❤️ BCS theory 🐸

"A commemorative plaque placed in the Bardeen Engineering Quad at the University of Illinois at Urbana-Champaign. It commemorates the Theory of Superconductivity developed here by John Bardeen and his students, for which they won a Nobel Prize for Physics in 1972. BCS theory or Bardeen–Cooper–Schrieffer theory (named after John Bardeen, Leon Cooper, and John Robert Schrieffer) is the first microscopic theory of superconductivity since Heike Kamerlingh Onnes's 1911 discovery. The theory describes superconductivity as a microscopic effect caused by a condensation of Cooper pairs. The theory is also used in nuclear physics to describe the pairing interaction between nucleons in an atomic nucleus. It was proposed by Bardeen, Cooper, and Schrieffer in 1957; they received the Nobel Prize in Physics for this theory in 1972. History Rapid progress in the understanding of superconductivity gained momentum in the mid-1950s. It began with the 1948 paper, "On the Problem of the Molecular Theory of Superconductivity", where Fritz London proposed that the phenomenological London equations may be consequences of the coherence of a quantum state. In 1953, Brian Pippard, motivated by penetration experiments, proposed that this would modify the London equations via a new scale parameter called the coherence length. John Bardeen then argued in the 1955 paper, "Theory of the Meissner Effect in Superconductors", that such a modification naturally occurs in a theory with an energy gap. The key ingredient was Leon Cooper's calculation of the bound states of electrons subject to an attractive force in his 1956 paper, "Bound Electron Pairs in a Degenerate Fermi Gas". In 1957 Bardeen and Cooper assembled these ingredients and constructed such a theory, the BCS theory, with Robert Schrieffer. The theory was first published in April 1957 in the letter, "Microscopic theory of superconductivity". The demonstration that the phase transition is second order, that it reproduces the Meissner effect and the calculations of specific heats and penetration depths appeared in the December 1957 article, "Theory of superconductivity". They received the Nobel Prize in Physics in 1972 for this theory. In 1986, high-temperature superconductivity was discovered in La-Ba-Cu-O, at temperatures up to 30 K. Following experiments determined more materials with transition temperatures up to about 130 K, considerably above the previous limit of about 30 K. It is believed that BCS theory alone cannot explain this phenomenon and that other effects are in play. These effects are still not yet fully understood; it is possible that they even control superconductivity at low temperatures for some materials. Overview At sufficiently low temperatures, electrons near the Fermi surface become unstable against the formation of Cooper pairs. Cooper showed such binding will occur in the presence of an attractive potential, no matter how weak. In conventional superconductors, an attraction is generally attributed to an electron-lattice interaction. The BCS theory, however, requires only that the potential be attractive, regardless of its origin. In the BCS framework, superconductivity is a macroscopic effect which results from the condensation of Cooper pairs. These have some bosonic properties, and bosons, at sufficiently low temperature, can form a large Bose–Einstein condensate. Superconductivity was simultaneously explained by Nikolay Bogolyubov, by means of the Bogoliubov transformations. In many superconductors, the attractive interaction between electrons (necessary for pairing) is brought about indirectly by the interaction between the electrons and the vibrating crystal lattice (the phonons). Roughly speaking the picture is the following: > An electron moving through a conductor will attract nearby positive charges > in the lattice. This deformation of the lattice causes another electron, > with opposite spin, to move into the region of higher positive charge > density. The two electrons then become correlated. Because there are a lot > of such electron pairs in a superconductor, these pairs overlap very > strongly and form a highly collective condensate. In this "condensed" state, > the breaking of one pair will change the energy of the entire condensate - > not just a single electron, or a single pair. Thus, the energy required to > break any single pair is related to the energy required to break all of the > pairs (or more than just two electrons). Because the pairing increases this > energy barrier, kicks from oscillating atoms in the conductor (which are > small at sufficiently low temperatures) are not enough to affect the > condensate as a whole, or any individual "member pair" within the > condensate. Thus the electrons stay paired together and resist all kicks, > and the electron flow as a whole (the current through the superconductor) > will not experience resistance. Thus, the collective behavior of the > condensate is a crucial ingredient necessary for