Government, said: "The Government is helping Peterborough to realise its vision for the future, with a confirmed Town Deal worth up to £22m to help make this a reality.
"This funding will help Peterborough to increase the number of jobs available for local people, by supporting local businesses and entrepreneurs to success, and encouraging inward investment.
"Every area of the country is going to benefit from our shared prosperity, so we can unlock jobs and opportunity for local people in all of our regions."
In total there are 101 towns which have been selected to work toward a Town Deal, and all of them were given a funding allocation with proposals being submitted to the Ministry of Housing, Communities and Local Government.
Work begins on major new government hub in Peterborough which will 'boost the area'
'No child will go hungry in Peterborough' this half term according to city council
The first lot of towns submitted proposals in July, before they were reviewed by officials and a final decision was made by ministers.
More Town Deals are due to be announced during November.
The Town Deals build on the Government's commitment to decentralising funding and decisions away from Whitehall, and instead investing in the growth of local economies and devolving powers through ambitious City and Growth deals, providing more than £9 billion of funding to Local Enterprise Partnerships (LEPs) and introducing 8 metro mayors in England.
The Government is working with Peterborough City Council and the Cambridgeshire and Peterborough Combined Authority to create better transport links, more connectivity and world-class education opportunities across the country.


I really don't understand the lack of enthusiasm for this show (currently a 3.9).
You have a strong to very strong Maze, Gin, DWD, C&P, SASS, NMINML, Hood and Antelope in the same show. Plus another really good outing for Soul Planet. I mean, just look at that second set... what am I missing here? Seems like this show is stronger than the night before, though the ratings don't reflect that at all.
...and Antelope delivers. One reviewer once likened Antelope to pizza - even when it's bad, it's good. This version definitely functions as the pizza-on-top of what was a great Nashville run - and having to wait 7 shows to get it must've made it that much sweeter for those there.
Overall, good-great show in which I think the sloppy playing/ transitions should be overlooked for the replay value of the Gin and the whole second set. This show didn't have many peaks or directed-jamming, but it did have a super lose and type II flow that was very enjoyable to hear from the couch.
some slow songs in the first set all in a row, albeit one's I like...and a not particularly inspired (again imo) version of farmhouse. or 555. MFMF was played pretty well. Enjoyed it. Maze was incredibly sloppy. 'Strong to very strong'? I disagree. Gin, while jammed and played without a net, was not enough to save some of the other parts; for me.
Second set is decent. Buoyed by strong song selection, but not necessarily by performances. Glad you enjoyed it. It's all subjective. But those things, imo, are what you are missing. Onward to Chicago!
I'm surprised by the low rating. I thought this show held its own at this stage in the tour. I loved the space theme in the 1st set! The Gin set closer was on fire. Never a dull moment in the 2nd set. I was in it to win it when they landed on that funky Boogie out of NML. Super funky stuff. Even the Antelope encore was on fire. You could tell Trey was feeling IT.
Soul Planet > 2001 was unexpected but surprisingly as fun. Gin was very solid. But this was probably the least interesting first set of fall so far given the magic that has been happening. Set two delivered ! Great and inspired jamming. solid 4 star show at least. Give the gin and second set a listen. Soul planet got a little phunky too.
I tuned in for the webcast.
Soul Planet & 2001 was a fun and funky way to kick off the show, although I do not like the former song, the jam was solid enough and the 2001 kept things moving. 555, Farmhouse, Halfway to the Moon & Waste were all objectively pretty poor renditions (although the Halfway jam at least kept me engaged). The error on the first notes of the Waste solo was particularly egregious. MFMF was a good set list call, but I didn't find this version too solid. Trey seemed to be really having an off night, and the slop fest of a Maze that followed was another confirmation. That said, hard not to fist pump to that tune.
Bathtub Gin offered the set some saving grace, and was frankly a very interesting version, with multiple movements and false returns to the theme. Very organic jam that covered tons of ground without ever leaning on the Bliss crutch for too long. Only thing missing was a massive peak, but I will take this type of jam all day. Great stuff. Overall pretty weak set, but the Gin is definitely worth a listen.
Set II had some killer song selection and on paper looks like a real winner. In execution I found it fun, but not overly compelling. Disease is a reliable workhorse and this version is plenty enjoyable, but not overly noteworthy in comparison to many other second set opening outings. The move into Crosseyed was good though, and that tune is also a reliable bit of fun. This one had some interesting moments. Nothing too long and they chopped into Scents, with Trey struggling with the opening to my ears (again an off night for him it seemed). Scents had lots of teases and a full on Party Time jam, which must have been a hoot live in venue, but this type of show is not always the best from the couch. Boogie On is always welcome and I enjoy the late second set placement they seem to be slotting it in lately (7/23/17 and 7/24/18) and just like night one of BGCA in the summer they go for a Hood to follow, which is nice.
Antelope encore is of course fun, if not too well played. Overall this wasn't a "bad" show per se, and I am thinking live would have been a lot of fun, however, in my opinion this show was pretty weak with Trey struggling quite a bit and nothing too notable outside the Gin. Just one man's opinion from his couch though!
