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25i-nbmd (nbmd-2c-i, cimbi-29) is a derivative of the
25i-nbmd (nbmd-2c-i, cimbi-29) is a derivative of the phenethylamine hallucinogen 2c-i, discovered in 2006 by a team at purdue university led by david nichols. it acts as a potent partial agonist for the 5ht receptor with a ki of 0.049 nm at the human 5ht receptor. the corresponding 4-bromo analogue 25b-nbmd has been used for molecular dynamics studies on the shape of the 5-ht receptor.
wikipedia
e44eea24283a4b4b355fba5b24d003e61242d942
5208 royer is a stony marian asteroid from
5208 royer is a stony marian asteroid from the central regions of the asteroid belt, approximately 8 kilometers in diameter. it was discovered on 6 february 1989, by astronomer eleanor helin at the palomar observatory. the s-type asteroid has a rotation period of 3.87 hours and was named after american priest and amateur astronomer, ronald royer.
wikipedia
a602780b12b616664be0b7317d7739360753a189
according to the survey carried out by the
according to the survey carried out by the neowise mission of nasa's wide-field infrared survey explorer, royer measures 7.884 and 8.081 kilometers in diameter and its surface has an albedo of 0.2854 and 0.270, respectively, while the collaborative asteroid lightcurve link assumes a standard albedo for stony asteroids of 0.20 and calculates a diameter of 9.40 kilometers based on an absolute magnitude of 12.5.
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5d5cea324d364e91b40aa7dde7b0121bd900ff64
in 2004, a rotational lightcurve of royer was
in 2004, a rotational lightcurve of royer was obtained from photometric observations by brazilian and argentine astronomers. lightcurve analysis gave a rotation period of 3.866 hours with a brightness amplitude of 0.44 magnitude (u=2). in 2016, a modeled lightcurves using photometric data from various sources, rendered a sidereal period of 3.88494 and two spin axes of (258.0°, 74.0°) and (54.0°, 37.0°) in ecliptic coordinates.
wikipedia
5320f59ef55e1554a9d73fcd13f42ef1760297db
this minor planet was named after reverend ronald
this minor planet was named after reverend ronald e. royer, an american priest as well as amateur astronomer and astrophotographer. he has been a member of the los angeles astronomical society (laas) since 1946 and received the g. bruce blair award in 2001. the official naming citation was published by the minor planet center on 6 april 1993 (m.p.c. 21957).
wikipedia
b9ad215832d5cf3735058951a99eb8ef4ef66084
it orbits the sun in the central asteroid
it orbits the sun in the central asteroid belt at a distance of 2.5–2.7 au once every 4 years and 2 months (1,535 days; semi-major axis of 2.6 au). its orbit has an eccentricity of 0.05 and an inclination of 16 ° with respect to the ecliptic. the body's observation arc begins with a precovery taken at palomar observatory in november 1953, more than 35 years prior to its official discovery observation.
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f076bc7daf1717737ff51a8615120324257642d1
5208 royer (prov. designation: 1989 ch) is a
5208 royer (prov. designation: 1989 ch) is a stony marian asteroid from the central regions of the asteroid belt, approximately 8 kilometers (5 miles) in diameter. it was discovered on 6 february 1989, by astronomer eleanor helin at the palomar observatory. the s-type asteroid has a rotation period of 3.87 hours and was named after american priest and amateur astronomer, ronald royer.
wikipedia
a1141a1fb9ad7242e54cbd24661004d5a6d7605b
adolph frank "aggie" kukulowicz was a canadian professional
adolph frank "aggie" kukulowicz was a canadian professional ice hockey player and russian-language interpreter. he played four games in the national hockey league for the new york rangers, then played 12 combined seasons in the minor leagues and senior ice hockey leagues. he won two turner cup championships with the st. paul saints in the international hockey league, and was a 1964 allan cup champion with the winnipeg maroons. he was fluent in russian and polish, had a brief coaching career with gks katowice in poland, and later worked as a european scout for the philadelphia flyers. kukulowicz spent six years in moscow working for air canada. he was a regular member of alan eagleson's travelling entourage, and was the interpreter and travel coordinator for the canada men's national ice hockey team at the 1972 summit series and 1974 summit series. he later worked as an interpreter for the international ice hockey federation (iihf) from 1975 to 1993, which included the ice hockey world championships, the canada cup, and the super series. kukulowicz was inducted into both the manitoba hockey hall of fame and the manitoba sports hall of fame and museum, as a member of the winnipeg maroons. he was honoured by the iihf with the paul loicq award in 2004, in recognition of significant contributions to international ice hockey.
