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September 03, 2015 Updated 13:57 GMT
Homepage : Features
Homepage : Features : From Darfur to Calais: One refugee's story
Imogen Lambert
From Darfur to Calais: One refugee's story
"The jungle" in Calais [Getty]
Date of publication: 3 September, 2015
Feature: Souliman Keir, currently in Calais, is going to desperate lengths to reach the UK. Here, he shares the story of his journey from Sudan.
refugee, crisis, Calais, Sudan, UK, jungle,
For the past five months, Souliman has been living in a make-shift refugee camp in Calais, commonly referred to as "the jungle", along with another estimated 4,000 refugees.
Leaving Sudan was not "a decision" for him. Desperate hardship in his home country drove him to live in these conditions in France, as he desperately tries to reach the UK.
"I had to leave Sudan - none of us had a choice," he said. "We felt we had to run, there was killing and people destroying land."
Keir is a member of a tribe from Darfur, in the west of Sudan. Due to fighting between the indigenous population and the government, Darfur has been in a state of emergency since 2003.
There were 19.5 million refugees worldwide
at the end of 2014 [Getty]
"My father disappeared when I was four - it was difficult for us - we moved from one village to another," said Keir.
Despite a difficult childhood, he did well in school and was able to attend Sudan University in Khartoum and study in the engineering faculty.
"I was very active - I started in societies which attempted to do things like spread peace through education," he told al-Araby.
Darfuri students in Khartoum play an important part in political activism in Sudan, but they have been increasingly targeted by government campaigns to restrict their work.
Keir said he was targeted by under-cover intelligence officers posing as friendly students, attempting to solicit information and even recruit him into government service.
However, due to witnessing the disaster of Darfur - where the UN estimates 300,000 were killed and a further 3,000,000 displaced - Keir had other ideas.
"I didn't politically support the government in Sudan and didn't want to work for them after I graduated," he said.
After Keir finished his degree, he was unable to obtain his certificate, and no one would give him a clear reason.
While he and other Darfuri students were protesting this mistreatment, they were taken into a police station, questioned, and security services created a "file" for him. From that point, he says, his problems escalated.
Keir went on to launch alrahma, meaning "mercy", a small association which aimed to help the local community.
The group was involved in activities to alleviate problems plaguing Darfuri neighbourhoods, including making containers to collect rain water, helping with rebuilding, giving out books, and collecting money from business owners to help fund their activities.
The government refused to register the organisation.
"They suspected it was political," Keir said. "It wasn't, it was just a charitable organisation."
One day, while Keir and other members of his association were travelling from Khartoum to Darfur's el-Fasher refugee camp, they were detained in an airport.
"They took all our equipment and laptops. We were detained in the airport for a while, and taken to another place around 50 minutes away," he said. There, they were interrogated.
"They kept telling us: 'you are accused of crimes against the country'," Souliman said. "They asked where we live, what we wanted... they accused us of taking information from Khartoum to rebels in Darfur.
"They accused us of being spies and rebels and were treated very badly - we were beaten, and not given any food, they threatened to kill us," he said.
"When they were torturing me I didn't know if I was dead or alive - going in and out of consciousness… I stayed in the prison for two months - my family didn't know what happened to me."
When Keir left prison he fled the humanitarian crisis and his personal political difficulties in Sudan and walked hundreds of miles to Libya - the first stage of his perilous journey.
Reaching Europe
"I was caught twice in Libya by gangs with guns - the first time I paid them with money, the second time I was in a car and the gangs shot the driver in the chest," he said.
Reports of kidnappings of refugees in Libya are very common, and are often aimed at extorting money or forcing refugees to work in camps. However, despite the dangers, Keir continued.
"I couldn't go back to Sudan," he said. "Back home they took my brother and questioned my family over where I was."
An Afghan flag flies above
some of the makeshift shelters [Getty]
Yet making the dangerous crossing from Libya to Italy took several attempts before he made it to Europe.
"It's destiny, if you are lucky you can succeed," said Keir.
He lost money after a middle man for a smuggler failed to pass the money to his boss. The second time he attempted to travel, the boat started sinking.
"We were a tiny boat of 100 people - one side was broken... it was very dangerous," Keir said. "One of the times we tried to cross, the boat was broken and water was coming in and air was coming out."
Keir said that refugees making the crossing were given a phone and the number for the Italian coastguard. As the boat was sinking, one of the passengers made the call.
The boat was judged to be outside the jurisdiction of the search and rescue team.
"Sometimes you call and maybe they will come, maybe not. Maybe the next day," said Keir.
Fortunately, the boat drifted back to land - in neighbouring Tunisia.
After walking back to Libya (again), they boarded a sea-worthy boat packed with 500 people.
When Keir finally arrived in Italy he ran from having his finger-prints taken - so as to avoid the effects of the Dublin Regulation, the EU deal which agreed that refugees must apply for asylum in the first EU country they arrive in.
"I needed to sleep in the street with no money - I took a train to the border of France, hiding in the bathroom," he said.
He arrived in Nice exhausted and hungry. He found a meal in a mosque and continued his journey.
"It is not easy to take a train from Nice to Paris, and I should be very careful because there are a lot of controls and if you are caught by the police your fingerprints are taken," he said.
He therefore took a roundabout route to Paris, via Marseille and Lyon, before venturing on to Calais.
He lives in the camp known as "the jungle", which has become a make-shift home to thousands of refugees who hope to travel to Britain.
"We are living in shelters of plastic that we build ourselves, and take the materials from organisations," he said.
It sometimes it takes a long time to receive materials to build a shelter, and new arrivals to the camp sleep in the open air.
The refugees use a local centre which provides food and allows them to charge their phones. Keir says the refugees wait for hours to use the centre's facilities.
Crossing the Channel
Keir has tried multiple times to reach the UK from Calais on the back of trucks.
"We go where the trucks are… We should be careful not to be seen," Keir says.
"We read the registration plate and check the addresses on boxes in the truck to see if it's going to the UK," he said.
"If it is, we climb in a box, as far away from the door as possible, cover ourselves with clothes. It's good to be as a team - so people help each other.
"There are three checkpoints - two French and one British - the British one is the most difficult to cross. If you are lucky you will pass," he said.
However, the measures are making it increasingly hard for refugees to get through.
Hiding inside freight trucks gives one route to Britain [Getty]
"If they find anyone [in one load of trucks] they check all the trucks with lasers - you feel the rays when they use this."
When the trucks are being X-rayed, those inside move around quickly, trying to avoid detection.
"We try to change our place, and quickly go back to the same place," he said.
"Another way is to enter is between the wheels of the truck [clinging to the axle]," Keir said.
"I think Sudanese people are the only ones who try this. We lie down in between the wheels with warm clothes and hold on tight - its very dangerous," he said.
"Calais is different now - one year ago when the police caught you, they put you in detention and released you - but the police are not kind and don't treat you well."
He says the French police use many tactics to attempt to prevent the migrants from gathering in Calais.
"Sometimes they put us in a car and drive us far - almost to Belgium, they even put people in planes," Keir said.
As reaching the UK by truck becomes more difficult, and as the truckers' strikes have ended, many are attempting to use trains - which involves hiding until a train comes near.
Then ensues a race to the train, away from police attempting to stop them from boarding.
Although some have now decided to attempt to stay in France, Keir is determined to reach the UK.
"They say that life is better and they take care of you from the beginning and its quicker to do your papers," he said.
Family and language ties provide another appealing support network.
"A friend who lost many members of his family is trying to go to the UK to see his sister, he doesn't care what happens to him until then," Souliman said.
"The situation is very tough and very bad, days pass by very badly."
One refugee's journey from a Syrian prison to London
Blog: Revolution, prison and torture on the road from Damascus.
A tale of two brothers
Feature: Nasr and Sabr were determined to leave Syria and reach Sweden to claim asylum. But getting there was a gamble with death itself.


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Q: Cannot catch click event on FeatureLayer in ArcGIS API for JavaScript 4? I've got a SceneView with a FeatureLayer, and I'm trying to catch every click on a PictureMarkerSymbol to display additional data under the map.
The map works well, so do symbols and popups, but I never catch any event, am I missing something?
require([
    "esri/Map",
    "esri/views/SceneView",
    "esri/layers/FeatureLayer",
    "esri/renderers/UniqueValueRenderer",
    "esri/symbols/PictureMarkerSymbol",
    "dojo/on"
], function(
    Map, SceneView, FeatureLayer, UniqueValueRenderer, PictureMarkerSymbol, on
) {

    var map = new Map({ ... });
    var view = new SceneView({ ... });

    view.then(function() {

        var renderer = new UniqueValueRenderer({ ... });
        var pins = [...];
        pins.forEach(function (element) {
          renderer.addUniqueValueInfo(element,
            new PictureMarkerSymbol({ ... })
          );
        });

        layerMarkers = new FeatureLayer({
            title: "Labels Layer",
            url: "...",
            definitionExpression: "...",
            renderer: renderer,
            outFields: ["*"],
            popupTemplate: { ... }
        });

        layerMarkers.on("click", function (evt) {
            console.log(evt.graphic.attributes);  // No output??
        });

        map.add(layerMarkers);

    });
});

A: I finally figured out how to catch these events.
I'm not allowed to listen for click events on a FeatureLayer, nor on a Map, but I still can listen it on my SceneView, and use the hitTest() function to get the related symbol:
// Listen for SceneView click events
view.on("click", function (evt) {
  // Search for symbols on click's position
  view.hitTest(evt.screenPoint)
    .then(function(response){
      // Retrieve the first symbol
      var graphic = response.results[0].graphic;
      if (graphic) {
        // We now have access to its attributes
        console.log(graphic.attributes);
      }
    });
});

redpajama_set_name: RedPajamaStackExchange


Anyone who tailgates on a regular to semi-regular basis has seen them; limos in every size, shape and color at their favorite sporting events. And while it might not make much sense to some onlookers, those who have discovered limo tailgating, will be the first to agree… when it comes to cheering on your team in true luxury, nothing else even comes close.
There are so many valid reasons to consider hiring a limo for your next tailgate party. Aside from all of the conversations you'll be sure to inspire around you, an SUV or Hummer H2 limousine can serve as the perfect combination of outdoor fan fun, and the prestige and convenience of being surrounded by absolute total luxury and convenience.
If you've never seen the inside of a tailgate-ready stretch limo, you're in for both a shock and a treat. Regardless of which vehicle you select for game day, be it a Hummer H2 limo, a stretched monster truck, or even an exotic bus or Coach limo, you will be amazed at how spacious they are from the inside. It's common to forget that you're actually in a vehicle, while en route to the stadium or event center. But that all changes when you notice the stares of awe from curious vehicles and onlookers.
One of the beauties of taking a limo to the big game, is that there are so many options to make your event uniquely your own. If it's a guy's adventure, you might want to consider a Hummer H2 limo, a Yukon Denali, or a stretched heavy-duty pickup. On the exact flipside, if you're heading to the game with just the ladies, a pink H2 limo or something with a more female-themed appearance is sure to be a hit.
When you hire a limo for your tailgate party, not only will you be the talk of the stadium, you'll also have the peace of mind in knowing that your entire group is assured a safe, timely transport. Our drivers have many years of experience chauffeuring for sporting events, and will do everything they can to make you feel like a VIP.
If you're in the Syracuse or Western NY area, and would like more information on hiring a limo for your group's next tailgating adventure, call the experts at Syracuse Bus Limo., one of the most trusted and reputable limo companies in WNY.