superconductivity. =Details= BCS theory starts from the assumption that there is some attraction between electrons, which can overcome the Coulomb repulsion. In most materials (in low temperature superconductors), this attraction is brought about indirectly by the coupling of electrons to the crystal lattice (as explained above). However, the results of BCS theory do not depend on the origin of the attractive interaction. For instance, Cooper pairs have been observed in ultracold gases of fermions where a homogeneous magnetic field has been tuned to their Feshbach resonance. The original results of BCS (discussed below) described an s-wave superconducting state, which is the rule among low- temperature superconductors but is not realized in many unconventional superconductors such as the d-wave high-temperature superconductors. Extensions of BCS theory exist to describe these other cases, although they are insufficient to completely describe the observed features of high- temperature superconductivity. BCS is able to give an approximation for the quantum-mechanical many-body state of the system of (attractively interacting) electrons inside the metal. This state is now known as the BCS state. In the normal state of a metal, electrons move independently, whereas in the BCS state, they are bound into Cooper pairs by the attractive interaction. The BCS formalism is based on the reduced potential for the electrons' attraction. Within this potential, a variational ansatz for the wave function is proposed. This ansatz was later shown to be exact in the dense limit of pairs. Note that the continuous crossover between the dilute and dense regimes of attracting pairs of fermions is still an open problem, which now attracts a lot of attention within the field of ultracold gases. = Underlying evidence = The hyperphysics website pages at Georgia State University summarize some key background to BCS theory as follows: * Evidence of a band gap at the Fermi level (described as "a key piece in the puzzle") : the existence of a critical temperature and critical magnetic field implied a band gap, and suggested a phase transition, but single electrons are forbidden from condensing to the same energy level by the Pauli exclusion principle. The site comments that "a drastic change in conductivity demanded a drastic change in electron behavior". Conceivably, pairs of electrons might perhaps act like bosons instead, which are bound by different condensate rules and do not have the same limitation. *Isotope effect on the critical temperature, suggesting lattice interactions : The Debye frequency of phonons in a lattice is proportional to the inverse of the square root of the mass of lattice ions. It was shown that the superconducting transition temperature of mercury indeed showed the same dependence, by substituting natural mercury 202Hg with a different isotope 198Hg. * An exponential rise in heat capacity near the critical temperature for some superconductors : An exponential increase in heat capacity near the critical temperature also suggests an energy bandgap for the superconducting material. As superconducting vanadium is warmed toward its critical temperature, its heat capacity increases massively in a very few degrees; this suggests an energy gap being bridged by thermal energy. * The lessening of the measured energy gap towards the critical temperature : This suggests a type of situation where some kind of binding energy exists but it is gradually weakened as the temperature increases toward the critical temperature. A binding energy suggests two or more particles or other entities that are bound together in the superconducting state. This helped to support the idea of bound particles - specifically electron pairs - and together with the above helped to paint a general picture of paired electrons and their lattice interactions. Implications BCS derived several important theoretical predictions that are independent of the details of the interaction, since the quantitative predictions mentioned below hold for any sufficiently weak attraction between the electrons and this last condition is fulfilled for many low temperature superconductors - the so-called weak- coupling case. These have been confirmed in numerous experiments: * The electrons are bound into Cooper pairs, and these pairs are correlated due to the Pauli exclusion principle for the electrons, from which they are constructed. Therefore, in order to break a pair, one has to change energies of all other pairs. This means there is an energy gap for single-particle excitation, unlike in the normal metal (where the state of an electron can be changed by adding an arbitrarily small amount of energy). This energy gap is highest at low temperatures but vanishes at the transition temperature when superconductivity ceases to exist. The BCS theory gives an expression that shows how the gap grows with the strength of the attractive interaction and the (normal phase) single particle density of states at the Fermi