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211fc242e99982c32ac23a831b7444f90456e517
kukulowicz died on september 26, 2008, in toronto,
kukulowicz died on september 26, 2008, in toronto, due to heart failure. he was predeceased by his wife and daughter. memorials for him were scheduled at the cathedral church of st. james, and the gabriola golf and country club.
wikipedia
491ff5817c9ca761f7c7481316cb77924128d355
kukulowicz met his wife diane in 1956, while
kukulowicz met his wife diane in 1956, while he was playing for new westminster. he was reportedly trying to impress her with his skating skills during a public skate. the couple later had one daughter and two sons. he was a resident of gabriola island, and member of the local golf and country club. he was reported to enjoy drinking a vodka martini or canadian club after a game of golf. alan eagleson described kukulowicz as "a gregarious man who made everyone feel like his best friend", and said that "aggie loved everyone and everyone loved aggie". kukulowicz was friends with sergei makarov and igor larionov. he attended the 35th anniversary of the 1972 summit series, held in moscow during august 2007.
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9a26a72da39928d83a285c248667e9e2ca076503
as a member of the 1964 allan cup
as a member of the 1964 allan cup champion winnipeg maroons, kukulowicz was inducted into both the manitoba hockey hall of fame, and the manitoba sports hall of fame and museum in 2003. he was honoured by the iihf with the paul loicq award in 2004, in recognition of significant contributions to the iihf and the international game.
wikipedia
f572a515656245bd48399ccd54821c473423c83c
kukulowicz worked as an interpreter for the international
kukulowicz worked as an interpreter for the international ice hockey federation (iihf) from 1975 to 1993, which included the annual ice hockey world championships. he attended all five canada cup tournaments from 1976 to 1991, and was able to provide sports broadcasts with information on soviet players who were not well known at the time. during a pre-taped interview on hockey night in canada for the super series '76, he translated while off-camera and speaking into an earpiece worn by valeri kharlamov. kukulowicz translated at the 1980 super series, and acted as a liaison between the nhl and the soviet teams. he also coordinated trips for nhl teams going to the soviet union, and was a reference for hotels, meals and cultural programs.
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ae201dd6a3110926c70fac53482b0c38bf8d0362
kukulowicz was involved in negotiations for many hockey-related
kukulowicz was involved in negotiations for many hockey-related contracts, and was called the " henry kissinger of hockey". he became friends with alan eagleson, and was his interpreter and a regular part of eagleson's travelling entourage. kukulowicz relocated to toronto after six years in moscow. he became a sales manager for air canada, marketing airline sales to travelling sports teams. he assisted in booking the canada men's national ice hockey team travels to and from europe, and was canada's interpreter at the 1972 summit series and 1974 summit series. he was respected by the soviets since he had lived in moscow. during this time, he acquired the canadian distribution rights to the soviet song " no coward plays hockey " written by aleksandra pakhmutova.
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258fdafd9f566807bb1c85ad52ffbe1ee2b35288
kukulowicz began working as a baggage handler for
kukulowicz began working as a baggage handler for air canada in 1964. when the airline was searching for someone with knowledge of polish, he was put into service as an interpreter between the prime minister of poland and the prime minister of canada. in addition to polish, kukulowicz spoke russian, ukrainian, czech, german and french. he became the airline's representative in russia in 1965, and opened an office in moscow. he moved into the hotel metropol moscow when he arrived, then later lived in an apartment complex designated for foreign persons when his family joined him. his time in moscow coincided with the cold war. while his apartment was being repainted, covert listening devices were found in the walls. he was followed by a kgb agent for six years, but the two men never spoke to each other. kukulowicz reportedly once bought two ice cream cones during the summer and gave one to his follower, who accepted it without saying anything.
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9db32db8d6603b1b4823eb02b2f8e60c14994b6c
in march 1965, kukulowicz was offered a job
in march 1965, kukulowicz was offered a job as a coach in poland, due to his ability to speak the polish language fluently combined with his playing experience. he was hesitant to accept a job behind the iron curtain despite the opportunity to visit family, and took the time to think it over before accepting. he served as coach of gks katowice in the polska hokej liga during the 1965–66 polska liga hokejowa season, along with fellow coach stanislav konopásek. his team placed fourth overall in the league's regular season with 22 wins. in the playoffs, he led the team to nine wins in eighteen games and placed third. he later worked as a scout for the philadelphia flyers in the 1970s. he was one of the first nhl scouts in europe, after flyers' coach fred shero had insisted on having a european scout.
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7e8f46b2dc863e00e29d16e0fd7b20d28e8768e0
during the 1964–65 season, the maroons played games
during the 1964–65 season, the maroons played games versus teams in the saskatchewan senior hockey league, and travelled to europe in february and march 1965 as the second canada men's national ice hockey team. kukulowicz had his first international playing experience during the tour, and played against the national teams from the soviet union, czechoslovakia, united states and sweden. he retired from playing during the season due to a serious on-ice accident.