"40 years of X-ray bursts: Extreme explosions in dense environments" is a workshop to be held at the European Space Astronomy Centre (ESAC) on June 17-19, 2015.
The aim of this workshop is to bring together world-leading experts (both theoreticians and observers) on Type I X-ray bursts in accreting neutron stars. The goal is to assess the status of the topic and define new challenges for our understanding of X-ray burst physics. The workshop will deal with our understanding of X-ray bursts as a standalone phenomena as well their connection with the surrounding environment, for example in relation to internal heating and cooling of the neutron star or accretion physics.
In order to encourage discussions and maximize collaborations, the attendance to the workshop is limited to about 40 people.
There is no workshop registration fee.
Stable/unstable burning on neutron stars - How does accretion play a role, and what are the left-overs?
Variability and X-ray bursts - What do oscillations, QPO, mHz QPO during bursts tell us?
Their relation to the external/internal environment - How do X-ray bursts influence the accretion disk and/or corona, as well as the inner neutron star (e.g., crust heating/cooling, seismology)?
Theory of X-ray bursts - How well do we understand X-ray bursts (flame spreading, nuclear physics, hydrodynamics, model atmospheres, etc.)?
Future of X-ray burst science - What should we learn from new observations (ASTROSAT, LOFT, NICER, etc.) and new model calculations (KEPLER, MAESTRO, ODT, etc.)?


RANCHO MURIETA, Sacramento County (October 26, 2018) – A motorcyclist was seriously injured after a traffic collision in the area of Jackson Road and Murieta Drive Friday, according to California Highway Patrol dispatch team.
The accident took place at approximately 4:20 p.m. near Sacramento Metro Fire District Station 59.
CHP received a call about a Harley Davidson motorcycle and a vehicle which collided for an unknown reason at the intersection of Jackson Road and Murieta Drive. Jackson Road is also known as Highway 16.
Sacramento Fire Department officials along with the paramedics responded to the scene and found the rider and the bike on the right hand shoulder as a result of the crash.
The patient was then transported to UC Davis Medical Center for treatment of major injuries. The name and condition of the motorcyclist at this time remained unknown.
Meanwhile the car involved, described as a blue Chevrolet Camaro, sustained front-end damage upon impact. Authorities are still investigating the cause of the incident.
A forensic examination of both the motorcycle and the Chevrolet Camaro, as well as photos that were taken of the scene, will help investigators determine the cause of the crash. Authorities will thoroughly look into how fast each driver was going, whether or not alcohol or drugs played a role, whether or not there were any mechanical issues with either the bike or the car, and whether or not one of the drivers involved was distracted or did not yield to the right of way motorist. The investigation will also consist of looking at measurements of evidence left by the motorcycle or the vehicle such as point of impact, their final resting positions, skid marks, and gouge marks.


Second Street Gallery presents drawings by Los Angeles–based artist Aaron Noble, whose dynamic imagery is inspired by comics, muralism, and graffiti.
Check out (and download) our January Activity book!
Check out (and download) our January activity book based on the works featured in "Fly Away" by Raushan Rucker and "Contested Bodies" by Matt Shelton and Nikolai Noel.


No, this is not a photo shoot. Gisele Bündchen dug her feet into the sand in Costa Rica last week, when she took her daughter, Vivian, to the beach for some fun in the sun.
Gisele revealed her svelte figure in a teeny-tiny bikini, taking a moment to stretch as she took in the picturesque ocean view. Meanwhile, Vivian played with a doting dog and a surfer pal, who picked her up as the water swept beneath her.
Gisele kicked off the Costa Rican fun over the weekend with a bikini photo shoot for H&M, which she followed up with a controversial helmet-free ATV ride with Vivian.
Tom Brady had a good reason for missing the family beach getaway. Tom and his Patriots were busy losing to the Denver Broncos in the AFC Championship game Sunday.


text:
Francesco Bracotti (born January 16, 1995 in Turin, Italy) is a professional racing driver from Italy who competes in single seaters.

Racing career

Karting
Bracotti was 4 years old when he tasted the asphalt the first time, on the go-kart circuit of Cattolica.
After years of amateur experiences between 50 babykart and 60 minikart he jumped to 100 junior category and started doing in 2008 the Piedmont regional championship, ending it in the 1st position.
In 2009 he took part to the Open Masters in the KF3 category and in some races of the WSK championship. He also participated in prestigious international events as Margutti and Industries trophies.
In 2010 he became an official driver of the Tecno Kart team and took part in the World Championship U-18 established by FIA.
Here he stood out with its capacities, in particular on the Spanish circuit of Aragon.
In 2011, again as a bearer of Tecno Kart he took part to the European Championship in Kf2 and, as the previous year, in the World Championship U-18.

Formula Renault 2.0

In 2012 Bracotti starts his single seaters career taking part in the Italian Formula Renault 2.0 championship as a driver of the team "Green Goblin by Facondini". In the first collective tests he immediately stands out as a competitive driver for the season.
In Monza, the first meeting of the championship, he gets a seventh and a fourth place; same placement in which he ends the first of the two races in Imola, where he also obtain the fastest lap.
Bracotti goes for the first time on the podium at the Red Bull Ring, in the second of the two races of the weekend. The Italian driver finished the first race in the fifth place, despite starting from the pit lane because of a technical failure, after having obtained the third position in the qualifying practise.
The race in Vallelunga is signed by two retires for Bracotti, who started from the first row in race-1 and was coinvolved in an accident at "cimini" corner.  In race-2 a technical failure to the rear suspension forced him to stop the car.
In end of the championship another retire, caused by engine problems,  in Mugello Circuit made he 4th in the junior ranking, in which he fought for the first position.

Racing Records

Career summary

Formula Renault 2.0 results

References and notes

External links

1995 births
Racing drivers from Turin
Living people

redpajama_set_name: RedPajamaWikipedia


Site Map - an exhaustive list of the pages on this site . . .
Water Rocket Index - build your own and predict the results at minimal cost. Featured on the . . .
Real Rockets . . .
Look at the pictures - I don't know how long it stayed up for but it went 270 feet down range.
2 stage - made from 2 x litre and 2 x 3 litre bottles.
Water Rocket Computer Model - Program available for Download - Postcardware.
Screen Shots and Details. Choose your design specification without getting wet.
Also, Download the Palette Editor program for the model to customise the 3D optimisations.
Also, Download the HTML Help pages in four languages (English, Portuguese, Spanish and Chinese) for the model.
View the Help Pages (English version) online.
Look at how an equation is "built"
Nose Separates at Apogee (NSA) - very simple to construct and easy to use.
Rubber ball nose - effective, simple and easy.
Water Rocket Index Site Awards Pages: 1; 2; 3; and, 4.
Are things getting a little Weird where you are? - Precautions for you at work - maybe there are some things that you should not know.
Microsoft Flight Simulator UFO model with Panel and Sounds - Free Download.
UFOs - What do you think?
Internet Security. A taste of what I write about - if you want me to write for you, go to the e-mail link on the page.
PC and MAC Joke Wallpaper pages.
and the Live Link to BBC World Service via Broadcast Com.
Copyright 1998 - 2003 P.A.Grosse.


text:
Вільнюський караїмський цвинтар — кладовище караїмів в Литві за адресою: Вільнюс, вулиця Жирню, 19.

Засноване в 1904 році на землі площею 500 квадратних сажнів, що була виділена Міською управою Віленському караїмському товариству. Цвинтар знаходиться поруч з Татарським (магометанським) кладовищем. Кладовище невелике: його площа становить приблизно 70x70 метрів. Приблизно третина цієї площі, зліва від входу, займають татарські могили, а дві третини справа — караїмські. Ділянки розділені ровом до 0,5 м в глибину і понад 1 м в ширину. На татарській стороні могили з зірками та півмісяцями. Орієнтація — із заходу на схід (в сторону Мекки). На караїмській стороні орієнтація могил з півночі на південь (у бік Єрусалиму). Караїмське і Татарське кладовища розділені земляним насипом (валом).

На караїмських надгробках, споруджених до 1930-х років, всі написи зроблені івритом і польською мовою. На передньому плані — могила Фелікса Малецького. На більш пізніх пам'ятках написи російською мовою, але на деяких є також і декілька слів караїмською. Так, на надмогильних камені батька і сина Кобецького зроблено напис караїмською мовою «яхшы учмах!» — «прекрасного раю!», а на могилі Катерини Юхневич (1895-1979) є такий напис: «ярых сагынч» — «світла пам'ять».

На кладовищі похований відомий вчений-сходознавець і караїмський громадський діяч Серая Маркович Шапшал.

