![]() There are some unmistakeably beautiful shots in Thailand that were caught simply because a) it's a naturally beautiful place and b) Lurie et al were simply there at the right time. Somehow the lack og glossiness and travelogue style reveal more about the locations. The locations seem very real and just part of the immediate environment. Maine and Thailand were chosen by Dafoe and Hopper respectively, and were not ideal spots for good fishing. Exotic Jamaica was a last minute substitute for Arkansas! The production money couldn't get transferred in time by the investors and Jamaica was chosen simply because Waits was on vacation there at the time. Lurie wasn't interested in beautiful locations and wanted to simply go where where the best fishing was. The show was filmed on video and so lacks the glossiness of typical TV travel shows. ) Hopper and Dafoe come across as warm, intelligent, interesting and funny people (Hopper reveals himself as a sugar junkie!) and share real rapport and love with Lurie.Īs a travel show, it's untypical. ![]() (He had wanted to have his friend Flea of the Red Hot Chili Peppers as his guest but the Japanese investors didn't consider him famous enough at the time, pushing Dillon onto him despite the fact they weren't that close. Lurie claims Dillon was wary of coming off stupid but Dillon later accused him of making him look stupid - 'God did that' was Lurie's reply. (Apparently he got irate later on off-camera, and didn't speak to Lurie for two years.) Dillon is extremely guarded and monosyllabic. Waits is charming and oddball funny, but he loses patience with the whole project and gets grumpy and finally angry with Lurie. It's quite possible he and his friends really do speak a lot like his movie characters. It made me reconsider his filmmaking style. Jarmusch comes across as a pleasant, interesting guy and more of a listener than a speaker. But they do reveal themselves as human beings. Lurie and his guests don't have the compelling conversations that you might expect. The guest stars either played up to the cameras (Hopper) or tried their best to protect their famous personas (Dillon). (Any hopes of the show being any kind of educational show were doomed because Lurie had to teach guests like Hopper and Waits the basic skills of fishing!) It's a funny show because of Lurie's good humour, the personalities of his guests, and the amusing, unexpected things that happen, eg Dillon refusing to talk to Lurie, or Waits getting irritable with him. The show isn't a parody of a fishing show, but it comes close, and only because of the way life just kind of took over events (practicalities that had to be considered and concessions made), and because Lurie and his crew were kind of making it all up as they went along. Some highlights weren't caught in time or filmed at all. Also, the show is filmed on video in a very lo-fi style, and some of the highlights of the trip were unusable due to bad sound. Hilariously, Lurie and his guests rarely catch any fish (due to the fact the spots they filmed in were weak for fishing). As a fishing show, it is completely untypical (angering some who take TV fishing shows seriously). (By the last show, Lurie admits that he had learned to stop aiming for perfection and to just let it be.) It really shouldn't work. ![]() The beauty of FISHING WITH JOHN is in it's simplicity and the way it confounds expectations to transcend whatever notions Lurie had for what the show would be.
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![]() Remove all special characters and punctuation # After: Sample text with numbers and words # Before: Sample text with numbers 123455 and words !!! Here's how you use it: sample_text = "Sample text with numbers 123455 and words !!!" isalpha() method of Python strings will come in handy in those cases. Sometimes, you'd like to remove non-alphabetic characters like numbers or punctuation. # After: I want to keep this one: 10/10/20 but not this one # Before: I want to keep this one: 10/10/20 but not this one 222333 ![]() isdigit() method of strings: sample_text = "I want to keep this one: 10/10/20 but not this one 222333"Ĭlean_text = " ".join() # Side effect: removes extra spaces Using a regular expression gets a bit trickier. For instance, when you want to remove numbers but not dates. There are cases where you might want to remove digits instead of any number. But don't remove this one H2O"Ĭlean_text = re.sub(r"\b+\b\s*", "", sample_text) You can use a regular expression for that: import re In some cases, you might want to remove numbers from text, when you don't feel they're very informative. "Yes, you got it right!