text:
West Indies captain says world champs will showcase style for home fans
NORTH SOUND, Antigua — Darren Sammy has promised his West Indies team will play like true world champions and entertain their home fans when they face Zimbabwe in the two-match T20 International Series this weekend. The world T20-winning captain was upbeat as he talked about his side's chances of beating the visitors, in what promises to be an action-packed doubleheader at the Vivian Richards Cricket Ground.
First ball on both days is 2 pm (1 pm Jamaica Time).
"We are world champions and every time we go out to play we have to play like world champions. We have to let other teams know we mean business. This is a format we have done well in and we will look to always dominate," Sammy said.
"We come here to play our brand of cricket – the brand which won us the World Cup for the people of the Caribbean. This is the first T20 International in the Caribbean since we won the World Cup and this is a great opportunity for the fans to come out and watch their world champions play. We anticipate a good turn-out and we will look to win for our loyal supporters."
The captain was speaking on Friday as he and team-mates completed their preparations for the two matches.
The West Indies have been on a good run in this format. After winning the ICC World T20 trophy last October they beat Bangladesh at the Sher-e-Bangla in Dhaka in December in and also whipped Australia at the Gabba in Brisbane last month.
They dominated the recent three-match One-Day Series against Zimbabwe at the Grenada National Stadium – by 156 runs in the first match; by seven wickets in the second match and by five wickets in the third match.
Sammy noted: "I know we have not taken Zimbabwe lightly. We will come out and play good, competitive cricket. Looking back at the One-Dayers, three disciplines fired. We have a good combination and we will look to improve our performances."
West Indies selectors have called up fast bowler Shannon Gabriel for the first time in T20 cricket and recalled allrounder Christopher Barwnell. Both were outstanding performers in last month's Caribbean T20. The strongly-built Gabriel bowled with pace to win the Player-of-the-Match award in the Grand Final. Barnwell, a powerful batting allrounder, played a superb match-winning knock against Jamaica in the Play-off. Sammy welcomed the inclusion of both and said he is quite impressed with their preparations for the series.
"They have been rewarded for a very good Caribbean T20 tournament. They both played really well for their teams and took them to the finals. They have both played at the international level before so this won't be altogether new for them. We will try to give everybody an opportunity. I expect to see them both play, if not in both games, at least in one game," Sammy said.
"We will look to provide opportunities and exposure to guys who have done well as we continue to look toward the T20 World Cup in 2014. We will look to win that tournament and defend our title. The T20 World Cup in 2012 was a perfect example of the players the selectors tried in the build-up and we saw how well that turned out for us."
Trinidad prime minister under pressure to dismiss Jack Warner
Minor charged by Grenada police after school principal attack


text:
Q: router.navigate not working and allows statements below it to execute I am calling 2 methods in the ngOnInit: one method checks for path parameters and the other one looks for query parameters in the url.
Here's the ngOnInit method:
ngOnInit() {
  this.getFlavorAndService();
  this.getQueryParams();
}

Here's the method that looks for path params:
getFlavorAndService(): void {
    this.routePathParamsSubscription = this._route.params.subscribe(params => {
      const flavor: string = params.flavor;
      const service: string = params.service;

      if (flavor) {
        if (this._dataService.flavors.includes(flavor)) {
          this.flavor = flavor;
        } else {
          this._router.navigate(['/page-not-found']);
        }
      } else {
        this._router.navigate(['', this._dataService.DEFAULT_FLAVOR, this._dataService.DEFAULT_SERVICE]);
      }

      if (service) {
        if (this._dataService.isEdsService(service)) {
          this.service = service;
        } else {
          this._router.navigate(['/page-not-found']);
        }
      } else {
        this._router.navigate(['', this._dataService.DEFAULT_FLAVOR, this._dataService.DEFAULT_SERVICE]);
      }
    });
  }

Here's the method that looks for query params:
getQueryParams(): void {
  this.routeQueryParamsSubscription = this._route.queryParams.subscribe(queryParams => {
    ..... some code

    if (isEmpty(queryParams)) {
      this._router.navigate(['', this._dataService.flavor, this.service]);
    } else {
      this._router.navigate(['', this._dataService.flavor, this.service], { queryParams: queryParams, queryParamsHandling: 'merge' });
    }
  });
}

My question is that, if an invalid flavor is passed I should be redirected to /page-not-found url and the remaining statements should not executed at all. Instead, when I pass invalid flavor or service, the webapp doesn't navigate to page-not-found url, and the remaining statements of the method get executed (from getQueryParams methods). It doesn't redirect,even if I use return this._router.navigate(['/page-not-found']);.
Should the app not get navigated to page-not-found and stop?

A: just to make sure constructor function should be as
import { ActivatedRoute, Router } from "@angular/router";
 constructor(private route: ActivatedRoute, private router: Router) {}

and use return this._router.navigate(['/page-not-found'])

redpajama_set_name: RedPajamaStackExchange


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A football team isn't just a group of men in the same uniform. A football team is a true passion for the game. This passion will push you to be better daily, and this article will teach you how to become a much better player.
Always wear your safety equipment when you play football. The risk of a severe injury is far too high. Possible injuries range from fractured bones as well as paralysis. These things that may prevent you from ever playing again.
Safety is an important issue in the game of football. Whether you are training at the gym, working out at the gym, or playing, keep yourself safe at all times. Wear proper protection while playing.
Understanding the offense's formation is key to being a good defensive player. You can have a good idea of the play by watching where the receiver is. Watch pro games and come up with a playbook of their plays.
You should be physically fit in good physical shape. Follow that with weight lifting and then cool down.
Watching how the professionals play football can teach you a fun way to improve your game. Watch them closely to learn new moves and try out to play.
To become a great player, you'll have to eat right and pay attention to the signals you body gives you. Any pain or limitations of physical ability should be reported to the team doctor.
The only thing that you really cannot alter about yourself is your height. You can always become faster, build strength, faster and more skillful with practice. If you choose to focus on working out, practice and work out, then you have the power to change almost anything about yourself.
You need to know all defensive positions of a football team. There are 8 members of them.The positions are nose tackle, two safety players, the corner back, nose tackle, defensive end and nose tackle. The safety positions are the strong safety and free safety.
Don't forget to mentally train your mind. Sit down and visualize yourself playing in the game. Studies show that meditation and visualization of success leads to success.
Enjoy time off with your friends and family in order to maintain a well-balance life.
Work out often as possible. Weight lifting is crucial to football position. Your strength conditioning can assist you in thriving on the game safely. Work out your whole body. Don't concentrate on your torso alone. You need strength in your legs to effectively push off when you are at the scrimmage line.
Your mind is telling you play the game. Psychology can make a crucial role in the game of football. Mental preparedness and toughness leads you to success and maximum performance when you play football.
Do not let yourself become too comfortable in the position that you currently play. Learn about different positions and commit yourself to helping your team during each game. This is a great way to improve the strength of your team and improves your chances for winning.
Always keep your chin up when you are tackling. You never want to make contact with your helmet top. It is illegal and it can cause severe injury.
You could help your team be victorious by remaining positive even when things seem dire. You never know when that positive attitude.
Always remember to do your stretching techniques.While it can feel a little boring, stretching warms your muscle and prepares you for the game ahead. A single hamstring can prevent you from being your game. Stretch often to avoid an injury later.
Scout out the other team before the game. Scouting your opponent will reveal a lot about how they play. You can understand their offensive and defensive strategies. This enables your own team for the game ahead.
Learn stress-busting techniques to help you relieve stress on game day. If you're too stressed, you may not perform as well. You can't really get yourself focused on the game if you don't take time for a proper warm up because you are distracted. Learn visualization methods and deep breathing techniques to assist you.
Your teammates can help you shine or pull you down. Teammates should encourage and challenge each other to become better players. Use what you learned and play a great game!


Bitcoin Prices Tumble After ETF Delay – Market Overreaction?
Biohacking Joins AI, Blockchain Among Technologies to Bring Competitive Edge – CIO Journal.
This week not only Lee, but also investment mogul Tim Draper has reconfirmedhis belief in Bitcoin's bigger and better future, telling the audience at his own Blockchain event Thursday that $250,000 was his BTC price target by 2022.
Previous Will Bitcoin Reach $25000 This Year?


text:
U.S. Rep. Sheila Jackson Lee Reintroduces Bill to Make Juneteenth Federal Holiday
TheHub.news Staff
Representative Sheila Jackson Lee, along with U.S. Senators John Cornyn, Ed Markey and John Cornyn, filed bipartisan bills last week to make Juneteenth a federal holiday.
"Juneteenth honors the end of the years of suffering that African Americans endured under slavery and celebrates the legacy of perseverance that has become the hallmark of the African American experience in the struggle for equality," Rep. Jackson Lee said in a statement.
Masks save lives. pic.twitter.com/AZVg42abT0
— Sheila Jackson Lee (@JacksonLeeTX18) October 6, 2020
On June 19, 1865, Union Army Maj. Gen. Gordon Granger rode into Galveston, Texas, to inform the slaves of their emancipation — more than two years after President Abraham Lincoln issued the Emancipation Proclamation on January 1, 1863.
Over recent years, commercial companies have recognized Juneteenth as a holiday, but activists are still rallying for formal recognition from the federal government.
But this fight is not unique.
It took 32 years to make Martin Luther King Jr.'s birthday a national holiday. King's birthday was approved as a federal holiday in 1983, but it was not until 2000 that all 50 states made it a state government holiday.
I am at @houstontranstar listening to @POTUS before addressing the freeze and water crises and COVID-19 in Congress. President Biden is here to listen to our needs and what we have done. pic.twitter.com/P1qycbGFiU
— Sheila Jackson Lee (@JacksonLeeTX18) February 26, 2021
Still, Rep. Jackson Lee is optimistic this battle will be won.
"Juneteenth celebrates African American freedom while encouraging self-development and respect for all cultures. But it must always remain a reminder to us all that liberty and freedom are the precious birthright of all Americans which must be jealously guarded and preserved for future generations. As it takes on a more national and even global perspective, the events of 1865 in Texas are not forgotten, for all our roots tie back to this fertile soil from which a national day of pride is growing. This is why we must establish the Juneteenth Independence Day, as a national holiday."
Juneteenth,Sheila Jackson Lee
Post written by: TheHub.news Staff
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redpajama_set_name: RedPajamaCommonCrawl


Though no longer available, Oblique Strategies was also released as an iPhone app.
I sometimes use the deck thinking about a specific creative problem. While looking at random cards using the app I realized the one flaw the deck has, these strategies only encourage further thinking concerning whatever you are working on. Though random and thought-provocking these questions and phrases are by definition about whatever brings you to the cards.
I started thinking that what I wanted and needed was a deck of cards, inspired by Oblique Strategies, that would instead take me away from what I was focusing on and introduce a new subject. A kind of controlled distraction. I wanted a question or a subject on something I didn't know, that I could research as quickly or deeply as I wanted in order to cleanse my thinking palette. That's how The Autodidact Deck was born. I developed a pack of 100 cards to be released here over time.
You can use the cards as they are posted to go on a self-learning adventure.