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93227f762c681eebcf36112b596b4ee80d6c89e0
kukulowicz returned home for the 1962–63 season, and
kukulowicz returned home for the 1962–63 season, and played senior ice hockey for the winnipeg maroons coached by gord simpson. the maroons won the manitoba senior hockey league that season, and reached the finals of the 1963 allan cup for the canadian national senior ice hockey championship, but were defeated by the windsor bulldogs in five games. the maroons went on a playing tour of europe in early 1964, and the team was unsure if it would have enough players to participate in the 1964 manitoba senior hockey league playoffs. the maroons managed to find enough players, won 12 of 13 playoff games, and captured the 1964 allan cup by defeating the woodstock athletics in four consecutive games. kukulowicz and his teammates were not paid salaries for the season, and the team donated proceeds from tickets to its home games to charities in winnipeg.
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c2b53f385b0698f65d03c99972d797cfd67a4626
kukulowicz returned to professional hockey with the st.
kukulowicz returned to professional hockey with the st. paul saints in the international hockey league during the 1959–60 season. he scored 38 goals, 80 assists and 118 points that season, and was named the 1959–60 ihl second team all-star. he scored six goals in the playoffs, and helped the saints win the turner cup as champions of the ihl. he scored another six goals in the 1960–61 season playoffs, and the saints repeated as the league's turner cup champions. kukulowicz moved to the minneapolis millers in the same league for the 1961–62 season, but did not get beyond the first round of that year's ihl playoffs.
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2f257810314dab5b405491a70a5f0b1dc85171b3
kukulowicz played the next five seasons in the
kukulowicz played the next five seasons in the western hockey league. he played the 1953–54 and 1954–55 seasons with the saskatoon quakers. on august 18, 1955, the new york rangers traded the nhl rights to kukulowicz and billy dea to the detroit red wings in exchange for bronco horvath and dave creighton. kukulowicz switched to the brandon regals for the 1955–56 season, a farm team of the red wings. he played for the new westminster royals during the 1956–57 season, and reached the finals for the lester patrick cup in the whl playoffs. he played the 1957–58 season for the seattle totems, and returned to the saskatoon quakers to begin the 1958–59 season. he played just 9 games for the quakers and switched to senior ice hockey teams for the remainder of the season. after 14 games for the quebec aces in the quebec senior hockey league, he moved to the cornwall chevies in the eastern ontario hockey league. he played 18 regular season games for cornwall, followed by the league's playoffs.
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f089a9e2689001e23380116277e3f26d2e8afe76
kukulowicz began playing junior ice hockey for the
kukulowicz began playing junior ice hockey for the brandon wheat kings in the manitoba junior hockey league. he scored 27 goals and had 30 assists in 36 games played during his first season. he transferred to the quebec citadelles in the quebec junior hockey league for the 1951–52 season, and led his team in scoring with 24 goals. he began the 1952–53 season in the nhl with the new york rangers, and scored a goal in his debut game. he finished the season with the quebec citadelles after playing three games in the nhl, and helped the citadelles reach the eastern canada junior finals. he returned to the nhl for the 1953–54 season, but played only one game due to a back injury from a body check. his nhl tenure included just four games, and he continued his playing career in the minor leagues and in senior ice hockey leagues.
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950de45bcd3f034b4ac8cc612aad0b0e14a3717e
by age 16, kukulowicz had drawn the attention
by age 16, kukulowicz had drawn the attention of national hockey league (nhl) scouts, and had grown to his full height of 6 ft 3 in (191 cm) tall. according to alan eagleson, when professional hockey agents attempted to sign him to a contract, "he was hiding under his bed at the instruction of his mother, who felt he was too young to begin a career in hockey". in 1949, kukulowicz signed a contract with a signing bonus of c$ 7,500, and was sent to develop in junior ice hockey.
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95cd6f006b80d3167a1968a85acd42b6308fbbd3
kukulowicz was born on april 2, 1933, in
kukulowicz was born on april 2, 1933, in winnipeg. he was raised in the north end of winnipeg by his parents who were polish canadians, and began playing hockey at age seven. he achieved high grades in school despite struggles to command the english language. he also played baseball in the summer as a youth and young adult. he was a right-handed pitcher for the canadian ukrainian athletic club team in the baseball manitoba senior league until the mid-1950s.
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0b2c66b72f68cb7e762ac2e6b8c900f69e47ee27
kukulowicz spent six years in moscow working for
kukulowicz spent six years in moscow working for air canada. he was a regular member of alan eagleson 's travelling entourage, and was the interpreter and travel coordinator for the canada men's national ice hockey team at the 1972 summit series and 1974 summit series. he later worked as an interpreter for the international ice hockey federation (iihf) from 1975 to 1993, which included the ice hockey world championships, the canada cup, and the super series. kukulowicz was inducted into both the manitoba hockey hall of fame and the manitoba sports hall of fame and museum, as a member of the winnipeg maroons. he was honoured by the iihf with the paul loicq award in 2004, in recognition of significant contributions to international ice hockey.