Nashville night two went "screaming through space" after a Soul Planet opener with Also Sprach immediately following without pause to deliberate on song two. Right from the get-go of Also Sprach Trey vocally teased Soul Planet. Indeed, as noted before, we are screaming through space! Next up we sprint on cobblestones past the track from 2001 into 555. Ascend was definately hyped after the first three tunes. Taking a lesson from Nashville night one the band decided to "cool it down" with Farmhouse. I never ever saw the northern lights but I did see CK5 dialed in and play the southern lights. A neat visual with the lights is the swirling effect in the smoke, fog or haze if you will. I hope you saw the swirling fog, I noticed night one and watched for it intently night two. With a full moon above we are forced to keep the pattern until June, all aboard for the tour, Page leads us Halfway to the Moon. The full moon and red lit Korean Veterans Boulevard bridge over the Cumberland River was a sight to behold for those who dared to look away from the stage. Just like life, everything comes in waves after the second lift off that we received during Halfway to the Moon it was time catch our breath and let the band back inside our head with Waste. What's that you say, you want a smoking finish to an already stellar set one? The great Music City was then treated to My Friend, My Friend with MYFE ending followed by a Maze that I'm happy to never get out of and an 18:45 Bathtub Gin. You can hear those crunchy keys right now can't you. Set one complete, "Mark it Dude".
Over some pre show drinks at Acme Feed and Seed, it was discussed what songs were being chased. What songs were likely candidates for the show considering what has been played recently, especially bus-outs. Would we have another guest sit in? History did repeat itself. Not with another sit-in for the Nosh Vegas shows but with a Down with Disease set two opener. Yes this was discussed during the pre show conversation. The word predictable was uttered pertaining to DWD. It should be noted that during the recent 2018 Dicks run that DWD was placed set one song two. The demons did not stop the fine folks in Nashville from dancing in their heads or on tera firma. I lost my shape, trying to act casual, it was many years ago now but I really can't be sure. Thanks to Phish for reminding me of this during Crosseyed and Painless. Scents and Subtle Sounds kicked off sans formal intro and at the 5:20 mark a CCR tease of a Run through the Jungle variety can be heard via guitar riff and is verbally confirmed at 5:54. At the the 6:59 mark Crosseyed is teased but we are all really still waiting for the Party Time tease at 8:10 into S&SS. There is a slow stream of power coming from the NMINML as set two groves on. The only proper way to continue this dance party is to next Boogie on Reggae Woman. Set two closes with Harry Hood, and you can most certainly feel good about it. What an amazing night. Pardon me, do you have any Encore, man? Run Like an Antelope was an amazingly high energy cap to a beautiful two day stand down by the river in Nashville, TN.
Howdy from the couch ya'll!
I agree with most above that this effort was average-good, with Trey really appearing to struggle in spurts (555, Maze, Scents, Boogie) but having a fantastic time on stage with some nice dance moves and recognition of the efforts of his teammates. I thought it was particularly inspiring to see him lay back in Boogie On and literally boogie on to the groove laid down by the other three. Being a gear head it looks to me that Trey is still getting familiar with his newish rig, particularly his new monster CAE switcher. On the webcast you could watch him drop out entirely and fiddle about with some stomp switches until he landed on the particular combination he wanted. Not that that is anything new but certainly more pronounced since the introduction of the super switcher for Fall TAB in 2017 (it's a 24 switch monster and can be seen in detail on treysguitarrig.com). His default position in a jam last night was lots and lots of echo and pitch bending (and maybe some reverse echo in the second set....), which led the whole band into deep space on multiple occasions.
Page ran away with our family's MVP voting. Every time I watch a webcast I am awed and inspired to see his ability to create phrases on the fly and the deftness with which he can subtly shift the song dynamic and direction by switching instruments. Oh yeah, and he ripped HTTM and Gin. It seems so much easier to isolate his sound within the mix when you can see his hands (as opposed to Mike- whose pick hand is moving even when he's not hitting a note).
Overall Fall 2018 has been a positive affair with some sustained chunks of real gutsy improvisation. I counted at least 4 distinct changes in last night's Gin that the entire band latched on to. And while none of them took off for the stratosphere as we might have hoped it is clear that the communication lines are open and the band appears happy, healthy and limber.
Stay safe on tour and be kind to each other. We love you music nerds.
The band had it all working tonight just never quite put it all together at the same exact time. Like 2/3ds here for a bit 1/2 here for a little , like I said consistent. Kept my attention all night . Fun run.
As someone who was actually at the show, and didn't webcast I think this show deserves a 4.3. The first set had an interesting flow. It got off to a really hot start, and then simmered down during Farmhouse but picked up with My Friend, My Friend. So overall, great song selection. I thought Maze after MFMF was a great call, and this Gin will probably go underrated for a while. A lot of people are saying they just jumped around a lot and never really found a groove, but I absolutely loved this one. Please listen to this Gin!
Set break: Not much to report here, grabbed another beer hit up the bathroom. I would like to point out that everyone I sat next to the two nights were just super awesome. Nothing like making new friends at Phish shows.
Set Two: Knew it would be Down with Disease. Wish this one was played a little longer, but onto Crosseyed we go. Crosseyed had some potential but Trey had other plans. Scents was a welcomed surprise for me. I liked all the teases in Scents. I was hoping the Fishman was gonna say "sucking on a lemon" to give a BD nodd. But no dice. I'll close with Hood, a strong Hood and a VERY strong Antelope.
This band is coming in hot to Chicago, and I expect Vegas to be off the charts as well.
In a world in which everything is so intense - be it sports, politics, physical health, etc. - it's nice to see four guys who have been playing together for 35 years still enjoy themselves. May we relax, have some fun, and cherish this band that will one day be no more.
I certainly could feel good about that Hood! Electric stuff there.
Before the Set 2 "Waiting" theme jumped off, Trey threw in a "Tired of Waiting for You" by the Kinks tease into his "Gin" solo. I heard it whilst couch streaming the show and upon further listening today, I confirm this tease. Surprised nobody else caught or failed to mention this. You heard it hear first. Pun intended. Happy New Year, Phish Heads!