level. Furthermore, it describes how the density of states is changed on entering the superconducting state, where there are no electronic states any more at the Fermi level. The energy gap is most directly observed in tunneling experimentsIvar Giaever - Nobel Lecture. Nobelprize.org. Retrieved 16 Dec 2010. http://nobelprize.org/nobel_prizes/physics/laureates/1973/giaever- lecture.html and in reflection of microwaves from superconductors. * BCS theory predicts the dependence of the value of the energy gap Δ at temperature T on the critical temperature Tc. The ratio between the value of the energy gap at zero temperature and the value of the superconducting transition temperature (expressed in energy units) takes the universal value ::\Delta(T=0)=1.764 \, k_{\rm B}T_{\rm c}, :independent of material. Near the critical temperature the relation asymptotes to ::\Delta(T \to T_{\rm c})\approx 3.06 \, k_{\rm B}T_{\rm c}\sqrt{1-(T/T_{\rm c})} :which is of the form suggested the previous year by M. J. Buckingham based on the fact that the superconducting phase transition is second order, that the superconducting phase has a mass gap and on Blevins, Gordy and Fairbank's experimental results the previous year on the absorption of millimeter waves by superconducting tin. * Due to the energy gap, the specific heat of the superconductor is suppressed strongly (exponentially) at low temperatures, there being no thermal excitations left. However, before reaching the transition temperature, the specific heat of the superconductor becomes even higher than that of the normal conductor (measured immediately above the transition) and the ratio of these two values is found to be universally given by 2.5. * BCS theory correctly predicts the Meissner effect, i.e. the expulsion of a magnetic field from the superconductor and the variation of the penetration depth (the extent of the screening currents flowing below the metal's surface) with temperature. * It also describes the variation of the critical magnetic field (above which the superconductor can no longer expel the field but becomes normal conducting) with temperature. BCS theory relates the value of the critical field at zero temperature to the value of the transition temperature and the density of states at the Fermi level. * In its simplest form, BCS gives the superconducting transition temperature Tc in terms of the electron-phonon coupling potential V and the Debye cutoff energy ED: ::k_{\rm B}\,T_{\rm c} = 1.14E_{\rm D}\,{e^{-1/N(0)\,V}}, :where N(0) is the electronic density of states at the Fermi level. For more details, see Cooper pairs. * The BCS theory reproduces the isotope effect, which is the experimental observation that for a given superconducting material, the critical temperature is inversely proportional to the mass of the isotope used in the material. The isotope effect was reported by two groups on 24 March 1950, who discovered it independently working with different mercury isotopes, although a few days before publication they learned of each other's results at the ONR conference in Atlanta. The two groups are Emanuel Maxwell, and C. A. Reynolds, B. Serin, W. H. Wright, and L. B. Nesbitt. The choice of isotope ordinarily has little effect on the electrical properties of a material, but does affect the frequency of lattice vibrations. This effect suggests that superconductivity is related to vibrations of the lattice. This is incorporated into BCS theory, where lattice vibrations yield the binding energy of electrons in a Cooper pair. * Little–Parks experiment One of the first indications to the importance of the Cooper-pairing principle. See also * Magnesium diboride, considered a BCS superconductor * Quasiparticle * Little–Parks effect, one of the first indications of the importance of the Cooper pairing principle. References=Primary sources= Further reading * John Robert Schrieffer, Theory of Superconductivity, (1964), * Michael Tinkham, Introduction to Superconductivity, * Pierre-Gilles de Gennes, Superconductivity of Metals and Alloys, . Schmidt, Vadim Vasil'evich. The physics of superconductors: Introduction to fundamentals and applications. Springer Science & Business Media, 2013. External links * ScienceDaily: Physicist Discovers Exotic Superconductivity (University of Arizona) August 17, 2006 * Hyperphysics page on BCS * BCS History * Dance analogy of BCS theory as explained by Bob Schrieffer (audio recording) * Mean-Field Theory: Hartree-Fock and BCS in E. Pavarini, E. Koch, J. van den Brink, and G. Sawatzky: Quantum materials: Experiments and Theory, Jülich 2016, Superconductivity "

❤️ Biathlon 🐸