Примітки

Караїми
Цвинтарі Вільнюса


text:
Asus VivoBook X507 (EJ215T) Review: Affordable laptop but with one hiccup too many
Asus VivoBook X507 (EJ215T) laptop review: We put it to test in terms of performance, in addition to design, display, keyboard and more.
Written by Tanmay Patange | Mumbai | Updated: June 12, 2018 6:32:30 pm
Asus VivoBook X507 with 15.6-Inch Display and up to 8GB of RAM was announced in India last month at a starting price of Rs 27,990. Asus has partnered with Paytm to sell their VivoBook X507 exclusively on Paytm Mall. Recently, Asus sent a 4GB RAM variant with Intel Core i3-6006U for review, and to be honest, it has been a turbulent journey with the laptop so far. Here is how Asus VivoBook X507 turned out to be during our review:
Asus VivoBook X507 price in India and availability
Asus VivoBook X507 with Intel Core i3-6006U and 4GB RAM costs Rs 27,990. The laptop is available to buy exclusively on Paytm Mall.
Asus VivoBook X507 features and specifications
15.6-inch (1,920 x 1,080 pixels) Full HD screen | Windows 10 Home | 364.8 x 266.4 x 21.9 mm dimensions | 1.68 kg | Intel Core i3-6006U running at 1.5GHz | Intel HD Graphics 520 | 4GB RAM | 1TB HDD | Connectivity: Wi-Fi, Bluetooth 4.0 | Ports: 2xUSB 2.0, 1xUSB 3.1 Type-A, 1xHDMI, 3.5mm headphone jack and MicroSD reader
Asus VivoBook X507 Review: Design and display
Asus VivoBook X507 sports a 15.6-inch (1,920 x 1,080 pixels) Full HD screen, which is a rare sight for any budget laptop that is priced under Rs 30,000, which is impressive. Again like the one I found previously on my Asus VivoBook S14 review unit, this one features an LED screen. So fortunately enough, I had no complaints about the screen being reflective or causing any glaring distractions whatsoever, which often tends to be the case with budget laptops.
Asus VivoBook X507 Review: The keyboard has a textured surface which feels nice to look at. Bezels around the screen are slim, resulting in more real-estate and screen-to-body ratio.
The design is fairly simple. The laptop feels reasonably light at 1.68kg, which is quite good for one that offers a 15.6-inch screen. Asus has tried to do something unique here with a wave-like top keyboard edge. The keyboard has a textured surface which feels nice to look at. Bezels around the screen are slim, resulting in more real-estate and screen-to-body ratio. Oddly, Asus has put the speakers on the bottom, which I personally find weird. But more on that later.
The VivoBook X507 has two colour variants: Icicle Gold and Star Grey. We got a Star Grey variant for review. It features a fingerprint reader that works flawlessly.
Asus VivoBook X507 Review: Performance and benchmarks
Asus sent a 4GB RAM variant of the VivoBook X507, which runs Windows 10 Home OS and Intel Core i3-6006U CPU under the hood. It also comes with an integrated Intel HD Graphics 520 unit based on Intel Skylake microarchitecture, which was released back in 2015. Although 4GB RAM laptops run just fine with Windows 10 (at least in the beginning), Asus VivoBook X507 is a whole different story. During my brief usage over the last couple of weeks, the laptop was barely usable most of the times. Boot time was longer than usual.
I remember at once instance, the laptop took around 10 minutes to boot. On top of that, Google Chrome tabs would freeze all of a sudden. In that case, all I could do was go to task manager and end the tasks manually before restarting them. To be doubly sure about the whole performance crisis, I decided to deep-clean the laptop once again, hoping to start using it from scratch and getting rid of the problem. But to my disappointment, the laptop showed no sign of improvement at all even after a reset.
Asus X507 Review: Web pages used to be unresponsive and take longer to load. Similarly, switching between the tasks was as troublesome as everything else.
Soon after setting it up, I looked into Task Manager to figure out what could be causing the performance slowdown. I came across certain resource-intensive background processes that were consuming a massive amount of hardware resources, thus leading to performance slowdown to an extent where nothing was usable. Web pages used to be unresponsive and take longer to load. Similarly, switching between the tasks was as troublesome as everything else.
Strangely gaming experience was not bad on this laptop. I tried a few 3 to 4-year-old games that are not overly resource-hungry like Insurgency. Though they ran just fine, the overall experience was not buttery smooth. I could observe an occasional lag but not as bad as it was during browsing. But again, this is not a gaming laptop, and there was nothing much to complain either given that it runs Intel HD Graphics 520.
Asus VivoBook X507 Review: Asus VivoBook X507 left me disappointed with the kind of performance that is simply not expected from a laptop that costs almost Rs 28,000.
I ran a few benchmark tests to see how the VivoBook X507 fares. The laptop recorded a Novabench score of 642. Novabench's baseline comparison also revealed that the overall score is 11% lower than budget laptops with Intel Core i5-7200U CPU and Intel HD Graphics 620. CPU score, on the other hand, was 23% lower. But surprisingly enough, the GPU score is 47% higher than average budget laptops running on Intel HD Graphics 620.
Overall, Asus VivoBook X507 left me disappointed with the kind of performance that is simply not expected from a laptop that costs almost Rs 28,000. Although I am not sure if the problem is limited to our particular review laptop, it is hard for me to recommend the VivoBook X507 to anyone as far as the day-to-day performance is concerned.
Asus VivoBook X507 Review: Keyboard, sound and battery
Typing experience on Asus Vivobook X507 is fairly average. Keyboard travel distance is short, which results in faster keystrokes. But it also increases the chances of making mistakes especially if you happen to be someone who is used to standalone keyboards. Additionally, I found it weird at first given that I am pretty much used to my personal laptop Dell Vostro 15 3558, which has a full-sized, more comfortable keyboard. But once I got used to this Asus, my typing experience got significantly better and I could type much faster.
Asus has a dedicated numeric keypad, however, unlike the traditional numeric pads, the key for number '0' is smaller. So more often than not, I ended up pressing './delete' key, which is situated right below the key for number '2.'
Asus VivoBook X507 Review: Keyboard travel distance is short, which results in faster keystrokes. But it also increases the chances of making mistakes especially if you happen to be someone who is used to standalone keyboards.
Sound experience is decent enough for its price. But given the fact that the Asus X507U has bottom-firing speakers, the sound gets muffled and you feel a vibration while typing, causing annoyance.
As for the battery performance, it manages to deliver up to 2 hours of backup while typing on Google Docs, having 10 different tabs opened on Google Chrome in the background and the screen brightness level set to maximum. I streamed Guardians of the Galaxy at 1080p on Netflix with screen brightness and sound level set to maximum, and the laptop could last close to 1 hour on a single charge. If you do absolutely nothing and keep the laptop idle with screen brightness level set to minimum, it can easily last up to 8 hours. The battery performance figures aren't very impressive here.
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Asus VivoBook X507 Review: Conclusion
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Do remember that the kind of experience I have described here may be limited to the 4GB RAM variant or to our test unit. But it is what it is. Furthermore, it has a sub-par battery life, which is again a deal-breaker. So, till Asus manages to fix these problems, I wouldn't recommend this laptop.
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\section{Introduction}

Particle physics with carefully engineered non-plane-wave states of initial particles is an emergent field
whose full potential is still to be explored.
Although examples of quantum electrodynamics processes in which the non-plane-wave nature
of colliding beams played important role were known since 1980's \cite{Blinov:1982vp,Kotkin:1992bj,Kotkin:2003jz},
a renewed interest was triggered recently by the experimental demonstration
of the so-called vortex, or twisted, states of photons and, especially, electrons.
A vortex state refers to a monochromatic wave with a helicoidal, corkscrew-like, wavefront
arising from the azimuthal phase factor $\exp(i\ell \varphi_r)$.
Such a wave propagates, on average, along axis $z$ and, due to its swirling current density,
also carries a non-zero orbital angular momentum (OAM) $z$-projection, $\ell\hbar$ per quantum.

Vortex photons are known since decades \cite{Allen:1992zz,Molina-Terriza:2007,Harris:2015,Paggett:2017,Knyazev:2019}
and have become a basis of numerous applications \cite{Zhan:2009,Torres:2011}.
A decade ago, following the suggestion of \cite{Bliokh:2007ec}, vortex electrons were experimentally demonstrated
\cite{Uchida:2010,Verbeeck:2010,McMorran:2011}.
They are now routinely used to probe magnetic properties of matter at the atomic scale,
to excite plasmons, and to test behavior of twisted electrons in external magnetic fields,
see reviews \cite{Bliokh:2017uvr,Lloyd:2017}.
In the past few years, neutral particles such as neutrons \cite{Clark:2015,Sarenac:2018,Sarenac:2019}
and, very recently, atoms \cite{Luski:2021} were also put in vortex states,
opening new promising venues for fundamental physics and applications.

From the high-energy physics perspective, a particle prepared in a Bessel vortex state
carries definite energy, definite longitudinal momentum, definite modulus of the transverse momentum,
and a non-zero OAM.
This OAM represents a new degree of freedom, which can be imposed on the initial state particles
to get additional information about their structure and interactions.
In the past decade, several groups theoretically analyzed high-energy collision processes involving
one or two particles in vortex states \cite{Jentschura:2010ap,Jentschura:2011ih,Ivanov:2011kk,Ivanov:2012na,Karlovets:2012eu,Hayrapetyan:2014faa,Stock:2015yha,Serbo:2015kia,Ivanov:2016oue,Karlovets:2016jrd,Zaytsev:2017lnr,Karlovets:2017qda,Afanasev:2017jdf,Sherwin:2018dah,Afanasev:2019rlo,Ivanov:2019pdt,Ivanov:2019vxe,Afanasev:2020nur,Sherwin:2020vyq,Afanasev:2021uth,Afanasev:2021fda}.
Many non-trivial effects were predicted in these and other publications,
many of which are impossible to achieve in conventional (approximately) plane-wave collisions.
For an overview of such processes with vortex electrons, see review \cite{Bliokh:2017uvr} and references therein.
Also, going beyond vortex states, Refs.~\cite{Karlovets:2016dva,Karlovets:2016jrd} address collisions of particles in general non-plane-wave states,
showing yet more ways to probe particle structure and dynamics.

In this paper, we add yet another process to this list: the decay of vortex muon.
Although muons in vortex states have not yet been demonstrated, we believe it can be done in the near future.
Anticipating these experiments, we find it timely to theoretically explore the emerging physics opportunities.

When vortex muons are produced, one may want to explore their behavior in external electric and magnetic fields,
in particular in storage rings.
One may wonder whether and for how long the vortex state of the muon survives in external fields,
how the vortex parameters and the spin evolve,
and how this evolution is affected by the inhomogeneities of the magnetic field of the ring.
All these effects can be monitored through the decay of muons $\mu \to e\bar \nu_e \nu_\mu$,
which is a self-analyzing process \cite{Miller:2007kk}:
namely, the correlations between the spectrum and the angular distribution of the emitted electron reveal the orientation of the muon spin.
It is this self-analyzing property which lies at the heart of several generations of
experiments measuring the muon anomalous magnetic moment $g-2$ with increasing precision \cite{Miller:2007kk,Logashenko:2018pcl}.

In this paper, we study how the spectrum and the angular distribution of the electron
reveal the parameters of the {\em vortex} muon, including its polarization state.
We will show that the most sensitive observable is not the angular distribution but the electron spectrum at a fixed emission angle.
Even for very small vortex cone opening angles, this spectrum shows dramatic, easily observable features
which would allow one to distinguish the vortex state from an (approximately) plane wave muon
as well as differentiate among various polarization states of the vortex muon.

The paper is organized as follows. In the next section we briefly review the well known properties
of the plane wave muon decays.
We rewrite the classical results in a form convenient for vortex muon calculations.
In section~\ref{section-vortex-decay}, we remind the reader of how polarized vortex fermions are described,
derive analytical results for unpolarized vortex muon decays and study them with illustrative examples.
In the same section we analyze the decay of a vortex muon in various polarization states and show how they can be detected.
Finally, in section~\ref{section-discussion} we discuss the results, briefly mention experimental prospects,
and draw conclusions.

\section{Plane wave muons}\label{PW}

Muon decay is a standard process worked out in many textbooks \cite{Okun:1982, Donoghue:1992dd}.
When calculating tthe muon decay, we limit ourselves to the Standard Model and neglect the electron mass.
The four-momentum of the initial plane wave muon is denoted as $p^\mu$, its energy and mass are labeled simply as $E$ and $m$.
We will also use the unit vector $\vec n$ in the direction of the muon momentum, so that
$p^\mu = E(1,\, \beta \vec n)$, with $\beta$ being the speed of the muon in units of $c$ and $\gamma = 1/\sqrt{1-\beta^2}$ is its relativistic factor.
The final electron carries the four-momentum $k^\mu = E_e (1, \vec n_e)$. The two neutrinos with four-momenta $q_1^\mu$
and $q_2^\mu$ escape detection but their invariant mass $q^2 = (q_1 + q_2)^2$
affects the electron energy: $q^2 = m^2 - 2 (pk)$. In particular, the maximal electron energy
is attained when the two neutrinos are collinear, so that $q^2=0$ and $2(pk)_{\rm max} = m^2$.