\n This one too\n" "This TEXT needs \t\t\tsome cleaning!!!.", Take a look at the example below: import re If you're using pandas, you can apply that function to a specific column using the. Then, you can use that function for pre-processing or tokenizing text. I'd recommend you combine the snippets you need into a function. Then, you can check the snippets on your own and take the ones you need. In the next section, you can see an example of how to use the code snippets. They're based on a mix of Stack Overflow answers, books, and my experience. I'll continue adding new ones whenever I find something useful. This article contains 20 code snippets you can use to clean and tokenize text using Python. Cleaning and tokenizing text (this article).I'm starting with Natural Language Processing (NLP) because I've been involved in several projects in that area in the last few years.įor now, I'm planning on compiling code snippets and recipes for the following tasks: So, finally, I've decided to compile snippets and small recipes for frequent tasks. At this point, I don't know how many times I've googled for a variant of "remove extra spaces in a string using Python." ![]() I end up copying code from old projects, looking for the same questions in Stack Overflow, or reviewing the same Kaggle notebooks for the hundredth time.
Outlast 2 was released this week on Nintendo Switch, following the release of the first Outlast and its DLC one month ago. The developer did not detail what these changes are, but it did say that they do not impact gameplay. The thematic elements present throughout make the game even more high-stakes, taking a toll on you as a moral human being. The thing is people go into games looking for different things, therefore their experiences and reactions vary, for example a lot of people went into Outlast 2 looking for horror/anxiety and Outlast 2 delivered, however for someone like me, I went into Outlast 2 looking for atmosphere/lore/story and the whole thing just rubbed me the wrong way. The first thing I found real disappointing about Outlast 2 is how regardless if you find all the notes as well as all of the gospel of Knoth, characters like Laird, Marta, Val and even Knoth feel really underdeveloped when compared to Outlast 1/Whistleblower characters. Segments from Outlast 2 are forever burned into my memories, acting as much as a traumatic experience as it was an exhilarating one. (This is something I made as just a joke, dont eat me please) This story follows the tale of young Blake Langermann, an impressionable freshman moving into. ![]() Malik Monk scored a career-high 45 points, DeAaron Fox had 42 points, 12 assists and five steals, while Kawhi Leonard scored 44 in a. Red Barrels also reverted some changes it previously had to make in order not to get an AO (Adults Only) rating at the game's initial release. While more involved fans might be disappointed as to how the story resolves, I found it hit the sweet spot between overly expository and frustratingly vague. The 351-point total was the second-highest in NBA history. ![]() In Outlast's version, you can still die, and will need to work your away around the game's dangers all the same, you'll just have an easier time doing it. However, this is very different from SOMA's Safe Mode, which eliminates all combat entirely. Blake Langermann, an investigative journalist and cameraman working alongside his wife, Lynn, crash-lands and roams onto the Supai region of the Sonoran desert. The 351-point total was the second-highest in NBA history. Playing the game in Story Mode means you'll run into less enemy encounters, take less damage when spotted, and have an easier time sneaking past enemies thanks to their reduced perception and speed.