text:
Suzanne Lippens (Gent, 25 mei 1903 – Knokke-Heist, 20 januari 1985) was piloot en de eerste vrouw in België die het vliegbrevet van amateur-piloot heeft gehaald op 27 juni 1928.

Biografie
Lippens was dochter van Maurice August Lippens, was in 1936 gehuwd met haar achterneef Leon Lippens, moeder van Leopold Lippens en Maurice Lippens. Reeds op jonge leeftijd ontpopte zij zich tot een sportieve vrouw die een avontuurlijke uitdaging niet uit de weg ging. Suzanne Lippens was de eerste vrouw in België die het vliegbrevet van amateur-piloot heeft gehaald op 27 juni 1928. In 1930 haalde ze een brevet zweefvliegen bij de Duitser Wolf Hirth. Lippens kwam voor de Tweede Wereldoorlog nog herhaaldelijk in de pers met bijzondere luchtvaartprestaties.

Na de oorlog werd haar echtgenoot burgemeester van Knokke. Lippens zette zich in voor diverse goede werken (dierenwelzijn, kinderbescherming, gehandicapten). Zij woonde te Knokke en overleed er op 82-jarige leeftijd.

Huis Lippens
Belgisch vliegenier

redpajama_set_name: RedPajamaWikipedia


text:
About Historic City News
Planned road closure report this week from Northeast FDOT
Historic City News
Florida Department of Transportation Community Outreach Specialist Allen Nelson has updated Historic City News with the weekly lane closure report containing information regarding ongoing construction projects and traffic impacts for the coming week. Our readers and subscribers will be updated every Friday by 5:00 p.m., with some unavoidable exceptions and state holidays.
Department of Law Enforcement reviews accomplishments during 2022
As we approach the end of the year, several State agencies reported highlights from some of their member's most significant accomplishments in 2022. Among them was the Florida Department of Law Enforcement. Many of the accomplishments of the Department are reflected in the regular reports published by Historic City News.
Combating local sand dune erosion by planting 19,000 sea oats
Florida Department of Transportation District 2 spokesperson Hampton Ray reported to Historic City News that over 40 staffers from across the District are supporting beach renourishment efforts along State Road A1A in Marineland by planting over 19,000 sea oats.
Fugitive from Ohio nabbed driving a stolen car
Historic City News was informed that the local Sheriff's Office had been notified around 7:20 p.m. on the evening of December 15, 2022, that the owner of a stolen vehicle was tracking its location in St Johns County. Deputies began an investigation and search for the stolen vehicle, resulting in its discovery at a gas station at International Golf Parkway and I-95.
Health officials issue mosquito-borne illnesses advisory
Noreen Nickola-Williams, Director of the Office of Public Health Practice and Policy for the Florida Department of Health in St Johns County, reported to Historic City News Friday that in partnership with the Anastasia Mosquito Control District an increase in mosquito-borne disease activity has been detected within the southeast quadrant of St Johns County.
Department of Health in St Johns County reopens for mission-essential services
Florida Department of Health spokesperson Noreen Nickola-Williams reported to Historic City News that the local Department of Health office in St Johns County will re-open for mission-essential services on Monday, October 3, 2022.
Public Notice of Pollution – City of St Augustine
Pursuant to Section 403.077, F.S., the Florida Department of Environmental Protection informed local Historic City News reporters that they have received the following Public Notice of Pollution for a reportable release that occurred within the City of St Augustine within St Johns County.
Southeastern St Johns county under flash flood warning
The National Weather Service in Jacksonville has issued a flash flood warning to Historic City News for southeastern St Johns County until 3:15 p.m. EDT today.