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Executives wishing to do business in Escazu and Santa Ana, Costa Rica will immediately observe a user-friendly venue from which to operate any business successfully. When searching for Costa Rican real estate or purchasing homes or condos in Escazu and Santa Ana , you must be sure to have a skilled professional working in your best interests; a real estate expert who has the comprehensive answers to your questions. I look forward to helping you purchase your Costa Rican real estate with us at Luxury Homes Costa Rica.


text:
\section{Introduction}

When publishing the design of his machine in 1784, little could Atwood have known that,  more than two centuries later,  students would be asked to predict the outcome of his experiment. The problem, traditionally offered  as an illustration of the principles of Newtonian mechanics, consists in deriving the acceleration $\ve a$ of two masses $M>m$ subject to the action of gravity $\ve g$ while attached to a massless and inextensible chain passing over a frictionless pulley. The well-known result is that
\begin{equation}
\ve a =  \frac{M-m}{M+m} \ve g\,
\label{eqn:AtwoodAccel}
\end{equation}
for the heavier of the two, with the second having the opposite acceleration. Little attention has been paid to the seemingly trivial case in which both $m=0$ and the chain has a finite linear density. If the mass of the chain nevertheless remains small compared to $M$, then equation \eqref{eqn:AtwoodAccel} immediately  gives that the remaining mass falls with acceleration $a=g$. However, a simple experiment (see, for example, figure \ref{fig:setup}b) reveals that this  apparent simplification actually has a dramatic effect on the resulting motion: the chain `lifts off' from the pulley in a complex motion.  This lift-off has some surprising features that we explore in detail in this paper. In particular, we show that the free end accelerates \emph{faster} than the end that is being pulled by the mass: in this sense, the free end `beats' the free fall of the mass. We also show that the chain eventually `snaps' in a manner that is reminiscent of the crack of a whip\cite{goriely2002shape,mcmillen2003whip}.

Thin  filamentary structures are as important in applications as they are ubiquitous in nature and industry; examples range from macromolecules such as DNA~\cite{Neukirch:2004cu} to the kilometric transoceanic cables laid on the ocean bed from telecommunication vessels~\cite{carter2009submarine}. On a human scale, textiles, hair and ropes are other examples of thin elongated structures in which one dimension greatly exceeds the two others (so that the objects may be modeled as one-dimensional). The thinness of such rod-like structures also makes them flexible so that they are frequently subject to large deformations in the three dimensional environment in which they evolve. This flexibility in shape in turn leads to rich bifurcation landscapes~\cite{brun2014introduction}, striking pattern formation~\cite{habibi2007coiling}, and intricate dynamical behavior.

Despite the range of length scales and materials encountered, many filamentary structures are well modeled by the Kirchhoff equations for elastic rods~\cite{audoly2010elasticity}. A particularly interesting limit of these equations is the case of inextensible strings in which inextensible rods have  negligible resistance to bending and twisting:  their  behaviour is dictated to a large extent by the geometric constraint of inextensibility. In fact, this constraint by itself is enough to give rise to complicated dynamics: while the simplest case of a straight string accelerating along its length may be understood by a simple application of Newton's second law, any closed shape is a solution of the governing equations with any constant tangential velocity \cite{Healey1990}. It is therefore the combination of acceleration and `turning a corner' that gives rise to the most interesting dynamics. In particular, moving inextensible strings  form surprisingly complicated shapes including arches~\cite{hanna2012slack} and the mesmerising `chain fountain'~\cite{biggins2014understanding,biggins2014epl}.

In this paper we consider the planar motion of a chain moving around a pulley subject to a constant acceleration at one end and free at the other end. We model the chain as an inextensible string in partial contact with a disk (the pulley) and investigate key features of the motion. This setup is perhaps the simplest geometry in which one can study how a string or chain `turns a corner' since the curvature of this corner is simply that of the pulley. We first describe in some detail the different phenomena that are observed experimentally and then analyze  the lift-off in detail by combining theoretical arguments with  numerical simulations.  Finally, we describe the  snapping that is associated with the  reversal of curvature that ultimately occurs close to the free end.

\section{Statement of the problem and experimental observations}
\label{phenomenon}

In the idealized setup of our problem, a mass $M$ is attached to the end of a chain of linear density (mass per unit length) $\rho_\ell$ placed around a circular pulley of radius $R$. The mass $M$ is released at time $t=0$ and subject to a constant acceleration $a$.   The chain  is initially held on the pulley with a known length  of chain, $L$, hanging free from the first point of contact $C$ (see Fig~\ref{fig:setup}a). In a typical experiment the total length of the chain is $L_\text{end}=2 L+\pi R$.

The realization of this thought-experiment was  carried out by using conventional ball and link chains purchased from the local do-it-yourself shop and hung over horizontal Pyrex beakers (Fisher Scientific) that were used as the frictionless pulley (the surface of the beaker being  smooth, the chain slides over the surface with very little friction). The mass $M{\gg \rho_\ell L}$ is released at time $t=0$ resulting in an acceleration $a\approx g$. Although not restricted in any other way than by a frictionless contact with the pulley, the motion of the chain was observed to be planar, $i.e.$~the motion remains in the $xy-$plane normal to the axis of the pulley and containing the chain at $t=0$.
In the subsequent modelling, we therefore assume that the motion remains planar throughout.

\begin{figure}
\centering
\includegraphics[width=\textwidth]{figure1.pdf}
\caption{ Experiments using ball chains. (a) Experimental setup: the free fall of a mass $M$ forces a
chain with initial hanging length $L=54\mathrm{~cm}$ to slide around a
glass cylinder of radius $R=4\mathrm{~cm}$.  The initial
length $L$ of the hanging part denotes the section of chain from the
free end $s=0$ to the first contact point with the cylinder $C$ before
the mass is dropped (which occurs at $t=0$).  The vectors $(\ve t, \ve
n)$ denote the tangent and the normal of the chain, respectively.  (b)~Time sequence ($\Delta t=2.5\mathrm{~ms}$) of the chain dynamics
successively lifting up from pulley (from $t=t_{\mathrm{LO}}$ onwards) showing
that a ballooning arch develops before the chain eventually `snaps' at
a time $t=t^*$ (reverses its curvature dramatically).  }
\label{fig:setup}
\end{figure}
Typically, the time evolution of the chain passes through three, qualitatively different, phases shown in figure  \ref{fig:setup}b:
\begin{itemize}
\item For $0\le t<t_{\mathrm{LO}}$ the chain follows the dynamics that might
naively be expected: it moves around the pulley at the speed that is
imposed by the accelerating mass.

\item At a time $t=t_{\mathrm{LO}}$ the chain starts to partially lose contact
with the pulley, lifting off so that for $t>t_{\mathrm{LO}}$ the hanging part
of the chain goes faster than the rest of the chain.  Due to the
excess length of the chain, an arch forms between points $C$ and
$C^*(t)$ defining an angle $\theta^*(t)$ (see figure
\ref{fig:setup}b).

\item After the free end goes past the last contact point $C$ (first
image of the last row in figure \ref{fig:setup}b) the arch flares up,
its curvature increasing rapidly until the free end eventually snaps
at time $t=t^{*}$ (the curvature there changes sign).

\end{itemize}

To complement our experiments, numerical simulations were carried out
using the Discrete Elastic Rod method, which provides a discretization
of the equations of motion for thin elastic rods using a Lagrangian
formulation~\cite{bergou2008discrete}.  This method, and its
counterpart for thin viscous threads, have been used and validated
previously~\cite{Jawed:2014gs,Audoly:2013cb}.  In the simulations, we
use a string model, i.e.~the bending and twisting stiffnesses are both
set to zero so that the Kirchhoff equations~\cite{audoly2010elasticity} simplify to the conservation of linear momentum:
\begin{equation}
\label{eqn:KirchhoffR}
\frac{\partial (T \ve t) }{\partial s} + \rho_\ell \ve g+  P \ve n= \rho_\ell \frac{\partial \ve v }{\partial t},
\end{equation} and inextensibility
\begin{equation} \left | \frac{\partial \ve x (s,t)}{\partial s} \right |  =1,
\label{eqn:KirchhoffR2}
\end{equation} where $\ve x (s,t)$ is the centre-line of the chain as a function
of the arc length $s$ and time $t$, $\ve{t}(s,t) = \frac{\partial \ve
x (s,t)}{\partial s}$ and $\ve{n}(s,t)$ are the unit tangent and
normal vectors to the chain axis, respectively (see
Figure~\ref{fig:setup}a).  Further, the variables $T(s,t)$ and $\ve
v(s,t) = \frac{\partial \ve x (s,t)}{\partial t}$ denote the tension
and velocity of the chain, and $P(s,t)$ represents the (frictionless)
reaction from the pulley on the chain, such that $P=0$ whenever there
is no contact.  This frictionless contact with the pulley is
implemented numerically using a geometrical method, \emph{i.e.}\ by
alternating dynamic steps that ignore contact forces, with projection
steps in which the configuration is projected onto the manifold of
admissible configurations.

We close the differential problem (\ref{eqn:KirchhoffR})-(\ref{eqn:KirchhoffR2}) using the boundary
 conditions at the two ends of the chain. Namely, the free end of the string is stress free and  we prescribe the acceleration $a$ of the chain's end attached to the mass in our experiments, that is:

\begin{align}
&T(0,t)=0 \\
&\dot {\ve v }(L_\text{end},t)= -a\,  \ve e_y
\label{eq:bc}
\end{align}
 where $\ve{e}_y$ is in the vertical direction and $L_\text{end}=2L+\pi R$ is the arc-length corresponding to the point where the mass is attached.
\begin{figure}
\centering
\includegraphics[width=.97\textwidth]{figure2.pdf}
\caption{Numerical simulations: (a) Comparison between the chain shape observed
experimentally (images in the background) and the prediction of
numerical simulations (overlaid dashed curve).  Here there are no
adjustable parameters ($L=54\mathrm{~cm}$, $R=4\mathrm{~cm}$, time
between two frames $\Delta t=0.9\mathrm{~ms}$).  (b) At each instant
before snapping, the chain may be divided into four zones.  (c) Plot
of the curvature $\kappa$ (dashed curve) and the chain speed $v$
(solid curve) as functions of the arc length.  (d) A numerical
reconstruction of the tension $T$ within the chain shows that it
varies linearly with arc length in regions (I), (III) \& (IV).  Region
(II) bridges regions (I) and (III), each of which is characterized by
a different acceleration.  For comparison, the dashed line shows the
tension as a function of arc length in the idealized solution with
uniform and constant acceleration $a$ where lift-off is prevented
(this artificial solution would give rise to a negative contact
pressure).}
\label{fig:DVR}
\end{figure}
Figure~\ref{fig:DVR} shows a direct comparison between experiments and
numerical simulations without any adjustable parameter.  The favorable
agreement between the two validates the approximations made in
modelling the chain as a string that is driven at constant
acceleration (our experiments are in fact conducted with a constant
force $M \ve g$ but the two methods are approximately equivalent since
$ \rho_\ell L \ll M$).  Of particular interest is the possibility
offered by the simulations to access the successive space derivatives
of the basic physical variables (such as curvature) with controllable
time resolution covering long periods of time.  Additionally, physical
quantities that are otherwise challenging to measure experimentally,
such as the tension within the chain, are readily available from
simulations.