wikipedia
1c488cd0a46c19bc7ec2b29ea11f3b5064298e6d
adolph frank " aggie " kukulowicz (april 2,
adolph frank " aggie " kukulowicz (april 2, 1933 – september 26, 2008) was a canadian professional ice hockey player and russian-language interpreter. he played four games in the national hockey league for the new york rangers, then played 12 combined seasons in the minor leagues and senior ice hockey leagues. he won two turner cup championships with the st. paul saints in the international hockey league, and was a 1964 allan cup champion with the winnipeg maroons. he was fluent in russian and polish, had a brief coaching career with gks katowice in poland, and later worked as a european scout for the philadelphia flyers.
wikipedia
95864a2dc62d08b7123840bedea075edd6c447b0
bergs has been professor of linguistics at the
bergs has been professor of linguistics at the university of osnabrück since 2006. he was there from 2008 to 2010 and has been dean of the department of linguistics and literature since 2016. his research focuses include language variation and change, construction grammar approaches to language analysis, language in context, the syntax-pragmatics interface and cognitive poetics. he also completed numerous teaching stays at the universities of bonn, santiago de compostela, wisconsin-milwaukee, catania, vigo, thessaloniki, athens and dalian.
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dd62cfb7540deb6165bf18bfa03cecd8d5344f1c
alexander bergs studied english, german, chemistry, education and
alexander bergs studied english, german, chemistry, education and philosophy at heinrich heine university in düsseldorf and general linguistics, english language and scots at edinburgh university. this was followed by his doctorate in 2002 on the subject of “social networks and historical sociolinguistics: studies in morphosyntactic variation in the paston letters (1421–1503) ”, and four years later his habilitation in english linguistics with the title "the expression of futurity in contemporary english: form, function, development".
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0a1c76b886316528b5155343ed0f1d124261564d
the 2020–21 ehf champions league was the 61st
the 2020–21 ehf champions league was the 61st edition of europe's premier club handball tournament and the 28th edition under the current ehf champions league format. due to the covid-19 pandemic, each local health department dictated the number of spectators allowed at a given match. barça defeated aalborg håndbold, 36–23, to win their tenth title.
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876a9700835fcb0a635af3cc114e245ff90d6ce6
in the group stage, teams are ranked according
in the group stage, teams are ranked according to points (2 points for a win, 1 point for a draw, 0 points for a loss). after completion of the group stage, if two or more teams have scored the same number of points, the ranking will be determined as follows:
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f2198721e9186faacc7aa0d1ed3094a72d086cb4
in each group, teams play against each other
in each group, teams play against each other in a double round-robin format, with home and away matches. after completion of the group stage matches, the top two teams from each group would have qualified directly for the quarterfinals, and the four teams ranked 3rd–6th advance to the playoffs, but on 10 february 2021, it was announced that all 16 teams advance from the group stage.
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a494bd82f970ba4916ca68fc880dbd78fe39d4b1
the draw was held on 1 july 2020
the draw was held on 1 july 2020 at the ehf headquarters in vienna, austria. the 16 teams were drawn into two groups of eight, with the restriction that teams from the same national association could not be drawn into the same group.
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a0982c496d168e350052af2ed5ffe9aa1d1f3302
a total of 24 teams from 16 countries
a total of 24 teams from 16 countries submitted their application for a place in the competition's group stage before the deadline of 10 june 2020. the final list of 16 participants was revealed by the ehf executive committee on 19 june. ten teams were registered according to fixed places, while six were granted wild cards.
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23edeeee399f7f8ba44e654eb835c922107367af
the knockout stage included four rounds: the round
the knockout stage included four rounds: the round of 16, quarterfinals, and a final-four tournament comprising two semifinals and the final. the teams were paired against each other in two-legged home-and-away matches, with the aggregate winners qualifying to the next round.
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38e0146097bfc7039fe9702330a4d4719f383fe5
the competition begins with a group stage featuring
the competition begins with a group stage featuring 16 teams divided in two groups. matches are played in a double round-robin system with home-and-away fixtures. in groups a and b, originally the top two teams qualify for the quarterfinals, with teams ranked 3rd to 6th entering the playoffs. after a decision by the ehf, all teams advanced.
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a7cb27f218de65c3c48c894ebda9bfa0b5e1d232
"ai no melody/chōwa oto" is kokia's 15th single,
"ai no melody/chōwa oto" is kokia's 15th single, released on january 1, 2006, a month before her greatest hits collection pearl: the best collection. the songs were used as the ending and opening theme songs for the animated film origin: spirits of the past. "chōwa oto" is a re-recording of her song "chōwa oto" from her gai records' management era album trip trip (2002).
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db229433f89a9f9d53724aa76e7914134b8a5aeb
the song debuted at no. 33 in its
the song debuted at no. 33 in its first week, however ranked in higher at no. 30 in its second. this was despite her second week's sales being less than half of her first week's (2,300 copies as opposed to 6,500). the song spent two more weeks in the top 100, and a single extra week in the top 200, eventually selling 12,700 copies in this time. because of this, "ai no melody/chōwa oto (with reflection)" is kokia's third best selling single, after " the power of smile/remember the kiss " and " kawaranai koto (since 1976) " in 2003.