Okay, so I know that Copacabana is the beach most people associate with Rio de Janeiro; however, if I only had one day to spend at a beach in Rio, I would choose to go to Ipanema beach over Copacabana for the day – and I would recommend that you do the same.
Don't get me wrong, Copacabana is amazing. To read all my thoughts on this beautiful part of Rio, check out my guide here.
But Ipanema is my favourite out of the two.
There are two main reasons I love Ipanema so much.
The first, is the geography and the setting of the beach. The geography of Rio de Janeiro is, I think one of the citys greatest marvels. It is truly stunning and for me, Ipanema beach epitomizes this uniqueness.
You have the gorgeous deep green of the mountain towering over one end of the beach. As you walk closer you can see specks of colour begin to pop up and stand out against the dense green, as the favela which climbs up the mountainside begins to come into view. On a slightly overcast day, the peak of the mountain and the range of mountains behind it fade into clouds above.
A second mountain range defines the rest of the beach, as concrete towers of hotels and apartments line the beachfront all the way down to Copacabana Fort in the distance.
These two contrasting backdrops create the unique context in which Ipanema beach sits. It's the juxtaposition of wild nature and concrete city life, of rich and poor that defines Ipanema; and epitomizes the city of Rio de Janeiro itself.
The second reason I love Ipanema is the general vibe that both the beach and the neighborhood have.
The beach is colourful, vibrant and filled with people from all walks of life.
Now, I will say that my viewpoint may be slightly skewed, as unbeknown to us we accidentally set up camp for the day in between the two rainbow flags which define a particularly colourful area of the beach.
Having said this, when we returned and spent a second day in a different area of the beach, I can confidently say that it was just as colourful, interesting and filled with the same great vibe as the first day.
Just like Copacabana, there are people walking up and down the beach trying to sell you everything from food and drink to bikinis and jewelry. You can also chose to pay to rent a couple beach chairs and an umbrella for the day if you like. When we were there during the off-season we paid around 15reis for two chairs and an umbrella for the day.
My one caution would be if you are a traveling family, that the beach is quite steep and is known to have quite a strong current at times. If you get the right tide then the slope of the beach flattens out in places and there can be some kid friendly areas for little ones to still play and have fun in the water.
The vibe that I love so much about the beach also transfers into the neighborhood of Ipanema itself.
Ipanema takes the slightly slower pace of Copacabana to the next level and the whole neighborhood has a relaxing, holiday beach vibe to it. The streets leading away from the beach are lined with trees and nicer apartment buildings and once you get a few blocks back you will find a wide variety of restaraunts, cafe's, bars and shops.
The metro station is a 10 minute walk from the beach max. and there is a street market in the square outside. You want to get off at General Osorio station and make your way to the beach from there.
The market is on the expensive side of things, however it's a great place to spend a bit of time walking through and looking at all the artwork and many hand crafted items.
Ipanema and Copacabana are both great parts of Rio. If you can visit both, I highly recommend you do. Although they are located right next to each other, both neighborhoods and beaches have something different to offer.
Copacabana is famous for a reason; but in my opinion, if you want the best "beach day" in Rio, then Ipanema is the way to go.