At any given time before the chain snaps ($0<t<t^*$), the chain may be
divided into four regions: (I) and (IV) denote the two straight,
vertical parts, respectively, (II) denotes the part of the chain not
in contact with the pulley and (III) the contact region.  For example,
in figure \ref{fig:DVR}b-d, only a small portion of the chain (III)
remains in contact with the pulley.  In this region the chain's speed
is prescribed by the free fall of the mass, as in region (IV).  In
region (I), the chain moves significantly faster than the imposed
acceleration, while remaining perfectly straight and tangential to the pulley.  In addition, the tension in the chain is larger than if the lift-off were artificially suppressed (shown as a dashed line
in figure \ref{fig:DVR}d).  The area (II) bridges the areas (I) and
(III)-(IV) and their corresponding physical quantities, resulting in a
ballooning shape (see figure \ref{fig:DVR}).

The length of the  chain that is initially hanging freely, $L$, turns out to play an important role in the problem and, therefore, we use $L$ as the length scale of the problem. It is then natural to use the quantity $(L/a)^{1/2}$ as the time scale of the problem. If the acceleration of the freely hanging part of the chain were to remain at $a$ throughout the motion, the length of the chain hanging beneath the point C then shrinks to zero at a time $t=\sqrt{2L/a}$.

From the 6 dimensional quantities of interest, we identify three
dimensionless parameters: \begin{equation} \pi_1= \rho_\ell L / M, \,\,\,\,
\pi_2 = R/L, \,\,\,\, \text{and} \,\,\,\, \pi_3 = g/a.
\label{eqn:DimlessPars}
\end{equation} In our experiments $M$ is chosen such that $\pi_1 \ll 1$; $\rho_\ell$
therefore enters in the problem as a multiplying factor for forces
only.  The value of $\pi_2 $ may easily be varied experimentally by
varying the radius of the pulley or, more simply, by varying the
length of chain that initially hangs freely.  By contrast, varying
$\pi_3$ is more difficult.  Our experiments are always performed with
$a=g$ and hence $\pi_3 = 1$.  However, the inclusion of a body force
acting on the chain complicates some of the analysis without changing
the qualitative behaviour, as shown in figure \ref{fig:DVR}.
Therefore, in much of the analysis we shall neglect the acceleration
due to gravity, i.e.~we assume $\pi_3=0$.  Experimentally, this case
could be obtained by placing the chain, pulley and the mass on a
smooth horizontal surface: at $t=0$, the mass is then pushed off the
table into the air~\cite{hanna2014jump} and allowed to fall under
gravity so that the acceleration of the chain is $a=g$ but the
effective gravity acting directly on the chain vanishes.  In the
simulations, the value of $\pi_3$ is set to 1 or 0 depending on whether
the results are to be compared with experiments or with our analysis.

\section{Prior to lift-off\label{sec:b4lift}}

We consider a pulley of radius $R$ around which a chain with linear density $\rho_\ell$ is hung.  We begin by including gravity as a body force, though later we will neglect it to simplify the ensuing calculations.
Initially, the length of chain between the free end (at
arc-length position $s=0$) and the chain's first point of contact with
the pulley is $L$ (i.e.~the point C in figure  \ref{fig:setup}  has arc-length coordinate $s=L$ at $t=0^-$).

At $t=0^+$, the end at arc length $s=L_\text{end}$ is pulled with
constant acceleration $a$.  Assuming that the chain remains in contact
with the pulley, $\ve v = v \ve t$, and
projecting \eqref{eqn:KirchhoffR} onto the tangential and normal
directions, and then using the Frenet formula $\partial\ve{t}/\partial
s=-\kappa\ve{n}$ with $\kappa$ the curvature, we find that
\begin{eqnarray}
\label{k1}
\frac{\partial T}{\partial s} - \rho_\ell g\cos\phi & = &  \rho_\ell \frac{\partial v}{\partial t} \\
\label{k2}
-{T\kappa}- \rho_\ell g\sin\phi+ P & = & -\rho_\ell {v^2\kappa} ,
\end{eqnarray} where $\phi$ is the angle between the local tangent to the chain and the upward pointing vertical and $\kappa=\partial\phi/\partial s$ is the curvature.  In particular, while the chain remains in contact with the pulley, $t<t_{\mathrm{LO}}$, we know that
\begin{align}
\phi(s,t) =\begin{cases} 0,& 0\leq s<\sc\\
 \frac{s-\sc}{R},& \sc\leq s<\sc+\pi R\\
 \pi,& \sc+\pi R\leq s
 \end{cases}
 \label{eq:phiBeforeLO}
\end{align} where
\begin{equation}
\sc(t)= L-at^2/2
\label{eqn:scDefn}
\end{equation} is the arc-length position of the first contact point between the pulley and the chain (the point labelled C in figure  \ref{fig:setup}). In the hanging part $\phi(s,t)=0$, and {so, integrating \eqref{k1} subject to $T(0,t)=0$, we find that} the tension $T$ may be written:
\begin{equation}
\label{eq:tension}
T(s,t) = \rho_\ell (a +g ) s  ,  \,\,\, s \in [0,\sc]
\end{equation}
In the region where the chain is in contact with the pulley, \eqref{k1} leads to
\begin{equation}
T(s,t) =  \rho_\ell a s +\rho_\ell g R \sin \phi + C_1, \,\, s\in[\sc,\sc +\pi R]
\end{equation} where the constant of integration $C_1=  \rho_\ell g \,\sc$ is found by requiring the tension to be continuous at $s=\sc$.

{In the freely hanging portion of the chain, $\eqref{k2}$ is identically satisfied by $P=0$. Elsewhere, \eqref{k2} can be viewed as an equation for the reaction of the pulley on the chain required for this motion to occur. From a simple rearrangement, we  find that}
\begin{equation}
P = -\rho_\ell \frac{v^2}{R} + 2  \rho_\ell g \sin\phi +  \frac{1}{R}\rho_\ell ( a s + g\sc), \quad s\in[\sc,\sc +\pi R].
\end{equation} Note that $P$ is a function of arc length $s$ and time $t$
through the angle $\phi$ and arc length of the contact point,
$\sc(t)$, in addition to the explicit dependence on $s$.  The minimum
value of $P$ at any particular time $t<t_{\mathrm{LO}}$ is attained at
$s=\sc$: \begin{equation} P_{\mathrm{min}}(t)= \rho_\ell\bigl[ \sc ( a+ g)- v^2
\bigr]/R=\rho_\ell\bigl[ ( a+ g)L- \tfrac{1}{2}at^2(3a+g) \bigr]/R.
\label{eqn:Pmin}
\end{equation}

The key to understanding why lift-off occurs is held by the expression
for the smallest reaction force $P_{\mathrm{min}}(t)$ \eqref{eqn:Pmin}.  At
sufficiently early times $P_{\mathrm{min}}>0$, and the contact pressure is
everywhere positive (it prevents the chain from penetrating the
pulley).  However, $P_{\mathrm{min}}$ vanishes at a time $t=t_{\mathrm{LO}}$
given by
\begin{equation}
\label{eq:tlo}
t_{\mathrm{LO}}=\sqrt{\frac{2L(a+g)}{a(3a+g)}}
=\sqrt{\frac{2\,L}{a}}\sqrt{\frac{1+\pi_3}{3+\pi_3}},
\end{equation}
and then becomes negative.  For time $t>t_{\mathrm{LO}}$, the
assumption~(\ref{eq:phiBeforeLO}) that the string is in contact with
the pulley over half a circle breaks down, as it predicts a negative
pressure (an adhesive force would be required to maintain contact).  The
negative values of $P$ are first attained in the neighbourhood of $C$,
which suggests that lift-off takes place there.  At time $t=t_{\mathrm{LO}}$,
the length of the hanging chain is \begin{equation}
s_C^{\mathrm{LO}}=\sc(t_{\mathrm{LO}})=\frac{2a}{3a+g}L=\frac{2}{3+\pi_3}L.
\label{eqn:HangingLengthLO}
\end{equation}

In \eqref{eq:tlo}, $t_{\mathrm{LO}}$ is less than the time $\sqrt{2L/a}$ when
the hanging part (I) shrinks to a point the mathematical
solution~(\ref{eq:phiBeforeLO}) ignoring the lift-off.  This confirms
that the hanging part (I) has a finite length when the lift-off takes
place. This is also consistent with $s_C^{\mathrm{LO}} = \sc(t_{\mathrm{LO}}) >0$.

Apart from factors obviously required by dimensional analysis, both
\eqref{eq:tlo} and \eqref{eqn:HangingLengthLO} appear to depend only
on the ratio $\pi_3=g/a$ of the acceleration due to gravity to the
imposed acceleration. They do not depend on the dimensionless group
$\pi_2=R/L$ involving the size of the pulley.  Furthermore, we note
that in the limit of zero gravity, $\pi_3=0$, one third of the
original hanging chain has passed around the pulley with two-thirds
still hanging; when pulling the chain using a heavy mass in free fall,
i.e.~imposing $\pi_3=1$, then one-half of the original hanging chain
has passed around the pulley with one-half still hanging.  Here,
incorporating gravity makes a quantitative, but not qualitative,
difference; either way, an appreciable fraction of the initially
hanging chain remains below the first contact point C.

From the above argument, we also gain some intuition into \emph{why} the chain lifts off: the tension at the contact point $\sc(t)$ is decreasing with time (because the length of hanging chain is decreasing) while the tension required to turn the chain  around the pulley increases (because the chain is moving faster and faster). Lift-off occurs when the excess tension in the chain due to the hanging length is `used up'.