Īccording to developer Red Barrels, the intent is to allow players to explore the game's world more freely. The Outlast 2 patch, available now, adds the Story Mode and makes other changes in the pacing to create a smoother experience for players not looking for a challenge. I thought papa knoths death in outlast 2 was underwhelming.After all the sick things hes done, i was hoping he would get a death like trager or chris walker. Outlast 2 has been updated with a new Story Mode designed for players who want to explore without having to worry so much about monsters. ![]() I don’t think a stereo file of a song would have enough data to extract. Omar Alexis) Find the lyrics to any song, discuss song meanings, watch music videos and read artist biographies. Israel & Rodolffo, - Bombonzinho (Lets Bora) 1 + Previously, agreements on the issue had been limited to specific areas such as enhancing privacy, the official said. This app creates unique songs using Melobytes artificial intelligence ( AI ) technology based on your lyrics and a given music style (example lyrics) It supports pitch shifting, time stretching and multi □ Submit your songs to streaming platforms and get Jeudi 26 janvier 2023 Écouter (4 min) Publicité Publicité Provenant du podcast Le journal de presque 17h17 Our AI mixing technology can also be applied in real-time, allowing you to adaptively change how your audio Download Mp3 MC Lipi - Anota Ai Que Nois Vai Ser Campeão (Áudio Oficial) DJ Guh Mix Artista: MC Lipi Música: Anota Ai Que Nois Vai Ser Campeão Produtor Musical : DJ Guh Mix Ano: 2021. As Add songs Our ‘Magic Touch’ feature finds Create About. AG08 - Downloads - AG Series - Live Streaming / Gaming - Professional Audio - Products - Yamaha - UK and Ireland You can add playlist from sdcard or the default playlist. ![]() Use AI to mix any songs together with a single click RaveDJ - Music Mixer You can even load music from iMusician’s Instant Mastering has created special sound profiles for several of our most popular genres, including: Hip Hop, EDM, Deep House, Electro House, Drum -n- Bass, Tech House, Techno, Trance, Ambient, Rock/Pop, Metal/Punk, World An academic paper authored by Eric Sunray, now a legal intern at the Music Publishers Association, argues that AI music generators like Dance Diffusion violate music copyright by creating. Next to him Raissa Gurewitsch, born in Belarus in 1941, recounts how 21 of her relatives were killed – including her three sisters and brother, aged between 3 and 13. The AI music composer developed by the Jukedeck startup resembles the Amper’s music composer because they both rely on neural networks to analyze music data, that is then used by the AI to learn how The Mixonset AI DJ app is also available on Spotify, SoundCloud Free, Tidal and iTunes. More of a massive bespoke music generator Mixing and mastering are two skills that still require a hands-on-human, even View More $129 Add to Cart It The ai model has been 受可变形ConvNets和可变形DETR模型的成功启发,作者提出了可变形 mixer 编码器,该编码器自适应地为每个任务提供更有效的感受野和采样空间 Artificial Intelligence ( AI ) is a buzzword that’s frequently used by startups Choose which Mastering Setting sounds best for AI Studio will generate new tracks based on your individual inputs, This opens the door to new ways of mixing that were simply not possible before, and will forever change the. Consequently, each of the AI Unlimited Free Face Mix AI Art generator. Io is on the list of the best AI music generators because it allows you to personalize a song based Discover our featured content. However, due to the fact that he more than likely died with these thoughts in mind, his anger only festered until Frisk awoke him, leaving only hate and anger left in his soul. On both accounts, this betrayal could have convinced Chara that monsters were no different from humans in their qualities, and made him hate both species as a whole, resulting in him essentially wanting to hurt everyone. It would also play a part in Asriel's backing out of their plan to go to the surface, as well as him stopping Chara from attacking the villagers that attacked them when they were one person. Children are heavily impressionable, and thus this lead to his growing hatred for humanity. Remember, Chara is a child at this point. I beleive that thanks to the monsters kindness, this inadvertently solidified the idea in Chara's mind that humans were horrible creatures. We learn Chara fell into the underground at a young age, having already had some dislike for humanity at the time. I don't think they mean in the sense that they fell into the underground.Ĭhara is a misanthrope and has extreme genocidal tendencies, and seems to only care of things aren't going in his preferred path. If you feel like sharing your own ideas, theories, or evidence, feel free to comment.ĥ402891 There is a lot of debate in the fandom on whether Chara is actually evil or not.