A (pure) polarization state of a plane wave muon is described by a four-vector $s^\mu$
orthogonal to the muon four-momentum $(sp) = 0$ and normalized as $s^2 = -1$.
In the muon rest frame, $s^\mu = (0, \vec s)$, with $\vec s^2 = 1$, where $\vec s$ can be interpreted as the spin
of the muon. In the laboratory reference frame, in which the muon is moving, it can be written as
\begin{equation}
s^\mu = \bigl(\gamma\beta (\vec s\vec n), \ \vec s + (\gamma-1)\vec n(\vec s\vec n)\bigr)\,.
\end{equation}
The Standard Model calculation of the polarized muon decay width summed over the final state polarizations gives
\begin{equation}
d\Gamma_{PW} = \frac{G_F^2}{48\pi^4 E} \frac{d^3 k}{E_e} \cdot \left[(pk)(3m^2 - 4(pk)) - m(sk)(m^2 - 4(pk))\right]\,.
\label{PWresult}
\end{equation}
In the muon rest frame we have $E = m$, $\beta=0$, $\gamma=1$, $(pk) = mE_e$,
and the maximal electron energy $E_{e\rm max} = m/2$ independent of the electron emission angle.
In this frame, denoting $E_e = \epsilon E_{e\rm max}$, we switch to integration over $\epsilon$:
\begin{equation}
d\Gamma_{PW} = \Gamma_0 \cdot \frac{d\Omega}{4\pi} \cdot 2 \epsilon^2 d\epsilon [3-2\epsilon + (1-2\epsilon)\cos\theta_{s,e}]\,,
\quad \Gamma_0 = \frac{G_F^2 m^5}{192\pi^3}\,, \quad \cos\theta_{s,e} = \vec s\,\vec n_e\,.
\label{PWresult-2}
\end{equation}
Integrating over $\epsilon$ from 0 to 1, we obtain the angular distribution $1-(\cos\theta_{s,e})/3$ which reveals the forward-backward asymmetry
with respect to the spin orientation. Finally, integrating over all angles gives the total decay width $\Gamma_0$.

\begin{figure}[H]
	\centering
	\includegraphics[width=0.48\textwidth]{Eemax}
	\caption{The maximal energy of the electron in GeV as a function of the emission angle $\theta$ from the decay
		of a muon moving with $\beta = 0.5$.}\label{Fig-EmaxPW}
\end{figure}

In the laboratory frame where the muon is moving, one can express the spectral-angular distribution as
\begin{eqnarray}
d\Gamma_{PW} &=& \frac{G_F^2}{48\pi^4 E}\, E_e dE_e d\Omega\, \Bigl\{
3 m^2 E E_e(1-\beta\, \vec n\vec n_e) - 4 E^2 E_e^2 (1-\beta\, \vec n\vec n_e)^2 - m(sk) [m^2 - 4 E E_e (1-\beta\, \vec n\vec n_e)]\Bigr\}\,,
\label{PWresult-3}\\[1mm]
&&\mbox{where}\quad (sk) = E_e\left[\gamma\beta\, \vec s \vec n - \vec s \vec n_e - (\gamma-1)(\vec s\vec n)(\vec n \vec n_e)\right]\,.
\end{eqnarray}
In this frame, the maximal energy of the electron depends on the emission angle:
\begin{equation}
E_{e\,\rm max} = \frac{m^2}{2E (1-\beta\, \vec n\vec n_e)}\,,\label{Emax}
\end{equation}
which is illustrated in Fig.~\ref{Fig-EmaxPW}.
The electron spectrum extends up to the absolute maximum $E_{e\,\rm abs\, max} = m^2/(2E(1-\beta))$,
and, near this maximal value, only directions close to the muon direction contribute to the decay width.

If we are interested in the angular distribution integrated over all energies,
we can again define $E_e = \epsilon E_{e\,\rm max}$, integrate over $\epsilon$ from 0 to 1 for any given direction,
and present the angular distribution as
\begin{equation}
d\Gamma_{PW} = \Gamma_0\, \frac{d\Omega}{4\pi} \, \frac{1}{\gamma^3}\, \frac{1}{(1-\beta\, \vec n\vec n_e)^2}
\left[1 + \frac{\gamma\beta\, \vec s \vec n - \vec s \vec n_e - (\gamma-1)(\vec s\vec n)(\vec n \vec n_e)}{3\gamma (1-\beta\, \vec n\vec n_e)}\right]\,.
\label{PWresult-4}
\end{equation}
Integration over all angles yields the total decay width $\Gamma = \Gamma_0/\gamma$, which reflects the relativistic time dilatation.

Notice that, anticipating transition to vortex muons, we do not use angles defined with respect to a fixed coordinate frame
but express the angular distribution in terms of the three unit vectors $\vec n$, $\vec n_e$, and $\vec s$.
However for future reference we give the angular distribution of the muon moving alone axis $z$
and polarized along the same axis, $\vec s = \vec n$:
\begin{equation}
d\Gamma_{PW} = \Gamma_0\, \frac{d\Omega}{4\pi} \, \frac{1}{\gamma^3}\, \frac{1}{(1-\beta\, \cos\theta)^2}
\left[1 + \frac{\beta-\cos\theta}{3(1-\beta\, \cos\theta)}\right]\,.
\label{PWresult-4.1}
\end{equation}
In this expression, $\theta$ is the electron polar angle.

\section{Vortex muon decay}\label{section-vortex-decay}

\subsection{Describing a polarized vortex muon}\label{subsection-describing}

A vortex state of any particle can be constructed as a superposition of plane waves
organized in such a way that a straight line of phase singularity, identified with axis $z$, appears in the coordinate space.
There exist different prescriptions for constructing such a state.
From the computational point of view, the simplest option is given by the so-called Bessel vortex state.
This is a monochromatic solution of the corresponding wave equation written as a superposition of plane waves
with the same energy $E$, same longitudinal momentum $p_z$, same modulus of the transverse momentum $|\vec p_\perp| = \varkappa$
but with different azimuthal angles $\varphi_p$, see further definitions and normalization conditions
in \cite{Jentschura:2010ap, Jentschura:2011ih, Ivanov:2011kk, Karlovets:2012eu}.
As we run through all the plane wave components inside a Bessel state,
the vectors of their momenta revolve around axis $z$ and cover
the surface of a cone with the opening angle $\theta_0$, defined as
\begin{equation}
\cos\theta_0 = p_z/|\vec p|\,, \quad \sin\theta_0 = \varkappa/|\vec p|\,.\label{cone}
\end{equation}
In realistic situations, this cone opening angle is small, a few degrees at most.

For a spinless particle, each plane wave component $|PW(\vec p)\rangle$ inside the vortex state is multiplied by the
phase factor $\exp(i \ell \varphi_p)$,
\begin{equation}
|\varkappa, \ell\rangle \propto \int d^2 \vec p_\perp\, \delta(|\vec p_\perp|-\varkappa) e^{i \ell \varphi_p}\, |PW(\vec p)\rangle
\propto \int d\varphi_p e^{i \ell \varphi_p}\, |PW(\vec p)\rangle\,,\label{vortex-spinless}
\end{equation}
which produces the phase vortex in the coordinate space: $\exp(i\ell\varphi_r)$ \cite{Jentschura:2010ap, Jentschura:2011ih}.
For particles with polarization degrees of freedom such as photons or fermions the construction is more subtle.
For fermions, one can construct exact monochromatic solutions of the Dirac equation \cite{Bliokh:2011fi, Karlovets:2012eu, Serbo:2015kia},
which are eigenstates of the total angular momentum $z$-projection operator $\hat j_z$
but not of spin $\hat s_z$ or OAM $\hat \ell_z$ operators individually.
The spin degrees of freedom in these solutions can be parametrized in a way similar to the vector $\vec s$ \cite{Bliokh:2011fi},
which, however, cannot be interpreted as the spin of vortex electron in the rest frame because there exists no reference
frame for all plane wave components simultaneously.
Alternatively, one can describe the polarization state of a vortex fermion with a given helicity which is
a conserved quantum number \cite{Karlovets:2012eu, Serbo:2015kia}.

Whatever the choice, one can define a twisted fermion in the same wave as in Eq.~\eqref{vortex-spinless}
bearing in mind that now each individual plane wave $|PW(\vec p)\rangle$ contains a bispinor $u_{p, s}$.
It must satisfy Dirac's equation and, therefore, it depends on the plane wave momentum $\vec p$ and cannot be taken out of the integral.

However, this dependence brings up not only technical difficulties but also novel opportunities
absent in the plane wave case.
Indeed, the spin degrees of freedom used to define $u_{p, s}$ can depend on $\vec p$ in a non-trivial way.
	As a result, a polarization state of a non-plane-wave fermion is, in general, described with a polarization {\em field} rather than polarization parameters.
For vortex fermions, the polarization field can exhibit polarization singularity along the phase singularity line.
Such singularities are well known for vector fields, in particular in optics, and were classied in \cite{Dennis:2002}.
For fermion fields, they were described in a similar way in \cite{Sarenac:2018} with applications to vortex neutrons.

\begin{figure}[!h]
	\centering
	\begin{tikzpicture}
	\draw [->,gray,thin] (0,0) -- (4.2,0);
	\draw (4.1,-0.1) node[below] {$z$};
	\draw [gray,thin] (0,0) -- (0,1.2);
	\draw [gray,thin] (0.2,0.25) -- (-0.2,-0.25);
	\draw [dotted] (0,1.2) -- (4,0);
	\draw [dotted] (0,-1.2) -- (4,0);
	\draw [dotted] (-0.2,-0.25) -- (4,0);
	\draw [dotted] (0.2,0.25) -- (4,0);
	\draw[->] (0,1.2) -- (2,0.6);
	\draw[->] (0,-1.2) -- (2,-0.6);
	\draw[->] (-0.2,-0.25) -- (1.9,-0.125);
	\draw[->] (0.2,0.25) -- (2.1,0.125);

	\draw[->,very thick] (0,1.2) -- (0.5,1.05);
	\draw[->,very thick] (0,-1.2) -- (0.5,-1.05);
	\draw[->,very thick] (-0.2,-0.25) -- (0.22,-0.225);
	\draw[->,very thick] (0.2,0.25) -- (0.62,0.225);

	\draw [dashed] (0,0) ellipse (0.2 and 1.2);
	\filldraw [black] (0,1.2) circle (1pt);
	\filldraw [black] (0,-1.2) circle (1pt);
	\filldraw [black] (-0.2,-0.25) circle (1pt);
	\filldraw [black] (0.2,0.25) circle (1pt);

\draw (0.0,1.45) node[right] {$\vec s$};
\draw (1,1.4) node[below] {$\vec n$};