\section{Lift-off}

\begin{figure}
\centering
\includegraphics[width=\textwidth]{figure3.pdf}
\caption{Experimental values of the time at which lift off occurs, $t_{\mathrm{LO}}$, plotted as a function of the chain length $L$.  This data, gathered with pulleys of radius ranging from $R=2.5\mathrm{~cm}$ to $R=7.5\mathrm{~cm}$ and two types of chain, collapses on a single master curve. The prediction derived in \S \ref{sec:b4lift} (see eq.~(\ref{eq:tlo})) is verified within $10\%$ (the solid curve corresponds to $t_{\mathrm{LO}}\simeq1.1\sqrt{L/g}$) . {In these experiments, $a=g$, i.e.~$\pi_3=1$.}}
\label{fig:LOdata}
\end{figure}

The prediction for the lift-off time, \eqref{eq:tlo}, presents a
natural test of the model assumptions, in particular with regard to
our neglect of the bending stiffness of the chain and the assumption
of a frictionless contact between chain and pulley.  Experiments were
performed with $a=g$ (i.e.~$\pi_3=1$) and a number of different pulley
sizes and initial hanging lengths (i.e.~varying $\pi_2$).  As shown in
figure \ref{fig:LOdata}, we find reasonable agreement between the
theoretical prediction for $t_{\mathrm{LO}}$ and that measured experimentally.
In particular, experiments confirm the result that the size ratio
$\pi_2=R/L$ does not affect the onset of lift-off.  We also found that
the value of $t_{\mathrm{LO}}$ is insensitive to the type of chain used (ball
chains and link chains give the same results).

However, we note that the onset of lift-off is difficult to assess
accurately in experiments owing to its slow initial dynamics (to be
discussed in detail in \S~\ref{after}); it is therefore natural that
experimental values of $t_{\mathrm{LO}}$ are slightly larger that theoretically
predicted (though they remain within 10\% of the theoretical value).
Furthermore, the favorable agreement between experiments and numerical
solution of the full model, which neglects any source of dissipation,
shown in figure \ref{fig:DVR}a suggests friction cannot be the cause
of the discrepancy.

\section{Behaviour just after lift-off}
\label{after}
We now turn our attention to the early phase of the motion, just after lift-off. In this phase, our experiments and numerical simulations show that the chain `balloons' off the pulley (see figure  \ref{fig:setup}b). For simplicity, we shall henceforth neglect the role of gravity, i.e.~we set $\pi_3=0$. This analysis is conducted hand in hand with numerical simulations for $\pi_3=0$, but  these results should not be compared with experiments (for which $\pi_3=1$). In Appendix \ref{sec:grav} we consider how the results of this section change when $\pi_3\neq0$; this analysis shows that the presence of gravity makes quantitative, rather than qualitative, changes to the motion around lift-off.

\subsection{Velocity after lift-off\label{sec:aftervel}}

\begin{figure
    \begin{center}
	\includegraphics[width=\textwidth]{figure4.pdf}
	%
	\caption{Behavior just after lift-off for $\pi_3=0$ (imposed
	acceleration at endpoint is $a=0.5$, $g=0$, $R=1$ and
	$L=4\pi$; the simulation timestep is $\Delta
	t=15\times10^{-4}$ and the mesh size is $\Delta s =
	6.3\times10^{-3}$).  (a) The speed of the hanging part of
	the chain for $g=0$ from numerical simulations (dotted blue
	curve) compared to the imposed velocity at the pulling end,
	$v=at$, (dashed line) and the prediction of
	eq.~\ref{eqn:vhanggeq0} (solid orange curve).  Inset: Error
	$\delta$ between the estimate \eqref{eqn:vhanggeq0} for
	$v_{\mathrm{hang}}$ and the numerical data{, shows that the expansion for
	$t-t_{\mathrm{LO}}\llt_{\mathrm{LO}}$ in \eqref{eqn:vhangtaylor} is correct at
	$O(t-t_{\mathrm{LO}})^2$}.  (b) $\Delta s$ denotes the length of chain
	that has lost contact with the pulley for $t>t_{\mathrm{LO}}$.  The
	corresponding angle is $\theta^*$ representing a region on the
	pulley of length $R\theta^*$.  The excess length $\Delta L$ is
	defined as the difference between these two quantities $\Delta
	L = \Delta - R\theta^*$ (c) The value of {the relative excess
	length} $\Delta L/L$ (solid) as predicted by equation
	\eqref{eqn:DeltaL} compares favourably with numerical data
	(dots); in particular the scaling prediction $\Delta L/L\sim
	(t-t_{\mathrm{LO}})^3$ is borne out by the data.}
	%
	\label{hsm}
    \end{center}
\end{figure}

The numerical simulations of the complete theoretical model (eqs~\ref{eqn:KirchhoffR}-\ref{eq:bc}) and experiments both suggest that the
portion of the chain {that is freely hanging at the instant of first
lift-off} (i.e.~$0\leq s<\sc(t_{\mathrm{LO}})$) remains straight (within numerical accuracy)
in the immediate aftermath of lift-off.  We therefore attempt to
repeat the calculation of \S\ref{sec:b4lift} but this time we treat
the acceleration in this straight portion, $\dot{v}_{\mathrm{hang}}(t)$, as an unknown.
Motivated by numerical observations, we assume that the length of the
straight portion of the chain is precisely the hanging length of the
chain at $t_{\mathrm{LO}}$, namely $\sc(t_{\mathrm{LO}})$, which we denote by $s_C^{\mathrm{LO}}$
as in \eqref{eqn:HangingLengthLO}.

Setting $g=0$ in \eqref{eqn:KirchhoffR}, and focusing on the straight, hanging part (zero curvature), and integrating we find that:
\begin{equation}
T=\rho_\ell \dot{v}_{\mathrm{hang}} s, \quad 0\leq s\leq s_C^{\mathrm{LO}}
\label{eqn:tensaccel}
\end{equation} where the length of the straight portion $s_C^{\mathrm{LO}}=L-\tfrac{1}{2}at_{\mathrm{LO}}^2$.
To close the problem, we note that at the end of this straight portion, the radius of curvature must change to some finite value (by construction), and further that there is no reaction force (since at this point the chain is no longer  in contact with the pulley). Substituting these results into \eqref{k2}, we then have that $T(s_C^{\mathrm{LO}},t)=  \rho_\ell v_{\mathrm{hang}}^2$ and hence, after combining with \eqref{eqn:tensaccel}, that
\begin{equation}
\dot{v}_{\mathrm{hang}}(t)=   \frac{v_{\mathrm{hang}}^2(t)}{s_C^{\mathrm{LO}}}.
\label{eqn:HSAnew}
\end{equation}

\noindent Integrating \eqref{eqn:HSAnew} subject to the initial condition $v_{\mathrm{hang}}(t_{\mathrm{LO}})=at_{\mathrm{LO}}$, we find that
\begin{equation}
v_{\mathrm{hang}}(t)=\frac{2}{3}\,\frac{L}{2t_{\mathrm{LO}}-t} =
a\,t_{\mathrm{LO}}\,\left(2-\frac{t}{t_{\mathrm{LO}}}\right)^{-1}
\textrm{.}
\label{eqn:vhanggeq0}
\end{equation} This simple approximation predicts that the velocity of the
hanging portion of the chain diverges as $t\to2t_{\mathrm{LO}}$.  {However, the
argument above only holds in the immediate aftermath of lift-off,
$t-t_{\mathrm{LO}}\llt_{\mathrm{LO}}$.  In the simulations, the reversal of curvature
actually occurs at a time $t^* \approx
1.365\sqrt{L/a}\approx1.67t_{\mathrm{LO}}$ (see figure \ref{snap}b-c), which is
earlier than that predicted by~\eqref{eqn:vhanggeq0}.

The Taylor expansion of \eqref{eqn:vhanggeq0} for $t-t_{\mathrm{LO}}\llt_{\mathrm{LO}}$
reads \begin{equation}
v_{\mathrm{hang}}(t)=a\,t_{\mathrm{LO}}\,\left[1+\frac{t-t_{\mathrm{LO}}}{t_{\mathrm{LO}}}+\left(\frac{t-t_{\mathrm{LO}}}{t_{\mathrm{LO}}}\right)^2+O\left(\frac{t-t_{\mathrm{LO}}}{t_{\mathrm{LO}}}\right)^3\right].
\label{eqn:vhangtaylor}
\end{equation} The first two terms in in the square bracket combine to give
$at$, which is the imposed pulling velocity: the correction to the
imposed constant acceleration is given by the following term and
occurs at order $(t-t_{\mathrm{LO}})^2$.  In figure \ref{hsm}a, we observe that
our numerical results for the velocity are in good agreement with the
prediction of eq.~\eqref{eqn:vhanggeq0} for times close to $t_{\mathrm{LO}}$
but then deviate with an error $\delta$ that is cubic in $t-t_{\mathrm{LO}}$.
This cubic error confirms that the first correction to the constant
acceleration motion, namely the term of order $(t-t_{\mathrm{LO}})^2$ in
\eqref{eqn:vhangtaylor}, is correct.  }

By differentiating \eqref{eqn:vhanggeq0} with respect to time, we obtain an expression for the excess acceleration of the free part of the chain
\begin{equation}
\Delta a=\dot{v}_{\mathrm{hang}}-a=a\left[\frac{t_{\mathrm{LO}}^{2}}{(2t_{\mathrm{LO}}-t)^{2}}-1\right],
\label{eqn:deltaa}
\end{equation} which is  positive for all $t>t_{\mathrm{LO}}$. Thus, even though the free end is not subject to external forces, it accelerates \emph{faster} than the end that is actually subject to the imposed (constant) acceleration.

A  quantity of interest is the arc-length of the region over which the chain has lost contact with the pulley for $t>t_{\mathrm{LO}}${, which we denote by $\Delta s$ (see figure \ref{hsm}b}). The above calculation does not give us enough information to determine this quantity. However, the result for $v_{\mathrm{hang}}$, \eqref{eqn:vhanggeq0},  can be used to determine the excess length of chain that has lost contact with the pulley, i.e.~the difference between the length of chain that has lifted off the pulley, $\Delta s(t)$, and  the arc length of the pulley from which it has lifted off, $R\theta^*(t)$, with $\theta^*(t)$  the angle subtended between the two contact points C and C$^*$ (see figure \ref{hsm}b). Denoting this quantity by $\Delta L(t)=\Delta s(t)-R\theta^*(t)$ we find that
\begin{equation}
\Delta L(t)=\int_{t_{\mathrm{LO}}}^t\left[v_{\mathrm{hang}}(t')-at'\right]~\mathrm{d} t'= \frac{2L}{3}  \log \left(\frac{t_{\mathrm{LO}}}{2t_{\mathrm{LO}}-t}   \right)-\frac{a}{2}(t^2-t_{\mathrm{LO}}^2).\label{eqn:DeltaL}
\end{equation}
We emphasize that this calculation does not allow us to determine $\Delta s$ and $R\theta^*$ separately, but only their difference.
The Taylor series of $\Delta L(t)$ for $t-t_{\mathrm{LO}}\llt_{\mathrm{LO}}$ reveals that
\begin{equation}
\label{approx}
\Delta L(t)\approx a{(t-t_{\mathrm{LO}})^3\over 3t_{\mathrm{LO}}}, \end{equation} \emph{i.e.}~the
excess length grows only relatively slowly after the start of
lift-off.  Note that the appearance of a leading-order behaviour at
order $(t-t_{\mathrm{LO}})^3$ here is consistent with our earlier finding that the
correction to the speed of motion is at order $(t-t_{\mathrm{LO}})^2$ in
\eqref{eqn:vhangtaylor}, since we have integrated this quantity in
time.