"The biathlon is a winter sport that combines cross-country skiing and rifle shooting. It is treated as a race, with contestants skiing through a cross- country trail whose distance is divided into shooting rounds. The shooting rounds are not timed per se, but depending on the competition missed shots result in extra distance or time being added to the contestant's total. History Norwegian ski-soldier (Drawing published in 1811). According to Encyclopædia Britannica, the biathlon "is rooted in the skiing traditions of Scandinavia, where early inhabitants revered the Norse god Ullr as both the ski god and the hunting god". In modern times, the activity that developed into this sport was an exercise for Norwegian people that was an alternative training for the military. Norwegian skiing regiments organized military skiing contests in the 18th century, divided in four classes: shooting at mark while skiing at top speed, downhill race among trees, downhill race on big hills without falling, and a long race on flat ground while carrying rifle and military pack. In modern terminology these military contests included downhill, slalom, biathlon, and cross-country skiing.Bergsland, Einar (1946): På ski. Oslo: Aschehoug. One of the world's first known ski clubs, the Trysil Rifle and Ski Club, was formed in Norway in 1861 to promote national defense at the local level. 20th century variants include (the military contest) – a 17 km cross-country race with shooting, and the military cross-country race at 30 km including marksmanship. The modern biathlon is a civilian variant of the old military combined exercise.Bø, Olav: Skiing throughout history, translated by W. Edson Richmond. Oslo: Samlaget, 1993. In Norway, the biathlon was until 1984 a branch of , an organization set up by the government to promote civilian marksmanship in support of national defense. In Norwegian, the biathlon is called (literally ski shooting).Kunnskapsforlagets idrettsleksikon (Encyclopedia of Sports), Oslo: Kunnskapsforlaget, 1990 In Norway there are still separate contests in , a cross-country race at 12 km with large-caliber rifle shooting at various targets with unknown range. Called military patrol, the combination of skiing and shooting was contested at the Winter Olympic Games in 1924, and then demonstrated in 1928, 1936, and 1948, during which time Norway and Finland were strong competitors. In 1948, the sport was reorganized under the Union Internationale de Pentathlon Moderne et Biathlon and became re-accepted as in Olympic sport in 1955, with widespread popularity within the Soviet and Swedish winter sport circuits. The first Biathlon World Championship was held in 1958 in Austria, and in 1960 the sport was finally included in the Olympic Games. At Albertville in 1992, women were first allowed in the Olympic biathlon. The pursuit format was added for the 2002 Salt Lake City Winter Olympics and the IBU added mixed relay as a format for the 2006 season. The competitions from 1958 to 1965 used high-power centerfire cartridges, such as the .30-06 Springfield and the 7.62×51mm NATO, before the .22 Long Rifle rimfire cartridge was standardized in 1978. The ammunition was carried in a belt worn around the competitor's waist. The sole event was the men's 20 km individual, encompassing four separate ranges and firing distances of 100 m, 150 m, 200 m, and 250 m. The target distance was reduced to 150 m with the addition of the relay in 1966. The shooting range was further reduced to 50 m in 1978 with the mechanical self-indicating targets making their debut at the 1980 Winter Olympics in Lake Placid. For the 2018/2019 season, fully electronic targets were approved as an alternative to paper or mechanical steel targets for IBU events.New Season, New Rules - International Biathlon Union - IBU - International Biathlon Union - IBU Governing body In 1948, the International Modern Pentathlon Union was founded, to standardise the rules for the modern pentathlon and, from 1953 also biathlon. In July 1993, the biathlon branch of the UIPMB created the International Biathlon Union (IBU), which officially separated from the UIPMB in 1998. Presidents of the UIPMB/IBU: * 1947–1949: Tom Wiborn (Sweden) * 1949–1960: Gustaf Dyrssen (Sweden) * 1960–1988: Sven Thofelt (Sweden) * 1988–1992: Igor Novikov (USSR/Russia) * 1992-2018: Anders Besseberg (Norway) * Since 2018: Olle Dahlin (Sweden) Championships The following articles list major international biathlon events and medalists. Contrary to the Olympics and World Championships (BWCH), the World Cup (BWC) is an entire winter season of (mostly) weekly races, where the medalists are those with the highest sums of World Cup points at the end of the season. * Biathlon at the Winter Olympics * Biathlon World Championships * Biathlon World Cup * Biathlon European Championships * IBU Cup * Biathlon Junior World Championships * Biathlon at the Winter Universiade Rules and equipment The complete rules of the biathlon are given in the official IBU rule books. =Basic concepts= A biathlon competition consists of a race in which contestants ski through a cross-country trail system whose total distance is divided into either two or four shooting rounds, half in prone position, the other half standing. Depending on the shooting performance, extra distance or time is added to the contestant's total skiing distance/time. The contestant with the