text:
Q: Property Editor not registered with the PropertyEditorManager error on Custom Validation Tag (java) I am using TomCat 5.5 with MyFaces 1.1 and am trying to implement a custom regex validation tag.
My RegExValidator class looks like this:
public class RegExValidator implements Validator, StateHolder {
  private String regex;
  private boolean transientValue = false;

  public RegExValidator() {
    super();
  }

  public RegExValidator(String regex) {
    this();
    this.regex = regex;
  }

  public void validate(FacesContext context, UIComponent component, Object toValidate) throws ValidatorException {

    if ((context == null) || (component == null)) {
throw new NullPointerException();
    }
    if (!(component instanceof UIInput)) {
        return;
    }
    if (null == regex || null == toValidate) {
        return;
    }

    String val = (String) toValidate;

    if (!val.matches(regex)) {
        FacesMessage errMsg = MessageFactory.createFacesMessage(context, Constants.FORMAT_INVALID_MESSAGE_ID, FacesMessage.SEVERITY_ERROR, (new Object[]{regex}));
        throw new ValidatorException(errMsg);
    }
}

public Object saveState(FacesContext context) {
    Object[] values = new Object[1];
    values[0] = regex;

    return (values);
}

public void restoreState(FacesContext context, Object state) {
    Object[] values = (Object[]) state;
    regex = (String) values[0];
}

public String getRegex() {
    return regex;
}

public void setRegex(String regex) {
    this.regex = regex;
}

public boolean isTransient() {
    return transientValue;
}

public void setTransient(boolean transientValue) {
    this.transientValue = transientValue;
}
}

My RegExValidatorTag class looks like this:
@SuppressWarnings("serial")
public class RegExValidatorTag extends ValidatorELTag {

private static String validatorID = null;
protected ValueExpression regex = null;

public RegExValidatorTag() {
    super();

    if (validatorID == null) {
        validatorID = "RegExValidator";
    }
}

public Validator createValidator() throws JspException {

    FacesContext facesContext = FacesContext.getCurrentInstance();
    RegExValidator result = null;

    if (validatorID != null) {
        result = (RegExValidator) facesContext.getApplication().createValidator(validatorID);
    }

    String patterns = null;

    if (regex != null) {
        if (!regex.isLiteralText()) {
            patterns = (String) regex.getValue(facesContext.getELContext());
        } else {
            patterns = regex.getExpressionString();
        }
    }

    result.setRegex(patterns);

    return result;
}

public void setValidatorID(String validatorID) {
    RegExValidatorTag.validatorID = validatorID;
}

/**
 * @param regex
 *            the regex to set
 */
public void setRegex(ValueExpression regex) {
    this.regex = regex;
}
}

My Taglibrary Descriptor looks like this:
<tag>
    <name>regexValidator</name>
    <tag-class>com.company.components.taglib.RegExValidatorTag</tag-class>

    <attribute>
        <name>regex</name>
        <required>true</required>
        <rtexprvalue>false</rtexprvalue>
    </attribute>
</tag>

My face-common-config.xml has a Validator tag like this:
<validator>
    <description>
        Validate an input string value against a regular
        expression specified by the "regex" attribute.
    </description>
    <validator-id>RegExValidator</validator-id>
    <validator-class>com.company.components.validators.RegExValidator</validator-class>
    <attribute>
        <description>
            The regular expression to test the value against
        </description>
        <attribute-name>regex</attribute-name>
        <attribute-class>java.lang.String</attribute-class>
    </attribute>
</validator>

And later on it is supposed to be used in a jsp file like this:
<tc:in value="${dataBean.currentBean.field}">
  <a:regexValidator regex="${dataBean.currentBean.validationRegEx}" />
</tc:in>

When calling the page, the following error comes up:

javax.servlet.ServletException: javax.servlet.jsp.JspException: org.apache.jasper.JasperException: Unable to convert string "[\d{4}]" to class "javax.el.ValueExpression" for attribute "regex": Property Editor not registered with the PropertyEditorManager
Caused by:
org.apache.jasper.JasperException - Unable to convert string "[\d{4}]" to class "javax.el.ValueExpression" for attribute "regex": Property Editor not registered with the PropertyEditorManager

I hope I provided enough details for someone to help me out on this...

A: I seem to have a similar problem like yours, I'm trying to find the solution but seems that the problem is when using Tomcat or the application server(WebSphere Application Server 7.0) JSF libraries, my problem is that the new application server has new JSF libraries (1.2) instead of the 1.1 libraries that my old application server had. (Version 6.1)
To be more specific. my problem is described here. http://www-01.ibm.com/support/docview.wss?uid=swg21318801

redpajama_set_name: RedPajamaStackExchange