Comparison of the predictions of this analysis, \eqref{eqn:vhanggeq0}
and \eqref{approx}, with the numerical solution of the fully nonlinear
problem (see figure \ref{hsm}) shows that these expressions are
asymptotically correct immediately after lift-off,
$t-t_{\mathrm{LO}}\llt_{\mathrm{LO}}$, and validates the underlying assumption (that the
hanging portion of the chain simply accelerates vertically upwards).

\subsection{Characteristics}

\begin{figure
\begin{center}
\includegraphics[width=\textwidth]{figure5.pdf}
\caption{ The parameter space $(t\sqrt{a/L},s/L)$ is mapped with the characteristics of the system, color coded as functions of the direction of propagation (given by the sign of $\mathrm{d} s/\mathrm{d} t$ in this plot). The time evolution of the position of the contact point $C$, obtained analytically before $t_{\mathrm{LO}}$ and numerically for $t>t_{\mathrm{LO}}$, is shown by solid blue curve. The envelope of characteristics emitted from $C$ at $t=t_{\mathrm{LO}}$ is highlighted by the shaded area. (The simulation timestep is $\Delta t=15\times10^{-4}$
    and the mesh size is $\Delta s = 6.3\times10^{-3}$.  Imposed
    acceleration at endpoint is $a=0.5$, $g=0$, $R=1$ and $L=4\pi$).  }
\label{caractfig}
\end{center}
\end{figure}

We now proceed to explain the size of the region of lift-off as a function of time. We show that the point of contact $C^*(t)$, as defined in fig~\ref{hsm}b, follows a characteristic of the wave equation describing the evolution of the small perturbations to the motion of the string. In other words, the motion of $C^*(t)$ can be viewed as a traveling front produced by the initial lift-off at $t_{\mathrm{LO}}$. To do so, we now consider the length of chain $\Delta s$ that makes up the `ballooning' arch  forming after lift-off. This length is defined to be $\Delta s(t)=s_c^*-s_c$, where $s_c$ and $s_c^*$ correspond to the arc-length coordinate of the contact points $C$ and $C^*$, respectively (see figure \ref{hsm}b).

For times close to $t_{\mathrm{LO}}$, lift-off takes place but it is mild; as a result, this lift-off can be described by $(i)$ extending beyond $t_{\mathrm{LO}}$ the solution maintaining contact with the upper half of the pulley (base solution) and $(ii)$ perturbing it to remove any negative contact pressure. The equations governing the perturbation are obtained by a standard linearization, and are linear wave equations. In these wave equations, the wave speed $c=\sqrt{T/\rho_\ell}$ is both time and space-dependent (recall that $T=T(s,t)$).  Assuming that the tension remains close to its value prior to lift-off{, i.e.~$T\approx\rho_\ell as$} as derived in eq.\eqref{eq:tension}, we  have $c=\sqrt{as}$, and the characteristics of the wave equation satisfy
\begin{equation}
\label{eq:cspeed}
\frac{\mathrm{d} s}{\mathrm{d} t}=\pm\sqrt{as}.
\end{equation}
yielding the expansion waves depicted in figure \ref{caractfig}.

When lift-off occurs, the chain is locally freed from the pulley at the point $s_C^{\mathrm{LO}}$ and this information propagates within the envelope formed by the two characteristics that depart from this point in the $(t,s)$ plot. Within this region, the tension in the chain is altered, i.e. the tension of the true solution does not match exactly that predicted by the base solution that ignores lift-off; beyond this region, information can only propagate at the wave speed at the edges, which is, by construction, given by the tension \emph{just} before lift off. The limited propagation speed of information about lift-off  results in the formation of an arch from the point $C$ to a second contact point $C^*$ (see figure \ref{hsm}b).  We hypothesize that the length of the arch $\Delta s(t)=s_c^*-s_c$ is simply the width of the envelope formed by the two characteristics that originate from $C$ at $t=t_{\mathrm{LO}}$ (see figure \ref{caractfig}). Deriving $\Delta s$ from eq.\eqref{eq:cspeed} yields
\begin{equation}
\Delta s =2\sqrt\frac{2}{3}\sqrt{aL}(t-t_{\mathrm{LO}}).
\label{caract}
\end{equation}
We  use numerical simulations to test the estimate~(\ref{caract}). As shown in figure \ref{deltas}a the agreement between the two is asymptotically correct immediately after lift-off (with the correct prefactor). This indicates that the propagation of lift-off front is indeed limited by the rate at which the perturbations can travel through the string. This argument correctly accounts for the short times dynamics, $\Delta s\sim (t-t_{\mathrm{LO}})$.

We also note that $ \theta^*$, the angle from $C$ to $C^*$ defined in
figure \ref{caractfig}b, follows the same scaling law and agrees well
with equation \eqref{caract}.  Indeed, recall that $\Delta L =\Delta s
- R \theta^*$; for $t-t_{\mathrm{LO}}\ll1$, we have shown $\Delta L \sim
(t-t_{\mathrm{LO}})^3$ in equation \eqref{approx} and $\Delta s \sim
(t-t_{\mathrm{LO}})$ above, it follows that $\Delta s$ and $R \, \theta^*$ must
be equal to leading order in $(t-t_{\mathrm{LO}})$, \emph{i.e.}~$\theta^*\sim \Delta
s/R$ as checked numerically in figure~\ref{deltas}b.

\begin{figure
\begin{center}
\includegraphics[width=\textwidth]{figure6.pdf}
\caption{Arch structure for $\pi_3=0$. (a) The evolution of $\Delta s/L$ {with time following
lift-off} determined numerically (blue dots) and compared to the
theoretical expression in~\eqref{caract} (orange solid line).  (b)
Test of the prediction $\theta^*\sim \Delta s/R$ derived at the end
of~\S\ref{after}. In both cases the numerical data corresponds to a simulation with timestep $\Delta t=15\times10^{-4}$ and the mesh size $\Delta s = 6.3\times10^{-3}$.  Imposed
    acceleration at endpoint is $a=0.5$, $g=0$, $R=1$ and $L=4\pi$.
}
\label{deltas}
\end{center}
\end{figure}

\section{Snapping}

We now describe the kinematics of the free end during snapping.  Let
$\phi(s,t)$ be the angle between the tangent $\ve t$ and the upward
pointing vertical axis.  We define the curvature $\kappa(s,t)=
\partial \phi(s,t)/\partial s$ (recall that the free end corresponds
to $s=0$).  We define snapping as a sudden change in maximal curvature
of the chain as depicted in figure \ref{snap}a-b,
\begin{figure
\begin{center}
\includegraphics[width=\textwidth]{figure7.pdf}
\caption{Snapping for $\pi_3=0$:  (a) Shapes of the chain right before and after snapping
occurs.  The angle $\phi(s,t)$ separates the tangent $\ve t(s,t)$ and
the the upward pointing vertical axis so that $\kappa(s,t)= \partial
\phi(s,t)/\partial s$, where $\kappa$ is the curvature of the chain.
(b) The maximal curvature of the chain $\kappa_M$ (attained at
position $s_M$) as a function of time and (c) the velocity of the free
end of the chain compared to the {constant acceleration} that drives
the motion.  The grey bands indicate the snapping time.  (The simulation timestep is $\Delta t=15\times10^{-4}$
    and the mesh size is $\Delta s = 6.3\times10^{-3}$.  Imposed
    acceleration at endpoint is $a=0.5$, $g=0$, $R=1$ and $L=4\pi$)}
\label{snap}
\end{center}
\end{figure}
which shows the time evolution of the largest curvature of the chain,
$\kappa_M$.  We observe that the arc-length position $s_M$ at which
this maximum curvature is observed travels towards the free end of the
chain as snapping approaches, as shown in figure~\ref{snap}b.  During
snapping, $\kappa_M$ has a singular behavior as well: the curvature
strongly increases and changes sign, as shown in the last three
configurations in figure \ref{snap}{a} and in figure~\ref{snap}b.
Note that for real ropes this singularity will be regularized by their
finite bending stiffness~\footnote{For chains made up of rigid links,
this singularity is regularized too, by the contact between successive
chain links.}.  Therefore, the singular behavior predicted by our
string model may be seen as the 'outer solution' of a regularized
model.  Note that snapping is associated with a rapid increase of the
free end velocity as illustrated in figure \ref{snap}c.  These
features are similar to what occurs in a cracking
whip~\cite{goriely2002shape} and a falling
chain~\cite{schagerl1997paradox,tomaszewski2005dynamics,tomaszewski2006motion,Grewal2011}.

Let us denote by $t^*$ the time of snapping, defined as the time where
the curvature diverges near the free end.  For optimal accuracy, we
analyze the snapping dynamics based on simulations having a relatively
large value of $\pi_2=R/L=\frac{1}{2\pi}$.  This allows us to use a
fine and uniform spatial discretization of the string.  To ease the
comparison between this specific simulation and the rest of our
results, we introduce a non-dimensionalisation with respect to the
space and time scales of the problem, namely $L$ and $\sqrt{L/a}$.
Dimensionless quantities are denoted by a bar, such as $\overline{t}^*
= t^* / \sqrt{L/a}$.  The dimensionless snapping time $\overline t^*$
is a function of $\pi_2$ and $\pi_3$; in the forthcoming analysis, we
focus on the particular case $\pi_{2}=1/(2\pi)$ and $\pi_{3} = 0$.

To measure the divergence of curvature from the simulations, we use a
curvature norm that is intended to capture the largest value of
curvature,
\begin{equation}
    \overline K(t) = \left(
    \int_{0}^1
    \left(\overline \kappa(\overline s, \overline t\,)\right)^p\,\mathrm{d}\overline s
    \right)^{\frac{1}{p-1}}
    \textrm{,}
    \label{eq:K}
\end{equation}
where $p\geq 2$ is an integer.  The value of the integer $p$ that is
used results from a trade-off: one should use values of $p$ as large
as possible, and $\overline K$ will then accurately capture the
maximum curvature; on the other hand, if $p$ is too large then
$\overline K$ fluctuates significantly as a result of discretization
errors.  In the following, we take $p=6$; we have verified that the
results are unchanged for $p=8$.