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a067b88f479aff2b4813d588b6eb3e93c6a49039
much promotion was centred on the music video,
much promotion was centred on the music video, including the contest for the lead actress and the video being able to be streamed from kokia's website. a special making of report was streamed on yahoo! 's japan streaming video site on november the 25th. a feature in the november 29 edition of sports hochi centred on the music video also. kokia appeared in various magazines in december, mainly anime-based publications. these included anican, animage, castvoice, jsbn, newsmaker and fashion magazine seventeen. kokia appeared on two tv shows in late december, bomber e and power jam.
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a0ab730df210c949024793f3a7382a703a1da75c
the kokia tree scene and the drama scenes
the kokia tree scene and the drama scenes now begin to merge: katsuji's character, dressed in white, appears near the tree. natsuo's character then visits a tree in a park where she and her former boyfriend used to spend time. both characters touch their respective trees. katsuji's tree begins to grow, and a leaf falls on natsuo as she watches the film in the cinema.
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3b4f157d5356caf798998d4d2ea96ec1b12f347b
the video is centred on two main views.
the video is centred on two main views. one is centred on kokia, singing in front of a tree, set inside against a beige backing. the second is a mini-drama performed by actor ryō katsuji (the voice of agito in origin: spirits of the past) and actress sachi natsuo. the beginning of the video features natsuo sitting down to watch a film, with nobody else in the cinema. an earlier scene of her is shown as she packs away belongings of her deceased boyfriend. underneath a manga on the floor, she finds a copy of kokia's "ai no melody" single.
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58db55f77622c2a0c4dd9a40a011fde349d20dac
a music video was filmed for the leading
a music video was filmed for the leading a-side, "ai no melody," directed by takatoshi tsuchiya (土屋隆俊). it was the last music video she created, until filming "the woman" from real world in 2010, four years later. it was shot near the beginning of december in the outskirts of tokyo. a vote was taken on kokia's official site as to which actress out of five potentials should be shot as the main character in the video, with sachi natsuo winning. the video was broadcast by streaming on kokia's site from the 18th of november, 2005.
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bbf050f28bddacd6676288adc50499deda0fc64f
there are three sections to the song's lyrics:
there are three sections to the song's lyrics: standard japanese, numbers and coded japanese. the numbers are a code that represents the letters of the latin alphabet (1=a, 26=z). when decoded, the numbers (3 25 15 21 23 and 1) wrote the song's name in wāpuro rōmaji (c y o u w a). the coded japanese section features reversed syllables (such as the lyric "nimiunooto denzush," when reversed gives "oto no umi ni shizunde" (音の海に 沈んで, sinking in a sea of sound)). both the standard japanese and coded section have lyrics which bring up many natural images (such as a "sea of sound," "drop of water," "quiet forest," etc.).
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8c2faadf5869cbaf7afa3b9130a0b77a9313d616
this leads into the chorus, sung in coded
this leads into the chorus, sung in coded japanese. the chorus' arrangement is backed with a more complex variety of instruments. this leads into a more pop-inspired bridge, backed with added sound effects. this then leads into the chorus twice more, and finally one single abridged chorus backed only with piano.
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477dcbdfd934346580176a51fee3098075b6fd1e
the song is sung in a 12 note
the song is sung in a 12 note scale. the song begins with a 1:50 introduction in three steps: first kokia sings japanese lyrics against background sound effects and the piano. this leads into a section with added percussion where kokia counts numbers in english. the final part of the introduction features kokia harmonising with herself without lyrics.
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a6d7dd7332c0e0fa2c6e5fc6a6b072532adc1ab8
the lyrics express the love for another, likening
the lyrics express the love for another, likening them to "sunbeams filtering through leaves," and saying that they had given the song's protagonist hope. the person feels that "because i have you, i'm able to be like myself." therefore, she sings a song born of the love they have for that person.
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5690d944171b99e82c85c4a88ca068e4638ac657
the song is a piano-backed ballad. the song
the song is a piano-backed ballad. the song begins piano-backed, and leads into a chorus backed with percussion, guitar, piano and strings. the majority of the verses have a minimal arrangement, mostly only piano with occasional strings and other sound effects.
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44393e1217f42a5ae5cf5b30ee11de95732b8937
" ai no melody/chōwa oto (with reflection) "
" ai no melody/chōwa oto (with reflection) " (愛のメロディー/調和oto 〜with reflection〜, melody of love/harmony, sound (with reflection)) is kokia 's 15th single, released on january 1, 2006, a month before her greatest hits collection pearl: the best collection. the songs were used as the ending and opening theme songs for the animated film origin: spirits of the past. "chōwa oto (with reflection)" is a re-recording of her song "chōwa oto" from her gai records ' management era album trip trip (2002).
wikipedia
75a0112d5189d71ee4e8d4913c9a3255242f97e8
the enzyme adp-phosphoglycerate phosphatase catalyzes the reaction this
the enzyme adp-phosphoglycerate phosphatase catalyzes the reaction this enzyme belongs to the family of hydrolases, specifically those acting on phosphoric monoester bonds. the systematic name is 3-(adp)-2-phosphoglycerate phosphohydrolase. this enzyme is also called adenosine diphosphate phosphoglycerate phosphatase.