\draw [->,gray,thin] (6,0) -- (10.2,0);
\draw (10.1,-0.1) node[below] {$z$};
\draw [gray,thin] (6,0) -- (6,1.2);
\draw [gray,thin] (6.2,0.25) -- (5.8,-0.25);
\draw [dotted] (6,1.2) -- (10,0);
\draw [dotted] (6,-1.2) -- (10,0);
\draw [dotted] (5.8,-0.25) -- (10,0);
\draw [dotted] (6.2,0.25) -- (10,0);
\draw[->] (6,1.2) -- (8,0.6);
\draw[->] (6,-1.2) -- (8,-0.6);
\draw[->] (5.8,-0.25) -- (7.9,-0.125);
\draw[->] (6.2,0.25) -- (8.1,0.125);

\draw[->,very thick] (6,1.2) -- (6.15,1.7);
\draw[->,very thick] (6,-1.2) -- (6.15,-1.7);
\draw[->,very thick] (5.8,-0.25) -- (5.7,-0.55);
\draw[->,very thick] (6.2,0.25) -- (6.45,0.45);

\draw [dashed] (6,0) ellipse (0.2 and 1.2);
\filldraw [black] (6,1.2) circle (1pt);
\filldraw [black] (6,-1.2) circle (1pt);
\filldraw [black] (5.8,-0.25) circle (1pt);
\filldraw [black] (6.2,0.25) circle (1pt);

\draw (6.2,1.6) node[right] {$\vec s$};
\draw (7,1.4) node[below] {$\vec n$};

\draw [->,gray,thin] (12,0) -- (16.2,0);
\draw (16.1,-0.1) node[below] {$z$};
\draw [gray,thin] (12,0) -- (12,1.2);
\draw [gray,thin] (12.2,0.25) -- (11.8,-0.25);
\draw [dotted] (12,1.2) -- (16,0);
\draw [dotted] (12,-1.2) -- (16,0);
\draw [dotted] (11.8,-0.25) -- (16,0);
\draw [dotted] (12.2,0.25) -- (16,0);
\draw[->] (12,1.2) -- (14,0.6);
\draw[->] (12,-1.2) -- (14,-0.6);
\draw[->] (11.8,-0.25) -- (13.9,-0.125);
\draw[->] (12.2,0.25) -- (14.1,0.125);

\draw [dashed] (12,0) ellipse (0.2 and 1.2);
\filldraw [black] (12,1.2) circle (1pt);
\filldraw [black] (12,-1.2) circle (1pt);
\filldraw [black] (11.8,-0.25) circle (1pt);
\filldraw [black] (12.2,0.25) circle (1pt);

\draw[->,very thick] (12,1.2) -- (11.8,0.9);
\draw[->,very thick] (12,-1.2) -- (12.2,-0.9);
\draw[->,very thick] (11.8,-0.25) -- (11.8,-0.8);
\draw[->,very thick] (12.2,0.25) -- (12.2,0.8);

\draw (11.5,1.3) node[right] {$\vec s$};
\draw (13,1.4) node[below] {$\vec n$};
	\end{tikzpicture}
	\caption{Three examples of non-trivial polarization states for vortex fermions: parallel (left), radial (center), and azimuthal (right).
	Long thin arrows illustrate the momenta of individual plane wave components inside a vortex state; the thick short arrows
	indicate the vector $\vec s$ for each plane wave component.}
	\label{fig-polarization-states}
\end{figure}

In this exploratory study, we will consider three benchmark options for the vortex muon polarization states,
which are illustrated in Fig.~\ref{fig-polarization-states}.
\begin{itemize}
	\item
	{\bf Parallel polarization}. For each plane wave component with a given direction $\vec n$, we choose $\vec s = \vec n$.
	A motivation for this choice comes from the observation that,
	when muon moves in an external magnetic field, its spin precession approximately follows the momentum.
	Thus, if a vortex muon is obtained from a forward polarized plane wave muon through interaction with an external mangetic field,
	the parallel polarization state will result.
	\item
	{\bf Radial polarization}. For each plane wave component with a given $\vec n$, we consider the plane spanned by axis $z$ and $\vec n$
	and define the unit vector $\vec n_t$ via $\vec n_t \vec n = 0$, $(n_t)_z > 0$. The radial polarization corresponds to choosing $\vec s = \vec n_t$.
	\item
	{\bf Azimuthal polarization}: with $\vec n$ and $\vec n_t$ defined above, we construct the azimuthally pointing unit vector
	$\vec n_\varphi = \vec n \times \vec n_t$ and assume that $\vec s = \vec n_\varphi$.
\end{itemize}
We would like to make a few remarks concerning these states.
In the plane wave limit, the parallel polarization state approaches the muon with spin along axis $z$.
On the other hand, for the radial and azimuthal polarizations, there are no plane wave counterparts because
the definition of such states requires the presence of a polarization singularity line.
These states represent novel forms of polarization possible for non-plane-wave fermions.
In the plane wave limit they will disappear, corresponding to the unpolarized case.

When exploring these polarization states, we would like to stress that do not claim that all these states can be easily created.
We just use them to illustrate the sensitivity of the muon decay to the polarization state beyond plane waves.
Once vortex muons are created, one should perform a detailed study of the effects taking into account the realistic parameters
achieved in the experiment.

Finally, notice that all of these polarization states are azimuthally invariant.
As a consequence, the final electron angular distribution
will be azimuthally symmetric.
Of course, other polarization states of Bessel vortex fermions can be defined, see various examples
in \cite{Sarenac:2018}. In many of these cases, the azimuthal symmetry of the angular distribution is broken.
Although we will not analyze such states below, our formalism can be readily extended to any of them.

\subsection{Decay of unpolarized vortex muon: exact results}

When passing from the plane wave to vortex muon decay, we still use the plane wave basis for description
of the final state, not attempting to measure the possible vortex nature of the emitted electron
but just exploring, as before, its energy spectrum and angular distribution.

In this case we do not need to recalculate the decay process itself. We know that each plane wave component
inside the vortex muon decays to a final state with its own kinematic configuration and, as a result, different
plane wave components do not interfere. Thus, the decay width of a Bessel vortex muon can be written
as an azimuthal average of the corresponding plane wave decay widths \cite{Ivanov:2011kk}:
\begin{equation}
d{\Gamma} = \int \frac{d\varphi_p}{2\pi}\, d\Gamma_{PW}(\vec p)\,,\label{vortex-decay-1}
\end{equation}
where $d\Gamma_{PW}$ is given by \eqref{PWresult-3} or \eqref{PWresult-4}.
Notice that this decay rate becomes independent of the value of OAM. This is an unavoidable feature
in processes involving only one twisted particle in a single OAM state.
Dependence on the value of the OAM may arise only if we measure the final particle OAM (which is very challenging experimentally)
or if we prepare the initial state in a superposition of different OAM states.

However, even without the access to the value of the OAM, one can certainly explore its non-trivial
momentum distribution. It is the vortex cone structure which will lead to significant modifications
for the vortex muon with respect to the plane wave case.

Let us first consider the decay of an unpolarized vortex muon.
We choose the direction of the final electron
to define the $(x,z)$ plane: $\vec n_e = (\sin\theta,\, 0,\, \cos\theta)$.
In this coordinate system, any chosen plane wave component inside the vortex muon
is defined by $\vec n = (\sin\theta_0 \cos\varphi_p,\, \sin\theta_0\sin\varphi_p,\,\cos\theta_0)$,
where $\theta_0$ is the cone opening angle given in \eqref{cone}.
Then, at fixed $E_e$, the angular dependence comes from the factor
$$
1-\beta\, \vec n\vec n_e = 1 - \beta (\cos\theta\cos\theta_0 + \sin\theta\sin\theta_0 \cos\varphi_p)
$$
which changes between $1 - \beta \cos(\theta-\theta_0)$ to $1 - \beta \cos(\theta+\theta_0)$.
According to Eq.~\eqref{Emax}, for any electron angle $\theta_0$,
these plane wave components produce {\em different} maximal energies of the electron, spanning the interval
\begin{equation}
\mbox{from}\quad E_{e1} = \frac{m^2}{2E (1-\beta\cos(\theta+\theta_0))}\quad \mbox{to} \quad
E_{e2} = \frac{m^2}{2E (1-\beta\cos(\theta-\theta_0))}\,.\label{Emax12}
\end{equation}
As a result, the electron spectrum acquires additional features.
For any given $\theta$, it contains two regions which differ by the range of plane wave components
inside the vortex muon contributing to the decay:
\begin{eqnarray}
\mbox{lower energy region:}& E_e < E_{e1}\,,& \mbox{contributing $\varphi_p$:} \quad 0 \le \varphi_p \le 2\pi\,,\nonumber\\
\mbox{higher energy region:}& \quad E_{e1} \le E_e \le E_{e2}\,, \quad & \mbox{contributing $\varphi_p$:} \quad -\tau \le \varphi_p \le \tau\,.\label{two-regions}
\end{eqnarray}
Here, the azimuthal range $\tau$ is given by the inverse of Eq.~\eqref{Emax} and can be presented as
\begin{equation}
\cos\tau = \frac{(E_e-E_{e1})E_{e2} - (E_{e2}-E_e)E_{e1}}{E_e(E_{e2}-E_{e1})}\,. \label{tau}
\end{equation}
One can see that, as $E_e$ goes from $E_{e1}$ to $E_{e2}$, the value of $\cos\tau$ goes from $-1$ to 1.

If $\theta > \theta_0$ (detecting electrons outside of the vortex cone),
the spectrum extends to {\em higher} energies than for the plane wave muon of the same energy.
Indeed, one sees that the end-point of the plane wave spectrum $E_{e\,\rm max}$ would lie between $E_{e1}$ and $E_{e2}$.
Angles $\theta < \theta_0$, corresponding to the region inside the cone, which is unavailable for the plane wave case,
display a more intricate situation. The upper energy limit $E_{e2}$ can be either higher than $E_{e\,\rm max}$ (for $\theta > \theta_0/2$)
or lower than $E_{e\,\rm max}$ (for $\theta < \theta_0/2$). Thus, the spectral-angular distribution is predicted to have a forward dip
for the vortex muon, in sharp contrast with the plane-wave muons.