We begin by assuming that as the singularity at $\overline t=\overline
t^*$ is approached, the curvature diverges according to a power law
$\overline \kappa\sim (\overline t^*- \overline t)^{-\alpha}$, for
some exponent $\alpha$ to be determined, on a region of size $\sim 1/
\overline \kappa$.  The region of divergence contributes an amount
$\sim( \overline t^*- \overline t)^{-(p-1)\,\alpha}$ to the integral
in equation~(\ref{eq:K}): as soon as $\alpha(p-1)>0$, this
contribution makes the integral diverge at the time of snapping
$\overline{t}^*$ and $\overline{t}^*$ can be identified from a
numerical plot of $\overline{t}$ as a function of time---the condition
$\alpha(p-1)>0$ is indeed satisfied as $p=6$ and $\alpha>0$, see
below.  One can check that the quantity $\overline K(t)$ diverges as
$\overline K\sim (\overline t^*-\overline t)^{-\alpha}$: a numerical
plot of $\overline{K}$ versus $\overline{t}$ yields the exponent
$\alpha$ as well, independently of the particular value of $p$ chosen
in the definition of $\overline{K}$.

The snapping time $\overline{t}^*$ and the exponent $\alpha$ entering
in the power law $\overline{K}(t)\sim |t-t^*|^{-\alpha}$ are best
determined from the simulations by plotting the quantity
\begin{equation}
\left(\frac{\mathrm{d}(\ln \overline K)}{\mathrm{d} \overline t}\right)^{-1}\sim \frac{\overline t^*-\overline t}{\alpha}
\end{equation}
as a function of $\overline t$, see figure~\ref{fig:mmtkaFits}a.
\begin{figure}
    \centerline{\includegraphics[width=.95\textwidth]{figure8.pdf}}
    \caption{ Searching for self-similar solutions in the snapping (for this
    particular simulation, the linear mass is $\rho_\ell = 5$ and the
    radius of pulley is $R=1$ and $L=2\pi$ such that
    $\pi_2=R/L=1/(2\pi)$.  There is no gravity and no bending
    rigidity.  The simulation timestep is $\Delta t=2\times10^{-4}$
    and the mesh size is $\Delta s = 3.14\times10^{-3}$.  Imposed
    acceleration at endpoint is $a=0.5$). (a) Identifying the singularity exponent $\alpha$ for the
    curvature and the critical time $\overline t^*$ using the quantity
    $\overline K(\overline t)$ defined in \eqref{eq:K}.  From our
    numerical simulations we find that
    $(\alpha,\overline{t}^*)=(0.659,1.41531)$ (red dashed line).  (b)
    These values may be checked in a standard log-log plot.  The wells
    are numerical artifacts: they correspond to values of $|\overline
    t^*-\overline t|$ as small as a few simulation steps, implying
    that the curvature is very peaked and prone to discretization
    errors.  (c) Configurations right before and after the snapping
    time, $1.405\leq \overline t \leq 1.42$ ($\overline
    t^*\approx 1.415$): darker configurations correspond to times
    closer to snapping and reference configurations are denoted by the
    symbols (\protect\tikz \protect\draw[black,fill=PineGreen!10]
    (-.11,0) -- (.0,.11) -- (.11,0)-- (0,-.11)--(-.11,0);),
    (\protect\tikz \protect\draw[black,fill=PineGreen!10] (0,0) circle
    (.75ex);) and (\protect\tikz
    \protect\draw[black,fill=PineGreen!10] (-.09,-.09) -- (.09,-.09)
    -- (.09,.09)-- (-.09,.09)--(-.09,-.09);) (d)~Collapse of the
    curvature in rescaled variables $(\tilde s, \overline
    \kappa/\overline K)$ using the same shading convention for $1.405\leq \overline
t \leq1.414$ (before snapping occurs).}
    \protect\label{fig:mmtkaFits}
\end{figure}

The points collapse onto a straight line, aside from a thin band of
width $\approx 15 \Delta \overline t$ where the large curvature is not
well resolved by the discretization.  A linear fit in
figure~\ref{fig:mmtkaFits}a yields both the snapping time $\overline
t^*$ (where the fitting line crosses the $t$-axis) and the exponent
$\alpha$ (the reciprocal of the slope).  This fit yields a value of
the exponent $\alpha = 0.659$ which is numerically close to 2/3 (we
do not know whether this is a coincidence) and $\overline t^*=
1.415$.  The latter is close to (but less than) the singular time
$2t_{\mathrm{LO}} \sqrt{a/L}=2\sqrt{2/3}\approx 1.63 $ found by extrapolating
the asymptotic behavior in the immediate aftermath after lift-off, see
equation~(\ref{eqn:vhanggeq0}).  These numerical values of
$\overline{t}^*$ and $\alpha$ have been obtained in the particular
case $\pi_{2}=1/(2\pi)$ and $\pi_{3} = 0$.  We suspect, however, that
the exponent $\alpha$ can be explained by a boundary-layer theory and
that it is actually independent on $\pi_{2}$ and $\pi_{3}$.
Unfortunately, we can offer no proof for this statement.

As observed in the experiments (see \S\ref{phenomenon}), the string
remains straight in the simulations along an interval of length
$\ell(t)$ comprising the free end, at all times until $t^*$.  This
straight portion of the string is apparent in figures~\ref{snap}a
and~\ref{fig:mmtkaFits}c.  It defines the region denoted by (I), which
is adjacent to the region (II) of large curvature (see
Fig~\ref{fig:DVR}c).  The dimensionless length $\overline{\ell} =
\ell/L$ is found numerically to scale like $\overline \ell\sim
(\overline t^{*}- \overline t)^\beta$, with $\beta = 1.08\pm0.2$ (fit
not shown).  The numerical accuracy on this exponent $\beta$ is not as
good as that of $\alpha$ as the determination of the straight region
is sensitive to numerical noise.  It is clear from our numerical data,
however, that the exponent $\beta$ is larger than $\alpha$, meaning
that the length of the straight region near the free end vanishes more
quickly than the {minimum} radius of curvature as $\overline t\to
\overline t^*$, $\overline t<\overline t^*$.

Next, we proceed to use our analysis to uncover a self-similar
behavior in the curvature profile.  Anticipating that the point of
maximal curvature plays a central role we introduce a weighing to
capture its position:
\begin{equation}
    \langle \overline s\rangle({\overline t}) = \frac{
    \int_{0}^1
   \overline s\,
  \overline  \kappa^p(\overline s,\overline t)\,\mathrm{d}\overline s
    }{
    \int_{0}^1
  \overline  \kappa^p(\overline s,\overline t)\,\mathrm{d}\overline s
    }
    \textrm{.}
    \label{eq:weightedAverage}
\end{equation}
By design, the weighting is concentrated in the region of large
curvature: $\langle \overline s\rangle({\overline t})$ yields the
typical value of $\overline s$ at time $\overline t$ in the region
(II) where the curvature diverges.

Finally we rescale the arc-length parameter to
\begin{equation}
    \tilde {s} = \frac{\overline s - \langle \overline s\rangle({\overline t})}{1/\overline K(\overline t)}
    \textrm{,}
    \label{eq:rescaledArcLength}
    \end{equation}
By design, $\tilde{s}=0$ lies in the centre of the region with high
curvature.  In this definition, the offset $\langle \overline
s\rangle({\overline t})$ allows us to ignore the straight region
entirely (which shrinks according to a different exponent).  We
consider a set of simulation snapshots such that $1.405\leq \overline
t \leq1.414$, {i.e.}~such that $0.001\leq \overline t^*-\overline
t\leq 0.01$.  This corresponds to the configurations bounded by the
symbols (\protect\tikz \protect\draw[black,fill=PineGreen!10] (-.11,0)
-- (.0,.11) -- (.11,0)-- (0,-.11)--(-.11,0);) and (\protect\tikz
\protect\draw[black,fill=PineGreen!10] (0,0) circle (.75ex);) in
figure \ref{fig:mmtkaFits}b-c, with darker plots corresponding to
times closer to the snapping time $\overline t^*$.

In figure \ref{fig:mmtkaFits}d, we plot the rescaled curvature
$\overline\kappa(s,t)/\overline K(t)$ as a function of the rescaled
arc-length $\tilde{s}$ and obtain a good collapse.  Note that the
unscaled maximum curvature $\overline K$ varies by a factor $\sim 5$,
from approximately 65 to 308, between the first and last snapshot in
this series.  Therefore, the collapse shows that the curvature
distribution is self-similar close to the snapping time $\overline
t^*$: consistently with our initial scaling assumption, the curvature
scales like $\overline \kappa\sim (\overline t^*-\overline
t)^{-\alpha}$ in a region of size $\overline s - \langle
\overline{s}\rangle\sim(\overline t^{*}-\overline t)^\alpha$.  Note that this analysis focuses on the behavior of the chain prior to snapping, so that $\overline t < \overline t^*$.

In summary, our analysis shows that the snapping singularity may
characterized by a self-similar solution, whose scaling behaviours
have been identified numerically.

\section{Conclusions}
In this paper, we have considered a degenerate version of Atwood's machine, in which a single mass pulls a chain around a pulley.  In stark contrast with the apparent simplicity of the setup we have found that the dynamics is extremely rich, successively displaying a ballooning instability of the chain and a snapping motion of its free end, reminiscent of what is seen in a cracking whip. We have shown that  the chain dynamics is well captured by a frictionless string model and that some of its features may be captured by simple arguments.  In particular we have shown that the geometry of the problem, through the imposed rotation of the chain around the pulley, is key to understanding how the end of the chain is able to 'beat' the free-fall that drives its motion.

Our observations can be used to speculate on the peculiar hunting techniques of a variety of amphibians. Indeed, instead of throwing their tongue in a straight motion (as observed in chameleons~\cite{Anderson:2010wm,chameleon}), certain species of toads~\cite{Deban:2011ve} and salamanders~\cite{Deban:2007td}  adopt an unfurling tongue strategy. Of course, the reasons for such a mechanism are many and varied but we believe that the increase of tip velocity observed in the case of a chain is  likely to reappear in problems involving a finite bending stiffness. It is then natural to wonder whether this geometrical amplification of acceleration may be  used by these amphibians to allow them to maximize their chances of capturing a prey?

Finally, we note that while we have been able to rationalize some of
the observations from experiment and simulation, others remain
elusive.  For example, predicting the shape of the ballooning region
either with simple arguments, or preferably analytically, remains
beyond our reach.  Difficulties in doing so arise from the fact that
the `base solution' of the problem is unsteady (since $a>0$).  An
interesting avenue of research would be to explore the case where the
chain is pulled at constant speed thus without any acceleration,
potentially allowing for analytical developments.  Similarly, there is
hope that the self-similar exponent $\alpha$ and $\beta$ identified in
the previous section can be explained by some boundary layer theory in
future work.