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3dd548196af853f9471f2e8f0cf3860cc0df8b78
this enzyme belongs to the family of hydrolases,
this enzyme belongs to the family of hydrolases, specifically those acting on phosphoric monoester bonds. the systematic name is 3-(adp)-2-phosphoglycerate phosphohydrolase. this enzyme is also called adenosine diphosphate phosphoglycerate phosphatase.
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914d7d1065acaebe7937508ec2722ccf086b1afa
(adp-ribosyl)hydrolase 1, also termed [protein adp-ribosylarginine] hydrolase and
(adp-ribosyl)hydrolase 1, also termed [protein adp-ribosylarginine] hydrolase and protein-nω-(adp-d-ribosyl)-l-arginine adp-ribosylhydrolase, is an enzyme that in humans is encoded by the adprh gene. this enzyme is a specific mono(adp-ribosyl)hydrolase that catalyses the removal of an adp-ribosyl modification from target arginine residues of protein substrates. the chemical reactions can formally be described as follows:
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88f9d63fa5c22590830564b5a0040742ea0f9ce5
(adp-ribosyl)hydrolase 1, also termed hydrolase and protein- n
(adp-ribosyl)hydrolase 1, also termed hydrolase and protein- n -(adp-d-ribosyl)-l-arginine adp-ribosylhydrolase (ec 3.2.2.19), is an enzyme that in humans is encoded by the adprh gene. this enzyme is a specific mono(adp-ribosyl)hydrolase that catalyses the removal of an adp-ribosyl modification from target arginine residues of protein substrates. the chemical reactions can formally be described as follows:
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8a1f8486bf6527d43d612b5346599a8caed60b82
alex f. t. w. rosenberg (1926–2007) was a
alex f. t. w. rosenberg (1926–2007) was a german-american mathematician who served as the editor of the proceedings of the american mathematical society from 1960 to 1965, and of the american mathematical monthly from 1974 to 1976. he should not be confused with alexander l. (sasha) rosenberg, a russian-american mathematician at kansas state university.
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01760027c8b8a974766b892dbc18cdde8fb2bc15
rosenberg married beatrice f. gershenson in 1952, with
rosenberg married beatrice f. gershenson in 1952, with whom he had two sons. they divorced in 1984, and he married his second wife brunhilde in germany in 1985. he died on october 27, 2007, in schwerte, germany.
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b546c0df578252918fea34bdd243fd65456a0c72
with gerhard hochschild and bertram kostant, he is
with gerhard hochschild and bertram kostant, he is one of the namesakes of the hochschild–kostant–rosenberg theorem, which they published in 1962 and which describes the hochschild homology of some algebras.
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3ea2e2f282534e20ca728a1da28a0ac4ede3a196
he moved to cornell university in 1961, and
he moved to cornell university in 1961, and served as department chair there from 1966 to 1969 where his phd students included vera pless, lindsay childs and david dobbs. in 1986 he moved again, to become chair of the mathematics department at the university of california, santa barbara. he was named emeritus at cornell in 1988, and retired from ucsb in 1994.
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747ae645aaa8ddb8d25a1e1319a2704b732e761c
after postdoctoral studies at the university of michigan,
after postdoctoral studies at the university of michigan, rosenberg taught at northwestern university from 1952 to 1961, becoming a us citizen in 1959. his students at northwestern included vera pless, later to be known for her work in combinatorics and coding theory.
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1e9ea0ec49fac77293ee6ba1664677a8033a8a11
rosenberg was born on december 5, 1926, in
rosenberg was born on december 5, 1926, in berlin. his family escaped nazi germany in 1939, moving to switzerland, to england, and then to ontario, canada. rosenberg graduated in 1948 from the university of toronto, with a b.a. in mathematics, and earned a master's degree there the following year. he completed his phd in 1951 at the university of chicago, with a doctoral thesis on ring theory supervised by irving kaplansky.
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be06bb27b64b17fac313daa5fa4189b9958e0ca9
alex f. t. w. rosenberg (1926–2007) was a
alex f. t. w. rosenberg (1926–2007) was a german-american mathematician who served as the editor of the proceedings of the american mathematical society from 1960 to 1965, and of the american mathematical monthly from 1974 to 1976.