shortest total time wins. For each shooting round, the biathlete must hit five targets or receive a penalty for each missed target, which varies according to the competition rules, as follows: * Skiing around a 150 m penalty loop—typically taking 20–30 seconds for elite biathletes to complete, depending on weather and snow conditions. * Adding one minute to the skier's total time. * Use of an extra cartridge (placed at the shooting range) to hit the target; only three such extras are available for each round, and a penalty loop must be done for each target left standing. In order to keep track of the contestants' progress and relative standing throughout a race, split times (intermediate times) are taken at several points along the skiing track and upon finishing each shooting round. The large display screens commonly set up at biathlon arenas, as well as the information graphics shown as part of the TV picture, will typically list the split time of the fastest contestant at each intermediate point and the times and time differences to the closest runners- up. =Skiing details= In the Olympics, all cross-country skiing techniques are permitted in the biathlon, allowing the use of skate skiing, which is overwhelmingly the choice of competitors. The minimum ski length is the height of the skier minus 4 cm. The rifle has to be carried by the skier during the race at all times. =Shooting details= The biathlete carries a small-bore rifle, which must weigh at least 3.5 kg, excluding ammunition and magazines. The rifles use .22 LR ammunition and are bolt action or Fortner (straight-pull bolt) action. Each rifle holds 4 magazines with 5 rounds each. Additional rounds can be kept on the stock of the rifle for a relay race. The target range shooting distance is 50 m. There are five circular shooting targets to be hit in each shooting round. When shooting in the prone position, the target diameter is 45 mm; when shooting in the standing position, the target diameter is 115 mm. This translates to angular target sizes of about 1 and 2.5 mrad respectively. On all modern biathlon ranges, the targets are self-indicating, in that they flip from black to white when hit, giving the biathlete, as well as the spectators, instant visual feedback for each shot fired. Ear protection is not required during biathlon shooting as the ammunition used is usually subsonic. An eyecup (blinder) is an optional feature of biathlon rifles. Competition format=Individual= The 20 km individual race (15 km for women) is the oldest biathlon event; the distance is skied over five laps. The biathlete shoots four times at any shooting lane (Lanes 1 - 15 are in prone while Lanes 16 - 30 are for standing),Even in English-speaking countries such as Canada and the United States each country may use different terms for the same thing in biathlon. For example: Stage (USA) vs. Bout (Canada), Shooting Point (USA) vs. Shooting Lane (Canada) in the order of prone, standing, prone, standing, totaling 20 targets. For each missed target a fixed penalty time, usually one minute, is added to the skiing time of the biathlete. Competitors' starts are staggered, normally by 30 seconds. A variation of the standard individual race, called short individual, was introduced during the 2018–19 Biathlon IBU Cup. The races are 15 km for men and 12.5 km for women and for each missed target 45 seconds will be added to the skiing time. =Sprint= The sprint is 10 km for men and 7.5 km for women; the distance is skied over three laps. The biathlete shoots twice at any shooting lane, once prone (Usually Lanes 1 - 15) and once standing (Lanes 16 - 30), for a total of 10 shots. For each miss, a penalty loop of 150 m must be skied before the race can be continued. As in the individual competition, the biathletes start in intervals. = Super Sprint = Introduced at the 2017–18 Biathlon IBU Cup, the Super Sprint is a shorter version of the sprint race. Unlike the traditional sprint race, the Super Sprint is divided into two segments – qualification and final. The qualification is done like the traditional sprint, but on an 0.8 km lap with total length of 1.6 km. Only the top 30 competitors qualify for the final, in which all competitors start simultaneously and do 5 laps on the same course (like in mass start) with total race length of 4 km. During the final the competitors have 3 spare rounds should they miss a target (like in relay race), but if not all targets are cleared during shooting instead of going to penalty loop, the biathlete is disqualified from the race. Changes were made for the following season with the course now being 1 km (0.2 km increase) meaning that the qualification race length will become 3 km, while the final race becomes 5 km in length. Also the number of spare rounds was decreased from three to one. =Pursuit= Olympic gold medalists Olga Zaitseva, Andrea Henkel and Marie Dorin-Habert at the World Cup pursuit race in Oberhof, 2013. In a pursuit, biathletes' starts are separated by their time differences