Next, performing the $\varphi_p$ integration within the limits \eqref{two-regions}, we obtain the spectral-angular distribution,
which can be generically written as
\begin{equation}
\frac{d\Gamma}{dE_ed\Omega}= \frac{4\Gamma_0}{\pi m^5} \cdot E_e^2 (3m^2 \cdot a - 4 E E_e \cdot b)\,,
\end{equation}
but with the coefficients $a$ ad $b$ displaying different behavior in the two energy regions.
In the lower energy region we get
\begin{equation}
a = 1-\beta \cos\theta_0 \cos\theta\,,\quad b = (1-\beta \cos\theta_0 \cos\theta)^2 + \frac{1}{2}\beta^2 \sin^2\!\theta_0 \sin^2\!\theta\,,
\end{equation}
independent of the energy. For the higher energy region, the range of the $\varphi_p$ integration depends on $E_e$ through
$\tau(E_e)$ given by \eqref{tau}, and we get
\begin{eqnarray}
a(E_e) &=& (1-\beta \cos\theta_0 \cos\theta)\frac{\tau}{\pi} - \beta \sin\theta_0\sin\theta\frac{\sin\tau}{\pi}\nonumber\\
b(E_e)&=& \left[(1-\beta \cos\theta_0 \cos\theta)^2 + \frac{1}{2}\beta^2 \sin^2\!\theta_0 \sin^2\!\theta\right]\frac{\tau}{\pi}\nonumber\\
&&- 2\beta\sin\theta_0 \sin\theta (1-\beta \cos\theta_0 \cos\theta)\frac{\sin\tau}{\pi}
+ \beta^2 \sin^2\!\theta_0 \sin^2\!\theta\frac{\sin2\tau}{4\pi}\,.
\end{eqnarray}
If we do not measure the energy of the electron and want just to explore its angular distribution,
we can integrate over all electron energies available for a fixed $\theta$.
For this calculation, it is convenient to insert the unpolarized version of Eq.~\eqref{PWresult-4} into Eq.~\eqref{vortex-decay-1} and
perform the $\varphi_p$ integral.
Here and below, we will make use of the integrals
\begin{eqnarray}
{\cal I}_2 &=& \frac{1}{2\pi}\int d\varphi_p \frac{1}{(a - b\cos\varphi_p)^2} = \frac{a}{(a^2-b^2)^{3/2}}\,,\nonumber\\[1mm]
{\cal I}_3 &=& \frac{1}{2\pi}\int d\varphi_p \frac{1}{(a - b\cos\varphi_p)^3} = \frac{1}{2}\frac{2a^2+b^2}{(a^2-b^2)^{5/2}}\,, \label{integrals}\\[1mm]
&&\mbox{where}\quad a = 1 - \beta\cos\theta\cos\theta_0,\quad b = \beta\sin\theta\sin\theta_0.
\end{eqnarray}
With these intergrals, we get
\begin{equation}
\frac{d\Gamma_V}{d\Omega} = \frac{\Gamma_0}{4\pi}\, \frac{1}{\gamma^3}\cdot{\cal I}_2 =
\Gamma_0\, \frac{1}{\gamma^3}\,\frac {1 - \beta \cos\theta\cos\theta_0}{\bigl\{ [1 - \beta \cos(\theta+\theta_0)][1 - \beta \cos(\theta-\theta_0)]\bigr\}^{3/2}}\,.\label{vortex-result-2}
\end{equation}
Notice the invariance of this result under the exchange $\theta_0 \leftrightarrow \theta$.

In the non-relativistic limit $\beta \ll 1$, we recover the usual isotropic decay rate.
Notice that the exact limit $\beta \to 0$ cannot be taken for vortex muons due to the non-zero $\varkappa$.
Even if one performs a Lorentz boost and sets $p_z=0$, one gets a non-zero value $\beta = \varkappa/\sqrt{\varkappa^2+m^2}$.
In the opposite limit of the ultrarelativistic muon $\beta \rightarrow 1$, $\gamma \gg 1$, we get
a narrow angular distribution peaked at $\theta = \theta_0$. The exact integration
over all angles still yields $\Gamma = \Gamma_0/\gamma$.
Finally, in the plane wave limit $\theta_0 \to 0$, we recover Eq.~\eqref{PWresult-4}.

\subsection{Decay of unpolarized vortex muon: numerical examples}

To illustrate the above analysis and to stress the modifications expected for vortex muons,
let us fix the muon energy at $E = 3.1$ GeV, which corresponds to the ``magic value'' $\gamma = 29.3$
used in all modern $g-2$ experiments \cite{Miller:2007kk, Logashenko:2018pcl}.
For the cone opening angle $\theta_0$, we choose two benchmark values:
\begin{equation}
\mbox{narrow cone:}\quad \theta_0 = 0.01 \approx 0.6^\circ\,, \qquad
\mbox{wide cone:} \quad \theta_0 = 0.1 \approx 6^\circ.
\label{two-cones}
\end{equation}
We consider the narrow cone to be closer to the realistic values, but we will also show results
for the wide cone to highlight strong distortions of the distributions.

\begin{figure}[!h]
	\centering
	\includegraphics[width=0.48\textwidth]{energy-range-001}\hfill
	\includegraphics[width=0.48\textwidth]{energy-range-01}
	\caption{The electron energy range for the decay of 3.1 GeV muons as a funuction of the electron emission angle $\theta$ in the forward region.
		The black line corresponds to $E_{e\,\rm max}$ from the plane wave muon.
		The two colored lines correspond to $E_{e1}$ and $E_{e2}$ from the vortex muon with
		$\theta_0 = 0.01$ (left) and 0.1 (right).}\label{Fig-Emax}
\end{figure}

Since for ultrarelativistic muons, the angular distribution of the emitted electron develops a sharp forward peak,
from now on we focus on the forward region $\theta < 0.2 \approx 12^\circ$.
In Fig.~\ref{Fig-Emax} we plot the angular dependence of the energies $E_{e1}$ and $E_{e2}$ defined in \eqref{Emax12}
as functions of the electron emission angle $\theta$ in the forward region and compare them with the maximal electron energy
for the plane wave muon case \eqref{Emax}.
The left and right plots correspond to the narrow and wide opening angles \eqref{two-cones}.

The key observation here is that, even for the narrow cone with $\theta_0 \ll 1$,
we observe a very significant shift of the two energies with respect to the plane wave case.
The ``higher energy'' region of the spectrum, shown in these plots with a lighter shading,
represent a sizable part of the total energy range.
In order to see what part of the spectrum is occupied by this new region, we compute
\begin{equation}
\frac{E_{e2}-E_{e1}}{E_{e2}+E_{e1}} = \frac{\beta\sin\theta\sin\theta_0}{1-\beta\cos\theta\cos\theta_0} \approx 2\frac{\theta_0}{\theta}\,,
\end{equation}
where the last estimate assumes $\beta \to 1$.
We conclude that even for very narrow vortex cones, we have access to a parametrically large part of the
electron spectrum, provided we can measure electrons emitted at angles $\theta$ comparable to $\theta_0$.
This part of the spectrum is unavailable in the plane wave case and represents a new kinematic feature of the vortex muon.

For wider cones, the difference between $E_{e1}$, $E_{e2}$, and the plane wave end point $E_{e\,\rm max}$ is dramatic, Fig.~\ref{Fig-Emax}, right.
For $\theta \sim \theta_0$, the energy spectrum extends far beyond what one would get, at these angles, from plane wave muons.
This is, of course, no surprise since the vortex muon contains plane wave components pointing close to the observation direction.

\begin{figure}[!h]
	\centering
	\includegraphics[width=0.48\textwidth]{angle-001}\hfill
	\includegraphics[width=0.48\textwidth]{angle-01}
	\caption{Electron polar angle distributions from the $3.1$ GeV vortex muon decays near the forward direction
	for $\theta_0 = 0.01$ (left) and 0.1 (right), plotted in red, compared with the plane wave muons (black lines).}\label{Fig-angular}
\end{figure}

Next we check how the electron angular distribution, integrated over energies,
differs with respect to the plane wave case.
In Fig.~\ref{Fig-angular} we plot the angular distributions \eqref{vortex-result-2}
in the forward region for the same two values of the cone opening angle.
For the realistic narrow cone, we just observe minor angular broadening,
which could also be mimicked by energy and angular smearing.
Thus, if we want to distinguish the vortex muon with a small opening angle from the plane wave muon,
the angular distribution alone is not a particularly revealing observable.
For a wide cone, the picture changes: we see a pronounced forward dip, as the angular distribution
peaks at $\theta = \theta_0$ and gets significantly depleted near $\theta = 0$.

\begin{figure}[!h]
	\centering
	\includegraphics[width=0.48\textwidth]{energy-spectrum-001-pi10}\hfill
	\includegraphics[width=0.48\textwidth]{energy-spectrum-01-pi10}
	\caption{Electron energy spectrum from $3.1$ GeV vortex muon decays at $\theta = \pi/10 = 18^\circ$
		for $\theta_0 = 0.01$ (left) and 0.1 (right) compared with the plane wave muons.}\label{Fig-energy}
\end{figure}

Since the angular distribution alone is not particularly useful, we turn to the energy spectrum
of electrons detected at a given emission angle $\theta$.
In Fig.~\ref{Fig-energy} we show how the electron spectrum is modified with respect to the plane wave muons.
The two plots correspond to the same electron polar angle $\theta = \pi/10 = 18^\circ$ with the two choices
for the opening cones \eqref{two-cones}.

Even for the narrow vortex cone, the modifications are quite substantial, Fig.~\ref{Fig-energy}, left.
The plane wave muon would result in a smoothly rising spectrum extending to $E_{e\, \rm max} = 36$ MeV for this observation angle.
In the vortex muon case with $\theta_0 = 0.01$, the spectrum follows this behavior in the lower energy region.
However, in the higher energy region, the spectrum exhibits a break and steadily drops to zero.
Notice that this higher energy region is quite large, extending from 34 to 39 MeV,
representing more than 10\% of the total energy range.

We conclude that the key observable is the energy spectrum at a small fixed angle, not the angular distribution.
It is this spectrum in its higher energy range that displays the clearest
distinction between the (approximately) plane wave and the vortex muons.

For larger opening cone values, we see a dramatic distortion of the spectrum, Fig.~\ref{Fig-energy}, right.
Instead of smoothly rising to the end-point, the spectrum first develops a cusp at $E_{e1} = 20$ MeV
then rises again, developing a second broad maximum, and finally drops to zero at the new end-point $E_{e2} = 77$ MeV.

\begin{figure}[!h]
	\centering
	\includegraphics[width=0.48\textwidth]{energy-spectrum-001-pi20}\hfill
	\includegraphics[width=0.48\textwidth]{energy-spectrum-01-pi20}
	\caption{The same as in Fig.~\ref{Fig-energy} but for $\theta = \pi/20 = 9^\circ$.}\label{Fig-energy2}
\end{figure}

For smaller observation angles $\theta$, the difference becomes even more pronounced. In Fig.~\ref{Fig-energy2} we plot the same energy spectra
but for $\theta = \pi/20 = 9^\circ$. For the wide cone, the difference is dramatic, both in energy range and in magnitude,
and it also grows for the narrow cone. Detecting such a behavior would be an unmistakable indication of the cone structure of the muon wave function.