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c80eacfdb2b61be8e7656520010edf4d76403ca5
the 2018–19 all-ireland senior club hurling championship was
the 2018–19 all-ireland senior club hurling championship was the 49th staging of the all-ireland senior club hurling championship, the gaelic athletic association's premier inter-county club hurling tournament. the championship began on 28 october 2018 and ended on 17 march 2019. cuala of dublin were the defending champions. they were eliminated by kilmacud crokes in the semi-final of the 2018 dublin championship. on 17 march 2019, ballyhale shamrocks won the championship following a 2-28 to 2-11 defeat of st. thomas's in the all-ireland final. this was their seventh all-ireland title overall and their first title since 2015. ballygunner's pauric mahony was the championship's top scorer with 1-42.
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2ebc16b8c31780b1acc3b5f506773f68e922a230
all matches are knock-out. two ten minute periods
all matches are knock-out. two ten minute periods of extra time are played each way if it's a draw at the end of normal time in the semi-finals or final. if the score is still level after extra time the match is replayed.
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ad41cfc34ecf0525ef828473a384f32bed854b02
all matches are knock-out. two ten minute periods
all matches are knock-out. two ten minute periods of extra time are played each way if it's a draw at the end of normal time in all matches including the final. if the score is still level after extra time the match is replayed.
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b740923809d9d40e72310058ebb044e321bce26a
leinster, munster and ulster organise a provincial championship
leinster, munster and ulster organise a provincial championship for their participating county champions. connacht discontinued their senior club championship after 2007 but they do organise intermediate and junior championships. the galway champions represent connacht in the all-ireland senior club semi-finals as galway club hurling is at higher level than the hurling in the other four connacht counties.
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only single club teams are allowed to enter
only single club teams are allowed to enter the all-ireland club championship. if a team which is an amalgamation of two or more clubs, a divisional team or a university team wins a county's championship, a single club team will represent that county in the provincial championship as determined by that county's championship rules. normally it is the club team that exited the county championship at the highest stage.
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c93d536b3e14baf0638890c193969aac51f658cf
on 17 march 2019, ballyhale shamrocks won the
on 17 march 2019, ballyhale shamrocks won the championship following a 2-28 to 2-11 defeat of st. thomas's in the all-ireland final. this was their seventh all-ireland title overall and their first title since 2015.
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9f4ea399391cf7fbdfcf05bbfff416a99b475095
the 2018–19 all-ireland senior club hurling championship was
the 2018–19 all-ireland senior club hurling championship was the 49th staging of the all-ireland senior club hurling championship, the gaelic athletic association 's premier inter-county club hurling tournament. the championship began on 28 october 2018 and ended on 17 march 2019.
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f8de8ef2dbad378b7707661653ff7c9fd519a53f
acoustic tweezers are a set of tools that
acoustic tweezers are a set of tools that use sound waves to manipulate the position and movement of very small objects. strictly speaking, only a single-beam based configuration can be called acoustical tweezers. however, the broad concept of acoustical tweezers involves two configurations of beams: single beam and standing waves. the technology works by controlling the position of acoustic pressure nodes that draw objects to specific locations of a standing acoustic field. the target object must be considerably smaller than the wavelength of sound used, and the technology is typically used to manipulate microscopic particles. acoustic waves have been proven safe for biological objects, making them ideal for biomedical applications. recently, applications for acoustic tweezers have been found in manipulating sub-millimetre objects, such as flow cytometry, cell separation, cell trapping, single-cell manipulation, and nanomaterial manipulation. the use of one-dimensional standing waves to manipulate small particles was first reported in the 1982 research article "ultrasonic inspection of fiber suspensions".
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a4eacdcc4782fc7445aa7ab4057bfa5fbbabdb79
the individual selective manipulation of micro-objects requires to
the individual selective manipulation of micro-objects requires to synthesize complex acoustic fields such as acoustic vortices (see previous section) at sufficiently high frequency to reach the necessary spatial resolution (typically the wavelength must be comparable to the size of the manipulated object to be selective). many holographic methods have been developed to synthesize complex wavefields including transducer arrays, 3d printed holograms, metamaterials or diffraction gratings. nevertheless, all these methods are limited to relatively low frequencies with an insufficient resolution to address micrometric particles, cells or microorganisms individually. on the other hand, interdigitated transducers (idts) were known as a reliable technique to synthesize acoustic wavefields up to ghz frequency.
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703fef416ef2340eed676a543ee491bb8ac0551a
while most acoustic tweezers are able to manipulate
while most acoustic tweezers are able to manipulate a large number of objects collectively, a complementary function is to be able to manipulate a single particle within a cluster without moving adjacent objects. to achieve this goal, the acoustic trap must be localized spacially. a first approach consists in using highly focused acoustic beams. since many particles of interest are attracted to the nodes of an acoustic field and thus expelled from the focus point, some specific wave structures combining strong focalization but with a minimum of the pressure amplitude at the focal point (surrounded by a ring of intensity to create the trap) are required to trap this type of particle. these specific conditions are met by bessel beams of topological order larger than zero, also called "acoustical vortices". with this kind of wave structures, the 2d and 3d selective manipulation of particles has been demonstrated with an array of transducers driven by programmable electronics.