from a previous race,Pursuit competition start intervals are determined by common rounding to the nearest whole second of the biathletes' time differences from the previous race the amount of time each biathlete lagged after the winner to the finish line. most commonly a sprint. The contestant crossing the finish line first is the winner. The distance is 12.5 km for men and 10 km for women, skied over five laps; there are four shooting bouts (two prone, two standing, in that order), and each miss means a penalty loop of 150 m. To prevent awkward or dangerous crowding of the skiing loops, and overcapacity at the shooting range, World Cup Pursuits are held with only the 60 top ranking biathletes after the preceding race. The biathletes shoot on a first-come, first-served basis at the lane corresponding to the position they arrived for all shooting bouts. =Mass start= In the mass start, all biathletes start at the same time and the first across the finish line wins. In this 15 km for men or 12.5 km for women competition, the distance is skied over five laps; there are four bouts of shooting (two prone, two standing, in that order) with the first shooting bout being at the lane corresponding to the competitor's bib number (Bib #10 shoots at lane #10 regardless of position in race), with the rest of the shooting bouts being on a first-come, first-served basis (If a competitor arrives at the lane in fifth place, they shoot at lane 5). As in sprint and pursuit, competitors must ski one 150 m penalty loop for each miss. Here again, to avoid unwanted congestion, World Cup Mass starts are held with only the 30 top ranking athletes on the start line (half that of the Pursuit as here all contestants start simultaneously). =Mass start 60= Starting in the 2018/2019 season, the Mass Start 60 becomes part of the International Biathlon Union (IBU) competition formats. The Mass Start with 60 starters does not replace the current Mass Start with 30 starters. Everyone skis the first lap together, but then only the first 30 stop to shoot and the second 30 keep skiing. At the end of the second lap the second 30 stop to shoot and the first 30 continue to ski. After the first two shoots are over (everyone's first prone) then the race continues like a normal one and they all shoot the other prone and two stands together. Or more simply: Bib 1-30 = lap-shoot1-lap-lap- shoot2-lap-shoot3-lap-shoot4-lap. Bib 31-60 = lap-lap-shoot1-lap-shoot2-lap- shoot3-lap-shoot4-lap. =Relay= The relay teams consist of four biathletes, who each ski 7.5 km (men) or 6 km (women), each leg skied over three laps, with two shooting rounds; one prone, one standing. For every round of five targets there are eight bullets available, though the last three can only be single-loaded manually one at a time from spare round holders or bullets deposited by the competitor into trays or onto the mat at the firing line. If after eight bullets there are still misses, one 150 m (490 ft) penalty loop must be taken for each missed target remaining. The first-leg participants start all at the same time, and as in cross-country skiing relays, every athlete of a team must touch the team's next-leg participant to perform a valid changeover. On the first shooting stage of the first leg, the participant must shoot in the lane corresponding to their bib number (Bib #10 shoots at lane #10 regardless of position in race), then for the remainder of the relay, the relay team shoots on a first-come, first-served basis (arrive at the range in fifth place, shoot at lane 5). =Mixed relay= The most recent addition to the number of biathlon competition variants, the mixed relay is similar to the ordinary relay but the teams are composed of two women and two men. Legs 1 and 2 are done by the women, legs 3 and 4 by the men. The women's legs are 6 km and men's legs are 7.5 km as in ordinary relay competitions. This event was first held at the Biathlon World Championships 2005 in Khanty-Mansiysk, and it was added to the 2014 Winter Olympics. In 2015, single mixed relay was introduced to the Biathlon World Cup by the IBU. Competing on a 1.5 km track, each team has a woman and a man, running respectively for 3 km + 3 km (2 + 2 laps) & 3 km + 4.5 km (2 + 3 laps), totalling 13.5 km. Specific to this format, relay happens immediately after the last shooting of each series, and not after a following lap as it happens normally. Either women or men starting is the result if a decision if the IBU Technical Committee. Since the last series has a supplemental lap between the last shooting and the finish line, it is most probable women will always start and men finish this race category. This event was first held at the Biathlon World Championships 2019 in Östersund. =Team (obsolete)= A team consists of four biathletes, but unlike the relay competition, all team members start at the same time. Two athletes must shoot in the prone shooting round, the other two in the standing round. In case of a miss, the two non-shooting biathletes