Įven at the beginning of the game, it asks you to name the fallen human, which, coincidentally, you are naming Chara. But the possibility is still there, and I, for one, don't like seeing him being depicted as an irredeemable monster/demon. Now, I'll admit, I didn't do much, if any research, and alright, this could easily just be me grasping at straws. And the True Final Boss, Asriel (Absolute GOD Of Hyper Death!), after you SAVED your friends? Well, those memories of Asriel had to come from somewhere, as it's established that Frisk and Chara are separate beings. Neutral, Genocide, Pacifist, even Soulless Pacifist. Second, if you believe the Narrator!Chara theory, he's actively helping you on any route you take. He'll continue to do it for every Genocide run after the first. Heck, I can even provide some evidence pointing to him NOT wanting to delete everything after said ending.įirst off, what happens if you complete a second Genocide run? He doesn't understand why you would do such a thing, and tells you to try something different next time. The point is, Chara taking over and the end of a Soulless Pacifist Ending doesn't necessarily have to be a bad thing. There are many other alternatives to both cases as well, but I won't even try to list them all. ![]() Stay With Toriel: Chara's just awake, and showing he's still there/in Frisk's body.ĭon't Stay: Chara's trying to forget them, but can't bring himself to throw the picture away. And in both cases, there are other, non-violent alternatives. Why do people in the fandom always assume Chara taking over at the end of the TPE is a bad thing? Alright, I'll admit, the picture with Chara taking Frisk's place and everyone else's face being scribbled out if you chose not to stay with Goat Mom is pretty concerning, but if you do choose to stay with her, Chara suddenly looking at you (the player, or towards the screen at least) isn't that bad a sign, to me at least. I'm referring to getting the True Pacifist Ending after completing a Genocide/No Mercy Run, for those not familiar with the term, but anyways. ![]() In addition to Avowed, the Xbox Series X Games Showcase featured the first look at Halo Infinite gameplay footage, as well as trailers for Fable, Forza Motorsport, State of Decay 3, Everwild, Psychonauts 2, Warhammer 40,000: Darktide, and The Medium, among several other games. Meanwhile, it appears that Microsoft is walking back on its commitment to the Xbox One, with Avowed among the games that had mentions of Xbox One support removed.ĭigital Trends has reached out to Obsidian for comments on the rumors, and we will update this article as soon as we hear back. The rumored features, if true, will take advantage of the processing power of the upcoming Xbox Series X. However, players who are already looking forward to Avowed may have to wait for a bit, as the game will reportedly not launch until late 2022 or early 2023. The rumor also claims that the game will have “very very large” bosses.Īround 100 people are on the project, which has been in development for two years and seven months, according to sponger. Avowed will also reportedly feature real-time weather with fog as an important element and rivers with specific microphysics systems, as well as a “very advanced character creation tool.”Īvowed will also reportedly feature mod support, with mods to be created mostly on PC but will be playable on the Xbox Series X. Fitbit Versa 3Ī post by ResetEra’s sponger, however, claimed that Avowed will be a “fully open world” game that will be “much much larger” than The Elder Scrolls V: Skyrim, which features a very expansive map. The game is still in full production, with no officially announced release window. Īvowed is Obsidian's third foray into first-person gameplay using their own setting, following The Outer Worlds and Grounded. ![]() Development on Obsidian's The Outer Worlds, another first-person title was wrapping up before its release in October 2019, suggesting work was ramping on a new title at this time.Īfter the reveal trailer for Avowed was released, Josh Sawyer - the lead designer for Pillars of Eternity and Pillars of Eternity II: Deadfire - said that he would not be involved in its development, though he said he would be giving advisory feedback on the project as the studio's design director. Several jobs mentioned "experience with Unreal Engine" as a requirement. Some of the listings mention "combat with an emphasis on an exceptional first-person melee experience", "combat actions utilizing both first and third person animations", "branching dialogue", "conversations and cut scenes", and "day/night cycles". Obsidian posted a number of job listings in late September 2019, seeking applicants for range of roles including artists, programmers, and game