\section*{Acknowledgment}

This publication is based in part upon work  partly funded by the European Research Council (ERC) under the European Union's Horizon 2020 research and innovation programme (grant agreement No 637334, GADGET to DV).

redpajama_set_name: RedPajamaArXiv


text:
The Yacht Path Vs. Small Vessels Certificate
InterviewsLatest News
Yachting engineers have recently faced a dilemma: should they continue down the traditional yachting route or try the new Small Vessels engineering certificate, which will be offered from September 2017.
Both newcomers to the industry and established yachting engineers have faced the same confusion that has cropped up in the pursuit of their dream superyacht crew job. We spoke to Shaun Towers from Warsash Superyacht Academy to find out more about the courses.
The Y4, Y3, Y2, and Y1 Route
Engineers wishing to begin a career in the yachting industry have traditionally completed the Y4 qualification, and progressed up to the Y1 qualification over time.
The Y4, Y3, Y2, and Y1 yachting qualifications were created in response to industry demand and underpin the importance of a standardised qualification structure for a yacht engineering career. While the current system has advantages and disadvantages, one major issue is that the qualifications are duplicated between levels.
Mr Towers elucidates: "The Maritime and Coastguard Agency run lots and lots of exams so they have parallel syllabuses for tugs, fishing vessels, and small work boats. The administration for them was getting too much, bearing in mind the financial constraints on government bodies in England."
These downfalls have necessitated the creation of the Small Vessels – a course that will centralise engineer certification for all small vessels. The English Maritime and Coastguard Agency, and the main training establishments, came together to simplify and streamline the educational process. For a while, the new Smaller Vessels course – which various institutions are offering from September – will be taught alongside the current Y4, Y3, Y2, and Y1 qualifications.
The Small Vessels Qualification
The English Maritime and Coastguard Agency and the main training establishments have restructured the new syllabus to make a more simple and encompassing course for all small vessels. They added new subjects and the syllabus avoids repetition.
Shaun, who was involved in the creation of the new syllabus, explains what makes it different: "We basically threw out all the inappropriate questions, which left gaps. We then collectively wrote probably another 200 questions to fill all the gaps. All the questions are now relevant to small vessels, whereas previously a lot of questions weren't because they were written by merchant navy engineers who had little to no knowledge of the yachting industry."
An engineer can now advance from beginner to advanced with an even workload and fewer complications. One less positive point Shaun makes about the course is that engineers might potentially not get the same level of training, as the Small Vessels qualification allows students to skip the process of logged sea time.
Shaun comments: "It could be argued that engineers will not get the same level of training; that they're actually moving up faster where they won't have the experience to back up their qualification. People are running before they can walk, which is happening in the entire industry anyway because of the shortage of skills. Most people are now doing the yacht route and they will move sideways at some stage to the new route. You can change from the yacht route to the new route at any stage of your career." (This process is fully outlined in MIN524)
Which Route Should Students Choose?
So which route should students should take in September? Before Shaun can answer the question he describes how seafarers' lack of seagoing experience may be dealt with: "Students will need to do extra courses before starting the Small Vessels qualification. You've got to do an AEC, which is an Approved Engine Course, and an AEC2."
Originally, it was agreed that once the MCA offered the new Small Vessel route, they would retire the old yacht route. Unfortunately, the MCA later decided that the yacht route would remain operative until 2021. There was only meant to be one course: the Small Vessels course. Students were not supposed to face this dilemma and the implications have been far-reaching.
Shaun describes the implication that this decision has had, saying that the problem is based on people trusting the established route. He expands by saying, "the new route is something different and most training establishments obviously have to offer commercially viable training. When there is sufficient demand the courses will be on offer at all institutions and the yacht route will slowly become a thing of the past. The other implication is that most yachts' Safe Manning Certificate will have to be updated by Flag to ensure statutory compliance."
Shaun offers this advice to those contemplating what to do:
"My advice to anybody at the moment is to start on the yacht route, because it's well tried, it's well tested. All the training providers are used to providing the training and obtaining good pass marks. The questions are going to be roughly identifiable. As soon as someone breaks ground and reaches into the new syllabus, there's going to be a lot of question there that are going to pose potential upsets, as they are unseen. Go on the proven route. Until you get to Y4, maybe Y3, then move sideways, because that's the only opportunity you've got at the moment. If you go on the yacht route, you've saved yourself two weeks of courses and all the associated expenses. There is a crossover point at every stage. Once you've moved across then you've got to progress up the new route."
What lies ahead for the Small Vessels qualification?
Rest assured that the Small Vessels course be implemented at every level eventually, but it may take a while. Shaun expresses his final thoughts on the future of the new qualification:
"The syllabus is in place. The exams are in place. It's down to each training provider to decide when they're going to get their course approved by the MCA and offer it to students. It's got to happen eventually. It's untenable for any training establishment to run two parallel courses, which are almost identical, apart from a few fine points."
It is said that the Small Vessels course will be available for students to start from September 2017. For more information, contact individual training providers.
NOTE: this information outlines the current situation. It will change as soon as training providers start offering the full range of courses and career routes as outlined in MSN1859.


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text:
Kollafjørður [] (dänischer Name: Kollefjord) ist ein Ort der Färöer auf der Insel Streymoy.

Ortsdaten und Lage
Der Ort Kollafjørður liegt am gleichnamigen Fjord und erstreckt sich an dessen Nordseite über eine Länge von ungefähr 8 Kilometern. Damit ist Kollafjørður das längste Dorf auf den Färöern. Verwaltungsmäßig gehört der Ort zur Hauptstadtgemeinde Tórshavn. Im Jahr 2016 lebten 761 Menschen im Dorf Kollafjørður selbst und insgesamt 940 Menschen, wenn man die beiden unmittelbar benachbarten Dörfer Oyrareingir und Signabøur mit einbezieht. Die Postleitzahl von Kollafjørður ist FO-410.

Vergangenheit und Gegenwart
Erstmals schriftlich erwähnt wird Kollafjørður im Jarðarbókin von 1584, wo der Ort unter der dänischen Bezeichnung Koldefiord erscheint. Spätestens seit dem Mittelalter befand sich hier eine lokale Thingstätte, das so genannte Várting. Im Ort befindet sich eine der zehn färöischen Holzkirchen. Sie stammt aus dem Jahr 1837.

Der bekannte färingische Landwirt und Dichter Jens Christian Djurhuus (1773–1853) lebte im Ortsteil við Sjógv (am Meer) und wird deshalb auch Sjóvarbóndin (der Meeresbauer) genannt.

Obwohl der Ort historisch zu Nordstreymoy gehört, wurde die bis 2001 eigenständige Gemeinde (Kollafjarðar kommuna) mit den Orten Kollafjørður, Signabøur und Oyrareingir in die Hauptstadtgemeinde Tórshavn (Kommune: Tórshavnar kommuna) eingemeindet.

Kollafjørður hat in den letzten 25 Jahren einen beträchtlichen Einwohnerrückgang hinnehmen müssen.
Wohnten 1989 noch 930 Menschen im Ort, so waren es im Jahr 2014 nur noch 734. Allerdings hat die Einwohnerzahl in den letzten zwei Jahren wieder leicht zugenommen. Haupterwerbszweig ist die Fischindustrie. Es gibt vor Ort einen Fischereihafen und fischverarbeitende Betriebe. Des Weiteren befindet sich in Kollafjørður die landwirtschaftliche Versuchsstation (Royndarstøðin) der Färöer, sowie ein Betrieb, der Fensterscheiben und Spiegelglas herstellt.

Der Ort hat auch einen eigenen Sportverein, der sich mit KÍF abkürzt. Der Verein betreibt eine Handball-, eine Volleyball- und eine Ruderabteilung. Die historische Verbindung zum Sundalag im Nordteil der Insel spiegelt sich heute noch in der sogenannten Sundalagsstevna wider, einem Ruderwettbewerb, der jährlich abwechselnd im Sommer in Hósvík, Hvalvík oder Kollafjørður stattfindet.

Der Bankraub von Kollafjørður
Im Januar 1985 kam es in Kollafjørður zum ersten bekannten Bankraub auf den Färöerinseln. Zwei Täter forderten das gesamte Geld der örtlichen Bank und konnten fliehen. Die Polizei musste erst aus dem benachbarten Tórshavn anrücken und verzichtete aus Unerfahrenheit auf eine Straßensperre, so dass ihnen die Täter vermutlich mit dem Auto entgegenkamen ohne erkannt zu werden.

Trotz der unanonymen Strukturen auf der Insel tappte die Polizei lange Zeit im Dunkeln und forderte Verstärkung aus Kopenhagen an. Lediglich die Körpergrößen der Tatverdächtigen war ihnen bekannt. So kam es zunächst zur Festnahme eines in Frage kommenden Nonkonformisten, der jedoch ein Alibi in Form einer Schwimmbad-Eintrittskarte vorzuweisen hatte.

Einer der beiden Täter wurde schließlich beim Ausgeben der Beute festgenommen. Beim Kauf eines 3000 Kronen teuren Videorekorders zahlte er ausschließlich mit 10-Kronen-Scheinen, da er bei der Beuteteilung sämtliche kleinen Scheine erhalten hatte.

Warme Wasserquellen in Kollafjørður
Kollafjørður geriet im Sommer 2014 in die Schlagzeilen als man im Ortsteil á Lygnnesi bei zwei Bohrungen in 165 m bzw. 200 m auf bis zu 26,2 °C warmes Wasser stieß. Der ergiebigste der beiden Bohrungsbrunnen stieß 33 Tonnen Wasser pro Stunde aus. Örtliche Geologen waren überrascht und suchten in der anschließenden Zeit nach einer Erklärung für diese Naturerscheinung.

Bilder

Persönlichkeiten
 Jens Christian Djurhuus (1773–1853) – Landwirt und Dichter
 Johan C. F. Dam (1863–1925) – Landwirt und Politiker
 Sverri Djurhuus (1920–2003) – Autor
 Johan Dalsgaard (* 1966) – Entertainer und Schauspieler
 Jens Marni Hansen (* 1974) – Sänger und Komponist

Siehe auch
 Liste der Städte und Orte auf den Färöern

Weblinks

 Kollafjørður, torshavn.fo

Einzelnachweise

Ort auf den Färöern
Streymoy
Geographie (Kommune Tórshavn)

redpajama_set_name: RedPajamaWikipedia


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The Activities Assistant assists with the planning and implementation of quality leisure/social events program designed to assist residents in maintaining their personal potential physically, socially and mentally. This position offers part time (.50 FTE/40 hours PPD) day and evening shifts with every other weekend opportunity.