must ski a penalty loop of 150 m (490 ft). The skiers must enter the shooting area together, and must also finish within 15 seconds of each other; otherwise a time penalty of one minute is added to the total time. Since 2004, this race format has been obsolete at the World Cup level. Broadcasting Biathlon events are broadcast most regularly where the sport enjoys its greatest popularity, namely Germany (ARD, ZDF), Austria (ORF), Norway (NRK), France (L'Équipe 21), Finland (YLE), Estonia (ETV), Latvia (LTV), Lithuania (LRT), Croatia (HRT), Poland (Polsat), Ukraine (UA:PBC), Sweden (SVT), Russia (Match TV, Channel One), Belarus (TVR), Slovenia (RTV), Bosnia and Herzegovina (BHRT), Bulgaria (BNT), and South Korea (KBS); it is broadcast on European-wide Eurosport, which also broadcasts to the Asia- Pacific region. World Cup races are streamed via the IBU website. The broadcast distribution being one indicator, the constellation of a sport's main sponsors usually gives a similar, and correlated, indication of popularity: for biathlon, these are the Germany-based companies E.ON Ruhrgas (energy), Krombacher (beer), and Viessmann (boilers and other heating systems). United States biathlete Jeremy Teela at the 2002 Winter Olympics. Biathlon records and statistics The IBU maintains biathlon records, rules, news, videos, and statistics for many years back, all of which are available at its web site. See also * Biathlon World Cup * Biathlon World Championships * List of Olympic medalists in biathlon * Paralympic biathlon * Nordic field biathlon and moose biathlon, Nordic biathlon variants using fullbore rifles Biathlon's two sports disciplines: * Cross-country skiing (sport) * Rifle shooting sports Other multi-discipline sports (otherwise unrelated to biathlon): * Duathlon * Nordic Combined * Triathlon * Pentathlon * Modern pentathlon * Heptathlon * Decathlon * Chess boxing * Omnium (track cycling) Notes and SourcesExternal links * Biathlonworld.Com – A cooperation between IBU and EBU; with race results/statistics, TV schedules, live competition results, and so on. = National Associations = * Belarusian Biathlon Union * Russian Biathlon Union * Russian Biathlon Union * Biathlon Canada * U.S. Biathlon Association * Biathlon Russia * Biathlon Ukraine * Biathlon Ukraine * BiathlonFrance.com Multisports Winter Olympic sports Cross-country skiing Racing Rifle shooting sports Military sports "

❤️ Bubble and squeak 🐸

"Bubble and squeak topped with poached egg. Bubble and squeak is a traditional British breakfast dish made from potatoes and cabbage. Historic recipes add meat to the bubble and squeak, although nowadays it is more commonly made without meat. The earliest-known recipe was in Mrs Rundell's A New System of Domestic Cookery in 1806.Rundell, Maria Eliza Ketelby (1808). Bubble and Squeak. In A new system of domestic cookery:Third edition. p. 42. Google Book Search. Retrieved on 6 January 2011. In modern times, it is a dish made with the pan-fried Sunday leftover vegetables from a roast dinner. The main ingredients are potato and cabbage, but carrots, peas, sprouts, or any other leftover vegetables may be added. The chopped vegetables (and cold chopped meat, if used) are fried in a pan together with mashed potatoes or crushed roast potatoes until the mixture is well-cooked and brown on the sides. The dish is so named because the cabbage makes bubbling and squeaking sounds during the cooking process.. It is often served with cold meat from the Sunday roast and pickles or brown sauce, or as an accompaniment to a full English breakfast. The name bubble and squeak is used primarily in England (for Scotland and Ireland In Canada where the term may have originated, it usually refers strictly to a dish of the leftovers of a cottage roll dinner. Scottish Recipes: Rumbledethumps Recipe see the section Similar dishes), and it may also be understood in parts of some other Commonwealth countries and the United States.Hearty Luncheon and Supper Dishes Reading Eagle, 17 July 1913.Forbes Lifestyle, Wine and Food Forbes, 17 November 2004. Bubble and squeak has been a popular dish since the late 1800s, as it was an easy way of using leftovers. In more recent times, ready-made pre-prepared versions have become available on the market. Similar dishes * Panackelty, from North East England * Rumbledethumps, stovies and clapshot from Scotland * Colcannon and champ, from Ireland * Stoemp from Belgium * Calentao, from Colombia * Biksemad, from Denmark * Bauernfrühstück and Stemmelkort, from Germany * Stamppot, from the Netherlands * Trinxat, from the La Cerdanya region of Catalonia, northeast Spain and Andorra * Pyttipanna, Pyttipanne and Pyttipannu (from the Swedish "pytt i panna"="small pieces in pan") from Sweden, Norway and Finland * Hash, from the United States * Aloo tikki, from India * Matevž, from Slovenia * Tortilla de verduras, from Chile References External links * English cuisine Potato dishes Cabbage dishes Brassica oleracea dishes Food combinations Breakfasts "