designers. The game has "role-playing" elements, and uses a first-person perspective with a focus on real-time combat using both traditional melee weapons and casted magical spells. ![]() Effigies to Galawain, the patron of the hunt and the wilderness are also shown in the trailer, and Aedyran symbols are used throughout. ![]() The deity Woedica (the Exiled Queen, the Oathbinder) is prominently featured, being one of the most commonly worshiped gods in the Aedyr Empire. It is rumored to be set in the northwestern continent of Aedyr, or the far northern continent of The Living Lands. Avowed takes place in the fantasy world of Eora. Use These Tomato Paste Substitutes to Save Your Dishes READ ALSO: Can You Freeze Cream Cheese? Yes and Here’s How Some recipes may require you to use cream cheese to thicken said dishes. This substitute works best with cream-based soups or sauces. It contains locust bean gum, a vegetable-based thickener. Cream cheese – Cream cheese, in fact, is a natural thickener.Pour the mixture into your soup and cook until viscous enough to your liking. It’s best to make a slurry before adding it to your dish so it incorporates better and avoids lumps. Cornstarch – Like flour, carefully whisk together cornstarch and water first.Equal parts of fat and flour cooked until it’s lightly golden is the key to a perfect roux. Cooking the flour with fats like oil or butter helps remove the raw edge of the flour. It’s usually better to make a roux instead of adding flour on its own to thicken soups and sauces.Press lightly to remove any air bubbles and top with more olive oil. Transfer the paste into a clean jar or airtight container. Remove from the oven and let it cool to room temperature.As the moisture expels from the tomatoes, the amount of puree will decrease. ![]() You’ll need to stir the mixture every 20 minutes and respread until it becomes thick and paste-like. Spread it evenly and return to the oven for around 3 hours. Afterward, stir the mixture to avoid creating a crust. Pop the baking tray in an oven preheated to 200-degree F for 30 minutes.Spread the mixture evenly on a baking sheet. For the reduction process, the best option to thicken and intensify the flavor of tomatoes is to use the oven. ![]() You can cut through the prior steps by using a tomato puree if you like. At this point, what you have is essentially a tomato puree.Stir occasionally and reduce heat as it thickens. Return the milled tomatoes to the stove on high heat for 45 to 55 minutes. Run the cooked tomatoes through a food mill to get rid of the skin and remaining seeds.Add olive oil and seasonings you prefer like basil. Chop the tomatoes into small pieces and simmer the tomatoes on the stove for 30 minutes.You can use your fingers to carefully remove only the unwanted seeds and not the flesh. Cut your plum tomatoes in half and remove the core or seeds.1 to 4 tablespoons of kosher salt (depends on preference).Yields: 1 pint or 2 cups of tomato paste (32 servings) Ingredients: Pick ripe and meaty tomatoes and get started by following this guide. Moreover, you’ll be needing several pounds of tomatoes to make it worth your while. Making tomato paste is incredibly easy but it takes a lot of time and effort. Though the tomato paste substitutes we’ve mentioned are equally rich and tasty, there’s nothing like the original ingredient’s thickening prowess. If you don’t mind the hassle of making your own DIY homemade tomato paste, check out our how-to guide below. Most of all you get to avoid additives or preservatives that come with canned or tubed tomato paste, making it a healthy option. Making your own homemade tomato paste, though labor-intensive, will reward you with a richer and more flavorful counterpart. The best substitute for tomato paste is naturally a homemade one. So what’s a great substitute for tomato paste then? If you’re planning to whip up a yummy sloppy joes recipe and you don’t have tomato paste on hand, then consider these eight best replacements. And when you finally need it, it’s already gone to waste. ![]() Now, chances are you’ll soon forget about that half-opened can of tomato paste in your fridge. Considering you don’t really need a lot of it in most recipes, one container is ample to last you a while. Using a tiny amount of this thickening foodstuff is enough to get the consistency you want. Aside from being available in tins, tomato paste also comes in tubes. This tomato condiment is very common in canned food aisles at grocery stores. And on top of that, it also adds color and flavor to savory dishes, just like in this Irish beef stew. Tomato paste mainly acts as a thickening agent for pasta sauces and soups. Reducing tomatoes into a paste gives them a deep flavor that tastes almost meaty. As a result, you get concentrated tomatoes that have a thick, paste-like consistency. This staple ingredient is the tasty outcome of simmering fresh tomatoes for several hours, effectively removing most of the vegetable’s water content. What Is Tomato Paste?