Melanie's Closet Project Blog: It's OURS!!!
I just got a call from Juana, our realtor. We got the keys, the money is in and the house is OURS!!!! We're moving, finally. I can't believe it! Mick also lost his first tooth today and I have some cute random shots of the kids playing outside. Many are a diaperless baby, so be warned!


text:
Q: Limit a table's cell's values to two values? I have a two-column table but I want all values in the first table to be either X or Y, and no other input should be allowed. How can I enforce this?

A: You can use a validation rule.
Restrict data input by using a validation rule
A Validation Rule on the column as follows will work.
="X" Or ="Y"

A: You might want to look at

*

*Create a validation rule to validate data in a field

*Validation rules


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These pens produce an ink that is only visible under UV light (black light). You can use one of these to add hidden clues or coordinates to your caches. They are permanent markers and will easily write on paper, card, and most other surfaces.
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text:
Mario Antonio Fara
Chemistry Manager
Antonio graduated in Chemistry from the University of Sassari (Italy) in 2003. He then joined the research group of Professor Mark Bradley at the University of Edinburgh (UK), where he obtained his PhD in Chemistry. After gaining work experience in different companies, Antonio joined DESTINA in September 2014 with the responsibility for chemistry development. Antonio has many years of experience in the design and synthesis of peptides, peptide nucleic acid (PNA) and small molecules.
Jan Groen
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Co-Founder and Executive Director
David Whitcombe
Mavys Tabraue Chavez
Assay Development Manager
Juan Enrique Cruz Romera
Legal Representative of DESTINA Genomica S.L.
Salvatore Pernagallo
Margaret Ilyine
Francisco Javier Lopez Delgado
Chemistry Scientist
Juan Jose Guardia Monteagudo
Antonio Marin Romero
Assay Development Scientist
Barbara Lopez Longarela


iPlant with Brigitte Mars is a wild plant medicinal reference that delivers accurate, dependable information on North American edible, medicinal, and poisonous plants.
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Wild plants are both beautiful and useful. Use this wild plant medicinal reference to begin your journey towards understanding and self-sufficiency.
Please note this reference is intended for educational purposes only. Plants can be powerful, so please be responsible and consult your doctor or registered herbologist before using any wild plant. Never use a plant or herb that hasn't been identified by a trained expert. Please share the Earth and harvest responsibly.


text:
Ца́о Шо (, род. ) — китайский легкоатлет, чемпион Азии и Азиатских игр.

Биография
Родился в 1991 году в Баодине провинции Хэбэй. В 2010 году стал чемпионом Азии среди юниоров и завоевал бронзовую медаль Азиатских игр. В 2012 году завоевал серебряную медаль чемпионата Азии в помещении, но на Олимпийских играх в Лондоне не смог завоевать наград. В 2013 году стал чемпионом Азии и серебряным призёром Восточноазиатских игр. В 2014 году стал чемпионом Азиатских игр.

Ссылки

Прыгуны тройным Китая
Легкоатлеты на летних Олимпийских играх 2012 года
Чемпионы Азии по лёгкой атлетике
Чемпионы Азиатских игр по лёгкой атлетике
Легкоатлеты на летних Олимпийских играх 2016 года


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Sequencing Education Center
Genetic Testing for Disease
What Is a Genetic Disease
Outsmart Your Genes
The Power of DNA Testing and Predictive Medicine
Importance of Whole Genome Sequencing
What Can Whole Genome Sequencing Detect
Whole Genome Sequencing Cost
Whole Genome Shotgun Sequencing
A Guide to DNA Tests
What Is a DNA Test
How Does DNA Testing Work
What Does a DNA Report Look Like
How Accurate Are DNA Tests
What Diseases Can Be Detected Through Genetic Testing
How to Choose a DNA Test for Diseases
Genetic Testing for Baby
Genetic Testing During Pregnancy
Genetic Testing for Autism
Genetic Testing for Breast Cancer
At Home Genetic Testing for Breast Cancer
Breast Cancer Genetic Testing Cost
Breast Cancer Genetic Testing: Pros and Cons
DNA Tests for Breast Cancer Genetic Testing
Effects of Medicine on the Body
How Long Do Side Effects Last
How Quickly Do Side Effects Happen
How to Reduce Side Effects of Medicine
DNA Tests for Medication Side Effects
What to Do When Medicines Have Side Effects
Genetic Testing for Weight Loss
Does DNA Work for Weight Loss?
Guide to a Weight Loss DNA Test
DNA Testing for Weight Loss Diets
Coronavirus and DNA
My DNA and COVID-19: What's My Risk?
Blood Type and COVID: Infection Risk and Severity
Where Can I Get My Blood Type Checked for Free
By Dr. Brandon Colby, MD, a medical expert specializing in clinical genomics, genetic testing, and personalized preventive medicine.
This is the second article in Sequencing.com's Education Center section: Genetic Testing for Diseases. In the last article, you learned about how genetic testing was used to identify diseases and how to choose a DNA test for diseases. In this article, you will learn how genetic diseases occur.
Genes play an important role in shaping who we are and what we experience in life. Scientists have worked for many years to bring to light the information genes contain that have such a huge influence on our future.
One of the areas of study genomic researchers have focused on is genetic diseases. Understanding what is a genetic disease can help you realize how incredibly important it is to know what you may suffer from during your lifetime.
Starting with the Basics: What Are Genes?
Understanding how genes work will give you a better appreciation of what is a genetic disease. Living organisms are made up of cells that have a substance called deoxyribonucleic acid (otherwise known as DNA).
DNA includes four chemicals:
1. Adenine
2. Thymine
3. Cytosine
4. Guanine
These chemicals are often referred to as A, T, C, G. These coiled strands are found in cells, and they are so tiny that it cannot be seen without a microscope. These DNA strands are about six feet long and there are billions of them in the body.
Genes are made up of A, T, C, G, and how they are put together dictates the functions of the body. For instance, genes help produce enzymes that aid in digestion and pigment to give eyes a particular color.
DNA wraps together inside of the body. Each wrapped DNA is called a chromosome. There are 23 pairs of chromosomes, which means there is 46 total.
When a baby is conceived, the woman's egg holds 23 individual chromosomes and the man's sperm holds 23 individual chromones, giving the fetus 23 paired chromosomes. These chromosomes are identified as X and Y. A male child received an X chromosome from the mother and a Y chromosome from the father. A female child gets an X chromosome from each parent.
Genes (segments of DNA) are on the chromosomes. Since there are pairs of chromosomes, there are two copies of each gene. The only exception is that boys may have only one gene on the X and Y chromosomes.
A person's characteristics come from a single gene or combination of genes. Since the body has around 25,000 different genes, the possible combinations of them are endless. This is why every single person is so unique.
Inheriting Genes and Genetic Disorders
Hereditary is passing genes from one generation to the next. Parents pass on their genes to their children. Those genes make up who people are and how their body functions.
Unfortunately, some genes can mutate or change. Genetic mutations can cause a gene to not do its job. Since there are two genes though, the unmutated one can usually end up doing the other gene's job. This is referred to as an autosomal recessive trait. If the second gene cannot do the job of the first gene, recessive diseases or characteristics may result.
There are two types of genes - recessive and dominant. Dominant genes will show their character despite the other gene being mutated.
For instance, if one gene increases the chances of heart disease while the other one doesn't if that other gene is dominant, the person is at a much higher risk for suffering from it. This is referred to as an autosomal dominant gene.
Not all gene mutations that can lead to diseases are inherited. Gene mutations can occur over time in a person's life due to environmental factors.
Gene mutations are not as common as many people believe because cells recognize environmental hazards and are quick to repair the damage. Unfortunately, they aren't always successful which is why some suffer from cancer even though there isn't a family history of it.
What Is a Genetic Disease?
A genetic disease is a medical condition caused by a gene mutation. The National Human Genome Research Institute has found more than 4,000 gene mutations that cause certain diseases.
What's important to know is that just because someone has a gene mutation, it doesn't necessarily mean that person will suffer from a disease or condition.
People carry about 5 to 10 gene mutations in their cells. Medical issues occur when the mutated gene is dominant or when recessive genes pair. Specific gene variants can interact that can increase the susceptibility to diseases as well.
Since every person inherits genes from their parents, the chance of suffering from a disease is at least 50% if the parent suffers from it. If a particular gene for a disease is inherited from the father and mother, the chances are very high the child will suffer from it.
Some diseases are caused by dominant genes, which can be difficult to avoid without preventive treatment, such as:
Recessive genes are different. A person can have a recessive gene for a disease and not suffer from it. However, that recessive gene can be passed on to a child. If the other parent also has that recessive gene, passes it on and it pairs with the other parent's recessive gene, that's when a single gene disorder occurs - such as Tay-Sachs disease, Cystic fibrosis, or sickle cell anemia, or sickle cell disease.
Recessive gene mutations on the X chromosome can be worrisome for males because they only have one X chromosome. Since females have two X chromosomes, they have a backup one that can do the job of the first one if it's mutated.
This is why males are more likely to suffer from color blindness and hemophilia since those are conditions that occur on the X chromosome.
Another genetic disorder that can occur is when a child gets too many or not enough chromosomes. An example of this type of genetic disease is Down syndrome in which the child ends up having an extra chromosome - number 21. Edward's syndrome or Trisomy 18 is another condition that results from an extra chromosome that causes developmental delays.
Genetic Testing for Genetic Diseases
Genetic diseases can be a concern for parents and family members, which is why many decide to have a carrier screening or prenatal genetic screening. A genetic test can identify gene mutations that could result in suffering from a medical condition, birth defect, or other abnormalities
Taking a DNA test to identify possible gene mutations is something that can be done at any time in a person's life. However, to understand the possibility of a child suffering from a particular health concern, genetic testing should occur before two people decide to have a baby but genetic testing during pregnancy is also possible.
Genetic testing for diseases can be done after birth as well. While genetic testing of parents can identify any possible issues that could result from conceiving after birth shows what the baby has inherited.
Preventive measures can be taken for most medical concerns to lower the risk of genetic diseases. Geneticists can help with this as soon as someone is born, and it's something that many parents do for their children who have a high risk of suffering from a genetic condition.
There's much more you can learn about genetic testing and diseases, such as What Diseases Can Be Detected Through Genetic Testing.
Dr. Brandon Colby MD is a US physician specializing in the personalized prevention of disease through the use of genomic technologies. He's an expert in genetic testing, genetic analysis, and precision medicine. Dr. Colby is also the Founder of Sequencing.com and the author of Outsmart Your Genes.
Dr. Colby holds an MD from the Mount Sinai School of Medicine, an MBA from Stanford University's Graduate School of Business, and a degree in Genetics with Honors from the University of Michigan. He is an Affiliate Specialist of the American College of Medical Genetics and Genomics (ACMG), an Associate of the American College of Preventive Medicine (ACPM), and a member of the National Society of Genetic Counselors (NSGC).