\subsection{Decay of polarized vortex muon}

The decay rate of a polarized vortex muon is given by the same Eq.~\eqref{vortex-decay-1} with
$d\Gamma_{PW}$ taken from \eqref{PWresult-3} for the spectral-angular distribution of the electron
or from \eqref{PWresult-4} if the energy-integrated angular distribution is concerned.
To specify the polarization state of the vortex muon, we need to
explicitly give the dependence of $\vec s$ on the plane wave momentum $\vec p$.
Let us begin with the energy-integrated angular distribution
and go through the polarization states outlined listed in Section~\ref{subsection-describing}.
\begin{itemize}
	\item
	The parallel polarization implies $\vec s = \vec n$, so that the plane wave decay rate \eqref{PWresult-4} now simplifies to
	\begin{equation}
	d\Gamma_{PW} = \Gamma_0\, \frac{d\Omega}{4\pi} \, \frac{1}{\gamma^3}\, \frac{1}{(1-\beta\, \vec n\vec n_e)^2}
	\left[1 + \frac{\beta - \vec n \vec n_e}{3(1-\beta\, \vec n\vec n_e)}\right]\,.
	\label{PWresult-5.1}
	\end{equation}
	As a result, the vortex decay rate has the following form
	\begin{equation}
	d\Gamma_{V} = \Gamma_0\, \frac{d\Omega}{4\pi} \, \frac{1}{\gamma^3}\, \left[{\cal I}_2 \left(1 + \frac{1}{3\beta}\right)
	- {\cal I}_3 \frac{1}{3\beta\gamma^2}\right]\,,\label{vortex-result-3}
	\end{equation}
	where the integrals ${\cal I}_2$ and ${\cal I}_3$ are given in Eqs.~\eqref{integrals}.
	In the plane-wave limit, one must recover the plane wave result \eqref{PWresult-4.1}.
	\item
	For the radial and azimuthal polarization states, one has $\vec s \vec n = 0$ for each plane wave component.
	In this case, the plane wave decay rate simplifies to
	\begin{equation}
	d\Gamma_{PW} = \Gamma_0\, \frac{d\Omega}{4\pi} \, \frac{1}{\gamma^3}\, \frac{1}{(1-\beta\, \vec n\vec n_e)^2}
	\left[1 - \frac{\vec s \vec n_e}{3\gamma (1-\beta\, \vec n\vec n_e)}\right]\,.
	\label{PWresult-5.2}
	\end{equation}
	After integration over all the plane wave components of the vortex muon,
	we get for the radial polarization state
	\begin{equation}
	d\Gamma_{V} = \Gamma_0\, \frac{d\Omega}{4\pi} \, \frac{1}{\gamma^3}\, \left[{\cal I}_2 \left(1 - \frac{\cos\theta_0}{3\beta\gamma \sin\theta_0}\right)
	+ {\cal I}_3 \frac{\cos\theta_0 - \beta \cos\theta}{3\gamma\beta\sin\theta_0}\right]\,.\label{vortex-result-4}
	\end{equation}
	For the azimuthal polarization state we get $\vec s \vec n_e = \sin\theta \sin \varphi_p$.
	Since the other factors in the integrand depend on $\cos\varphi_p$, we see that the spin contribution
	of the azimuthally polarized vortex muon vanishes after the $\varphi_p$ integration.
	Thus, the azimuthally polarized vortex muon will produce the angular distribution just as in the unpolarized case.
\end{itemize}

\begin{figure}[!h]
	\centering
	\includegraphics[width=0.55\textwidth]{polarized-angular-001}
	\caption{The electron angular distribution emitted from plane wave (black) and vortex (red) muons in various polarization cases:
		unpolarized (dotted lines), parallel polarization (solid lines), radial polarization (dashed line).
		The cone opening angle is $\theta_0 = 0.01$.}\label{Fig-angular-polarized}
\end{figure}

In Fig.~\ref{Fig-angular-polarized} we plot the above angular distributions in the forward region for the narrow cone with $\theta_0 = 0.01$.
Here, the plane wave muon cases are shown in black, vortex muon cases are shown in red.
The dotted lines, both for plane wave and vortex muons, correspond to the unpolarized case;
they are identical to Fig.~\ref{Fig-angular}, left.
The solid lines correspond to the parallel polarization for vortex muon and the $z$ polarization for the plane wave muon.
The red dashed line shows the radial polarization case, which is possible only for vortex muon.
We observe here the same pattern as before: when passing from plane wave to vortex muons with very small cone opening angle $\theta_0$,
we just see the forward peak to get slightly broader.
Thus, the main message from this plot is that the spectrum-integrated angular distribution is not of much help when distinguishing different polarization states.

\begin{figure}[!h]
	\centering
	\includegraphics[width=0.55\textwidth]{polarized-001-pi60}
	\caption{The electron spectra for plane wave (black) and vortex (red) muons in various polarization cases:
		unpolarized (dotted lines), parallel polarization (solid lines), radial polarization (dashed line).
		The cone opening angle is $\theta_0 = 0.01$, the observation angle is $\theta = \pi/60 = 3^\circ$.}\label{Fig-spectra-polarized}
\end{figure}

The distinction becomes much more clear when we look into the energy spectrum, especially in the higher energy region.
In Fig.~\ref{Fig-spectra-polarized} we show these spectra for the same five states:
unpolarized plane wave and vortex muons, parallel polarization for plane wave and vortex muons,
and the radial polarization. The spectra are given for the electron emission angle of $\pi/60 = 3^\circ$.
We see critically different patterns for various polarization options in the higher energy region,
which occupies at this observation angle the region from about $E_{e1}=700$ to $E_{e2}=1200$ MeV.

In particular, the spectrum of the electrons from radially polarized muons, which closely follows the unpolarized case below $E_{e1}$,
displays a strong second peak at high energies. The explanation of this effect is straightforward.
For lower energies, all plane wave components of the radially polarized muon contribute to spectrum,
and since all of them point in different directions, the end result looks almost like the unpolarized case.
However, in the higher energy region, only some of the plane wave components contribute, see Eq.~\eqref{two-regions}.
Therefore, the closer to the end point $E_{e2}$, the more the process resembles the transversely polarized case.

\section{Discussion and conclusions}\label{section-discussion}

Exploring collisions and decays of elementary particles prepared in vortex states with a non-zero orbital angular momentum
is a novel promising way to probe particle structure and dynamics.
Kinematic dependences, angular distributions, and spin effects have been predicted to
differ in a significant way with respect to the (approximate) plane wave case.
These predictions still await experimental verification, mostly due to the absence of suitable instrumentation
which would enable such studies. In order to stimulate instrumentation development,
one can theoretically explore what new features could become observable in experiments with vortex particles.

In this paper, we studied, for the first time, the peculiar features
which could be seen in decays of muons prepared in a vortex state.
We obtained the spectral-angular distribution of the emitted electron, both for unpolarized and polarized muons.
In the latter case, we took into account the richer list of opportunities which exists
for non-plane-wave fermions.

The hallmark feature of vortex particles is their ``cone structure'' in momentum space.
Thus, almost all studies of vortex particle collisions look into the modifications of the angular distribution
of the final state. However, when the cone opening angle $\theta_0$ is small,
these modifications with respect to the plane wave case are usually minor.

The key finding of this work is that it is the higher energy part of the electron spectrum, not the angular distribution,
that displays the strongest differences with respect to the plane wave muons and that
allows one to distinguish various polarization states.
Even for very small opening angles used in our numerical examples
we could observe very significant modifications of the energy spectrum, if the electron observation
angle $\theta$ is also small.
Fig.~\ref{Fig-spectra-polarized} offers a clear illustration:
for muons with $E= 3.1$ GeV and $\theta_0 = 0.01 \approx 0.6^\circ$ and for the electron observation angle $\theta = 3^\circ$,
we predict electron spectra to dramatically differ
for plane wave and vortex muons, as well as for different vortex muon polarization states.
In a sense, these findings confirm once again that muon decay is a self-analyzing process,
as it offers a clear information on the muon polarization state even beyond the plane wave case.

In this paper, we left aside the issue of producing vortex muons.
No experiment has tried it so far. However, we see no fundamental obstacles to producing such states.
It is true that traditional schemes for generating vortex states based on fork diffraction gratings
are not suitable for muons due to their large penetration depth. However, muons are charged particles
and, therefore, they can be manipulated with electric and magnetic fields.
If a nearly plane-wave muon passes through an aperture with an artificial magnetic monopole
(the tip of a magnetized needle), it will acquire orbital angular momentum proportional to the effective magnetic charge,
which has already been demonstrated for electrons \cite{Beche:2014}.
Alternatively, if muons can be emitted from a pointlike source placed inside a wide solenoid,
then, at the exit of solenoid, the muon wave function can acquire an OAM, just as it was predicted
for electrons \cite{Floettmann:2020uhc,Karlovets:2020tlg}.
Thus, ``twisting'' muons is technically possible, provided initial nearly plane wave muons can be created
with a sufficient transverse coherence length.

Once vortex muons are produced and accelerated, one could use the standard electron spectrometers and detectors
to explore the subtle features of vortex muons.
As demonstrated in this paper, the small electron observation angle $\theta$ serves as a magnification tool
for discerning the features which exist near the narrow cone of the vortex muon state.

Once a proof-of-principle experiment detects these modifications, a research program can begin
which would explore spin and OAM evolution of vortex muons in external magnetic fields.
There exist theoretical studies of how vortex electron could behave in external fields, in particular,
in the transverse magnetic field of a storage ring \cite{Gallatin:2012ai}.
This evolution may be difficult to track for electrons.
However, vortex muons, thanks to the self-analyzing nature of their decays, may offer a better glimpse
on this evolution.

Finally, we mention that, since the main effects discussed here are kinematic,
we expect that similar easily observable features may appear
in decays of other unstable relativistic particles.

\section*{Acknowledgments}

This work was supported by grants of the National Natural Science Foundation of China (Grant No. 11975320) and the Fundamental Research Funds for the Central Universities, Sun Yat-sen University.

redpajama_set_name: RedPajamaArXiv


A question I've had in my head since I first saw screenshots of the display preference pane on the new Retina MBP is this: Can it be made to run with what you could call a 1.0 UI scaling factor (same amount of pixels for the same widget as you'd get on a regular MBP or say, an iMac)?
To clarify, the preference pane appears to allow you to select between several predefined scaling factors from "Like 1920x1200" (UI scaling factor = 1.5) through "Like 1440x900" (UI scaling factor = 2.0) to "Like 1024x640" (UI scaling factor = 2.8125) and there is also a radio button for "Best for Retina display".
Does this radio button for "Best for Retina display" set the UI scaling to 1.0 or does it simply set the scaling to the "default" 2.0?
If the latter, has anyone checked if there's some defaults write com.apple.[...] 1.0 setting available which forces the scaling of the UI to 1.0?
SwitchResX: A reasonably simple solution, SwitchResX is a third-party preference panel that allows you to run custom resolutions on any display. Install the preference panel, select the Retina Display, and add a custom resolution setting for 2880×1800.
SetResX: Probably the easiest option of them all, SetResX is a little menu-bar app that allows you to run 2880×1800 easily.
scrutil: Slightly more advanced due to the nature of the command line, the free utility called screenutil gets the job done immediately with a quick entry into the Terminal.
ChangeResolution: ChangeResolution is a new tiny AppleScript front end to a command line utility that changes the resolution to 2880×1800.
Quicksilver can do it also if you enable the Displays plugin. I use it all the time. You can assign triggers to specific resolutions/actions as well.
The displays plugin allows Quicksilver to index the displays currently attached to your Mac, in order to set the Desktop picture and their resolution, colour depth and refresh rate.
Retina DisplayMenu lets you select specific resolutions (both HiDPI and standard resolutions) and is the app that I currently use.
Selected resolution in image above is the Best for Retina resolution.
Not the answer you're looking for? Browse other questions tagged lion display macbook .
How can I get full resolution on Mac Book Pro Retina?
How to run Macbook Pro retina on native resolution?
How to set screen resolution with a keyboard shortcut on Retina MBP?
Are the Retina MacBook Pro 15" suitable for PC (Windows) gaming?
MacBook Pro Retina 15" native resolution compromise?