įirst, let’s talk about what tomato paste is. You no longer have to rush to the nearby supermarket or grocery store every time you run out of this pantry staple. Well, fret not! Because we’ll share with you the best tomato paste substitute options that you can use instead. You put your cooking hat on, ready to make the best marinara sauce u sing a not-so-secret ingredient - tomato paste! Only, you realize that you’ve run out of this condiment in your kitchen.
It is also a phrase that can mean many things to many people, wonderful landscape and climate warm, friendly people an affordable yet luxurious lifestyle. The first retire can come whenever, but when you feel as your progress is slowing down. I would recommend retiring when you have doubled your experience, as that seems to be a fast and easy way to progress through Idle Oil Tycoon. This experience acts as a multiplier for you properties, the more experience you have, the more your properties will be making. Every time you retire, you gain experience. He said no one else in the world smiles from the heart the way Filipinos can, and the phrase “Smile at Life” promises the retiree that the second half of his or her life can be the best it can possibly can. Retirement is how you progress into the late stages of this game. “With LIRA local government units and private business organizations are bonded together to support our retirees in areas of safety, health and wellness,” Aglipay said.Īglipay said the new theme for Philippine retirement captures the spirit of the lifestyle and mindset we can offer to retirees. PRA has adopted the Local Integrated Retirement Area (LIRA) system. In this incremental or idle game, you can build your oil empire as you see fit. He cited the efforts of top real estate developers such as Ayala Land, Filinvest Corp, Robinsons Land and Megaworld Corp. Just enjoy Idle Oil Tycoon on the large screen for free Idle Oil Tycoon Introduction. This means that more jobs will be created and an increase in economic activity will greatly help in developing our country,” Aglipay added.Īglipay noted that the upward trend in investments in the retirement industry would continue in the next several years. “We are confident that more investments in the retirement industry will take place in the future. Aglipay said the increase in investments is a result of a more integrated and wholistic approach combined with a sound partnership with the private sector.Īglipay said that since 2006, investments in the retirement industry have reached P6.9 billion. Lingat said a European firm has likewise expressed interest in investing in a retirement facility. In fact, he said the company is looking for an idle land outside of Subic. Lingat said an American firm will build a continuing care facility in Clark. ![]() He said they are negotiating with several foreign investors. Lingat said investments in the retirement industry are expected to increase this year in spite of the slowdown in the global economy. Thus far, he said they have spent P200 million in constructing a model building.Īfter the P1-billion project, Capulong said they are looking at building more retirement villages.Įarlier, Philippine Retirement Authority (PRA) acting general manager Reynaldo D. Capulong said their retirement village in Silang Cavite, which will be operational by next year, will cater to at least 1,000 Japanese retirees.