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DELIVERING CRITICAL OVERSIGHT
Department of Transportation State Safety Oversight (SSO) Program
The rail transit industry has a strong safety record. A small percentage of transportation fatalities that occur in the United States are attributed to commuter rail, heavy rail and light rail. When this number is further broken down to include just rail transit fatalities, only 0.2 percent of all transportation fatalities are rail transit-related. However, significant accidents continue to occur, and the accident rate has not shown substantive improvement in recent years. Moreover, recent accidents have highlighted specific issues that need prompt government and industry attention.
In addition, the strong growth of rail transit and highway traffic continues to drive up the exposure of motorist, pedestrians and trespassers at highway-rail grade crossings and along the right-of-way. The State Safety Oversight Program (SSOP), currently managed by The Federal Transit Administration's (FTA) Office of Safety Review within the Office of Transit Safety and Oversight (TSO), is charged with delivering programs that ensure the highest possible level of safety and security for the nation's public transportation systems.
With a focus on the development of standards, criteria, plans, procedures, and processes for implementation by states and rail transit agencies (RTAs), Longevity supports safety oversight activities of State Safety Oversight (SSO) programs, and supports TSO-20's core functions – collecting safety data on rail transit agencies (RTA), conducting audits of SSO agencies State Safety Oversight Agencies (SSOA) that oversee RTAs, and providing outreach and technical assistance to those same RTAs and SSOAs.
With continuous evaluation of each state program, Longevity's agile teams provide programmatic and technical support (monitoring, technical assistance, networking, and dissemination of context, data analysis, and training across relevant fields), as well as training, guidance, and a forum for idea exchange.
By evaluating the development and implementation of state oversight and rail transit agency safety and security programs as per applicable regulations, requirements, and FTA guidance, we have impacted the development, and delivery of technical assistance and training, which guides state and rail transit agency program development and implementation. This has resulted in increased response rates to industry and government inquiries and needs related to FTA's safety and security program implementation, as well as smooth coordination with other FTA programs to ensure quality delivery of its safety and security program.
Increased program monitoring and technical assistance for special projects and interventions, which can include investigations or inspections at RTAs, on-site inquiries or investigations at SSOAs, direct administration of an SSO program, and imposing prohibitions or restrictions on an RTA.
Improvement in performance of inspections of transit agency facilities and infrastructure such as track and power systems.
Continuous monitoring and evaluation of hazard and corrective action plan (CAP) identification and resolution has improved investigation of accidents and incidents, as well as the development and documentation of procedures for performing safety oversight.
© Longevity Consulting
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Electric Bike Technologies LLC (makers of the E-BikeKit™ electric bike conversion kit) and AllCell Technologies have signed a Memorandum of Understanding to jointly promote and sell lithium-ion batteries for use in electric bike conversions. A central objective of the partnership is to displace many of the low quality imported batteries whose high failure rates have plagued the industry. In their place, the partners will be offering high-quality batteries designed and assembled in the U.S. backed by a two-year warranty and exceptional customer service.
By combining AllCell's lightweight, compact, and long-lasting batteries with Electric Bike Technologies' marketing, retailing, and customer service expertise the two firms are creating a compelling value proposition for both consumers and bike dealers. A few of AllCell's battery models are already available for purchase through the E-BikeKit website (www.e-bikekit.com), with an enhanced offering coming soon.
Electric Bike Technologies is a leading development, sales, and marketing company specializing in high performance electric bicycle products. Through the partnership, Electric Bike Technologies will offer AllCell batteries through a network of over 125 established E-BikeKit dealers in the U.S. as well as via www.e-bikebatteries.com, a new website devoted exclusively to selling electric bike batteries and accessories. In addition to offering a robust selection of high-quality batteries at competitive prices, the partners will ensure that every battery is shipped legally and safely, adhering to all applicable laws and shipping regulations.
AllCell's patented thermal management technology employs a phase change material (PCM) composite to rapidly absorb and distribute the heat generated during battery discharge. Because AllCell's proprietary PCM composite operates passively, it functions even when the bike is not in use, protecting the battery from solar loading on hot summer days as well. By preventing the lithium-ion cells from overheating, AllCell is able to build high energy density batteries with extended cycle life and maximum safety. Interested parties are invited to visit the AllCell booth (#40062) at the upcoming Interbike show from September 19-21 in Las Vegas.
"E-BikeKit's business has been growing rapidly, and we are excited to partner with an American lithium-ion battery supplier who matches our dedication to product quality, innovative design and customer satisfaction. AllCell's batteries with their unique thermal management technology will offer our customers and dealers the longest-lasting high energy density battery on the market. AllCell packs are reliable, safe and they are shipped in full compliance with current government regulations; they are the perfect match for any conversion kit application."
"Electric Bike Technologies is a perfect partner for AllCell. Their impressive roster of dealers and intuitive, easy-to-use e-commerce site will dramatically broaden the reach of our batteries. We look forward to working with their team to help develop the U.S. electric bike market with a high quality product offering and top-notch customer support staff."
Electric Bike Technologies (www.electricbiketechnologies.com) is a development, sales and marketing company specializing in affordable high-quality electric bicycle conversion kits, hub motors, batteries and components. Since 2008 the company has earned a reputation for delivering the best value and best user experience in electric bike conversion with their flagship product the E-BikeKit" conversion kit system (www.e-bikekit.com). With strong manufacturing partners in the US and Asia, a fast growing network of authorized dealers and a reputation for outstanding service, Electric Bike Technologies is committed to advancing the use of electric bikes in the United States and abroad.


We live in a tropical country without major natural disasters, but there is one problem that we have gotten used to: the heat!
Increasingly we suffer more and more due to the excessive heat, and according to the Intergovernmental Panel on Climate Change (IPCC), the planet's temperature may increase even more by 2100.
People speak a lot about environmental comfort and increasingly architects and engineers have begun to solve these problems with the use of modern glass. Did you know that with the use of high technology, there is a special glass which filters the sunlight selectively, reducing the heat input up to 80% inside, minimally reducing the brightness?
And the present glass can block the input of UV ray (Ultraviolet) in almost 100%, which prevents aging and discoloration of furniture, flooring, etc., which are consequences of the solar radiation.
The effective use of materials, the use of architectural strategies, and distribution of the spaces in relation to solar orientation are indispensable for thermally pleasant environments.
The shading coefficient is also widely used, it compares the incoming energy of a special glass with the common 3mm glass. When the SF or the shading coefficient is reduced, the heat decreases as well, and the product has better performance.
Let's consider a practical example of success and improvement: the restoration of the Cathedral of Brasilia. We from Avec Design used a glass with 50% LT (making the environment more pleasant) and the shading coefficient 0.38, which means the input of only 38% compared to the common glass, such as the old glass. Therefore, 2/3 of heat input was reduced, providing the thermal comfort in the interior of the cathedral.
The evolution of glass corrected the comfort problems in the Cathedral, because despite the genius project, these special glasses did not exist at the time.
Cautious choices in the projects are capable of generating thermal comfort that is often achieved only with the use of modern glass.


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Home › Dissemination activities › EU projects (incl. H2020) signed prior to the official Brexit will be supported
The Commission have made it clear that the referendum result changes nothing about eligibility for these funds. UK businesses and universities should continue to bid for competitive EU funds while we remain a member of the EU and we will work with the Commission to ensure payment when funds are awarded. The Treasury will underwrite the payment of such awards, even when specific projects continue beyond the UK's departure from the EU. The UK will continue to be a world leader in international research and innovation collaboration, and we expect to ensure that close collaboration between the UK and the EU in science continues. Details can be found at:
Statement of the British Treasury
https://www.gov.uk/government/uploads/system/uploads/attachment_data/file/545767/CST_letter_to_SoS_for_DExEU_August_2016.PDF
Statement of the British ministry for universities and science about H2020 projects
https://www.gov.uk/government/news/statement-on-higher-education-and-research-following-the-eu-referendum
Statement of the European Commission about H2020 and Brexit
https://ec.europa.eu/programmes/horizon2020/en/news/outcome-referendum-united-kingdom


Rob Evans, technical training manager at Linde Material Handling UK, discusses how apprenticeships can transform a company and solve the problem of a retiring workforce.
The UK has an estimated 10 million workers over the age of 50, comprising nearly one third of the entire UK workforce*.
Older workers are valuable members of staff, equipped with decades of expertise and knowledge of their trade.
In some industries, it's possible to retain these members of staff in their roles for as long as possible, however in the material handling sector, the nature of work can be labour intensive and means older workers are likely to retire sooner, rather than stay in the business.
A decade ago at Linde, we were faced with a large proportion of our workforce reaching retirement age imminently, meaning we were set to lose many of our skilled workers, including our engineers who are a key part of the company.
We knew something had to be done to regenerate and refresh our workforce, which is why we introduced a bespoke apprenticeship programme with the aim of recruiting and retaining young staff and to help plug our skills gap.
Each year, our apprentices spend five weeks at the Fork Truck Training Centre in Swindon where we donated five Linde trucks to make sure our apprentices build a comprehensive knowledge of our products.
We see our apprentices grow over the four years until they qualify and then move on into permanent roles at the company where they gain more responsibility, self-management and becoming valuable members of the team, constantly providing innovation.
My advice to others who may be facing similar problems or are simply looking to regenerate their workforce and utilise the expert knowledge of their older workers, is to invest in apprenticeships.
The long-term investment has innumerable advantages and serves as a solution to replace workers leaving the business, and at the same time expand and grow your company's skillset.
Our apprentices have not only helped develop the company, but are part of our culture, we work together and consider them part of the Linde family.
Linde apprenticeship applications for 2019 close on 31st March, applicants should contact shelley.brown@linde-mh.co.uk for more information.


Booking bus from Navsari to Jamnagar online is the easiest experience you can get because weve roped in the best and the most reliable bus operators like "Dwarkadhish Travels" providing lowest fare bus tickets for your smooth bus journey. Check out the popular bus operators connecting Navsari with Jamnagar.
As many as 3 bus operators connect Navsari to Jamnagar. Those traveling from Navsari by bus have various bus service operators to choose from. The best known operators that connect Navsari to Jamnagar, "Dwarkadhish Travels" provide buses with ticket prices as low as 550. One can avail Volvo bus, AC & Non-AC sleeper and seater buses from Navsari. Select the nearest and the most prefered pick up points, being the most popular ones amongst the rest. Some of the other relevant bus operators running from Navsari to Jamnagar are "Samay Travels"
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Book your Bus Ticket from Navsari to Jamnagar Fare starting from Rs.550 with 3+ operators. Use Bus Coupon Codes to avail great discounts on your bus ticket booking and Enjoy your Hassel Free Trip with Travelyaari.