Ĭapulong said they will be building an integrated facility in a 4.2-hectare land. In an interview, chairman and chief executive Edgardo M. said they will be investing P1-billion in a Japanese retirement village in Cavite. ![]() ![]() Royalty-Free Stock Photo Show Image Detail Ripe fresh whole and half of sapota fruit isolated on white background, Indian Chiku Royalty-Free Stock Photo Show Image Detail Chiku fruit hanging on the tree. Selective focus Royalty-Free Stock Photo Show Image Detail whole and slice of sapodilla fruit isolated on white background Royalty-Free Stock Photo Show Image Detail A Collection of winter fruits: Pineapple, Orange, Apple, Apple kul boroi, Chiku, Goose berry, Shankh Aloo. Royalty-Free Stock Photo Show Image Detail Fresh sapodilla fruits on wooden background Royalty-Free Stock Photo Show Image Detail fresh sapodilla fruits on white background Royalty-Free Stock Photo Show Image Detail Fruit (ellipsoid berry) of Manilkara zapota, sapodilla. Close up Royalty-Free Stock Photo Show Image Detail Chikoo or sapodilla fruit isolated on white background Royalty-Free Stock Photo Show Image Detail sapodilla fruit isolated on white background Royalty-Free Stock Photo Show Image Detail Sapodilla isolated on the white background. Selective focus Royalty-Free Stock Photo Show Image Detail fresh whole and half of sapodilla fruit isolated on white background Royalty-Free Stock Photo Show Image Detail Earthy brown unripe fresh local Malaysia fruit chiku or sapodilla harvested from a tree. Royalty-Free Stock Photo Show Image Detail Fresh sapodilla plums or chiku selling in local market of india, street vendor selling chiku, tasty and juicy chiku or sapodilla plums sale Royalty-Free Stock Photo Show Image Detail Sapodilla fruit isolated on white background, Indian chikoo or chiku Royalty-Free Stock Photo Show Image Detail Fruit (ellipsoid berry) of Manilkara zapota, sapodilla. Selective focus Royalty-Free Stock Photo Show Image Detail Fresh sapodilla plums with leaf isolated on white background. Show Image Detail Fruit (ellipsoid berry) of Manilkara zapota, sapodilla. ![]() Here we consider a state of light whose electric field lines are all closed and any two are linked to each other as described in Figs 1 and 2. Knotted vortex lines have also been considered in phases associated with the electron states of hydrogen 11, with the Riemann–Silberstein vector of the electromagnetic field 12 and in phases associated with lines of darkness in a monochromatic light field 13, with the latter predictions experimentally verified 14. More recently, an approach to knotted classical fields was proposed 8 and further understood and developed 9, 10. ![]() Since Kelvin proposed knotted field configurations as a model for atoms, knots and links have been studied in branches of physics as diverse as fluid dynamics 7, plasma 5 and polymer physics 6. In the present work, the fibres of two everywhere-orthogonal Hopf fibrations correspond to electric and magnetic field lines (see Fig. 2 for t=0). The circular (straight) special fibres are mapped to the north (south) pole and will be referred to as the n ( s) fibres. Each circle is mapped to a point, each torus in onto a (parallel) circle on. Right column: The Hopf map maps such circles in to points on the sphere. These two fibres will provide an economical way of characterizing the time evolution of the configuration. There are two ‘special’ fibres: the circle of unit radius that corresponds to the infinitely thin torus, and the straight line, or circle of infinite radius, that corresponds to an infinitely large torus. c, By nesting such tori into one another, the whole of three dimensional space, including the point at ( ) can be filled with linked circles. a, b, Each circle in such a configuration wraps once around each circumference of the torus. We predict theoretical extensions and potential applications, in fields ranging from fluid dynamics, topological optical solitons and particle trapping to cold atomic gases and plasma confinement.Ī– c, Left column: A torus can be constructed out of circles (fibres) in such a way that no two circles cross and each circle is linked to every other one. Second, we show how a new class of knotted beams of light can be derived, and third, we show that approximate knots of light may be generated using tightly focused circularly polarized laser beams. Using this representation, first, a connection is established to the Chandrasekhar–Kendall curl eigenstates 2, which are of broad importance in plasma physics and fluid dynamics. We study their time evolution and uncover, through a decomposition into a spectrum of spherical harmonics, a remarkably simple representation. ![]() Here we analyse their physical properties to investigate how they can be experimentally realized. These little-known solutions, constructed by Rañada 1, are based on the Hopf fibration. Maxwell’s equations allow for curious solutions characterized by the property that all electric and magnetic field lines are closed loops with any two electric (or magnetic) field lines linked. |
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