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b9c67b8d413e2d7cd6a195e08efa9efb15e8675a
acoustic tweezers provide a simple approach for tuneable
acoustic tweezers provide a simple approach for tuneable nanowire patterning. in this approach, ssaws are generated by interdigital transducers, which induced a periodic alternating current (ac) electric field on the piezoelectric substrate and consequently patterned metallic nanowires in suspension. the patterns could be deposited onto the substrate after the liquid evaporated. by controlling the distribution of the ssaw field, metallic nanowires are assembled into different patterns including parallel and perpendicular arrays. the spacing of the nanowire arrays could be tuned by controlling the frequency of the surface acoustic waves.
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8366e98bc64c86c98ac48378a73dad091418e938
polymer-dispersed liquid crystal (pdlc) displays can be switched
polymer-dispersed liquid crystal (pdlc) displays can be switched from opaque to transparent using acoustic tweezers. a saw-driven pdlc light shutter has been demonstrated by integrating a cured pdlc film and a pair of interdigital transducers (idts) onto a piezoelectric substrate.
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6525e66cbe2469be97c632de334cac5fe39da1d6
sitters et al. have shown that acoustics can
sitters et al. have shown that acoustics can be used to manipulate single biomolecules such as dna and proteins. this method, which the inventors call acoustic force spectroscopy, allows measuring the force response of single molecules. this is achieved by attaching small microspheres to the molecules at one side and attaching them to a surface at the other. by pushing the microspheres away from the surface with a standing acoustic wave the molecules are effectively stretched out.
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0a39630aea350609663b80ca9650f490c27c49b3
manipulating single cells is important to many biological
manipulating single cells is important to many biological studies, such as in controlling the cellular microenvironment and isolating specific cells of interest. acoustic tweezers have been demonstrated to manipulate each individual cell with micrometer-level resolution. cells generally have a diameter of 10–20 μm. to meet the resolution requirements of manipulating single cells, short-wavelength acoustic waves should be employed. in this case, a surface acoustic wave (saw) is preferred to a bulk acoustic wave (baw), because it allows using shorter-wavelength acoustic waves (normally less than 200 μm). ding et al. reported a ssaw microdevice that is able to manipulate single cells with prescribed paths. figure 6 records a demonstration that the movement of single cells can be finely controlled with acoustic tweezers. the working principle of the device lies in the controlled movement of pressure nodes in an ssaw field. ding et al. employed chirped interdigital transducers (idts) that are able to generate ssaws with adjustable positions of pressure nodes by changing the input frequency. they also showed that the millimeter-sized microorganism c. elegan can be manipulated in the same manner. they also examined cell metabolism and proliferation after acoustic treatment, and found no significant differences compared to the control group, indicating the non-invasive nature of acoustic base manipulation. in addition to using chirped idts, phaseshift-based single particle/cell manipulation has also been reported.
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4b37816ee26b15148a300ff604493003ef227367
a glass reflector with etched fluidic channels is
a glass reflector with etched fluidic channels is clamped to the pcb holding the transducer. cells infused into the chip are trapped in the ultrasonic standing wave formed in the channel. the acoustic forces focus the cells into clusters in the center of the channel as illustrated in the inset. since the trapping occurs close to the transducer surface, the actual trapping sites are given by the near-field pressure distribution as shown in the 3d image. cells will be trapped in clusters around the local pressure minima creating different patterns depending on the number of cells trapped. the peaks in the graph correspond to the pressure minima.
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269f9a648a9e32e0513299116d112661d1c454a3
the tunability offered by chirped interdigital transducers renders
the tunability offered by chirped interdigital transducers renders it capable of precisely sorting cells into a number (e.g., five) of outlet channels in a single step. this is a major advantage over most existing sorting methods, which typically only sort cells into two outlet channels.
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8093700a66af8f7cce5be8f5ed2637ef7060256d
in addition to focusing in a horizontal direction,
in addition to focusing in a horizontal direction, cells/particles can also be focused in the vertical direction. after ssaw is on, the randomly distributed particles are focused into a single file stream (fig. 10c) in the vertical direction. by integrating a standing surface acoustic wave (ssaw)-based microdevice capable of 3d particle/cell focusing with laser-induced fluorescence (lif) detection system, acoustic tweezers are developed into a microflow cytometer for high-throughput single cell analysis.
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45f8acb169a639a80b57941f3acd6b1e15fc5fcc
acoustic tweezers have been developed to achieve 3d
acoustic tweezers have been developed to achieve 3d focusing of cells/particles in microfluidics. a pair of interdigital transducers (idts) are deposited on a piezoelectric substrate, and a microfluidic channel is bonded with the substrate and positioned between the two idts. microparticle solutions are infused into the microfluidic channel by a pressure-driven flow. once an rf signal is applied to both idts, two series of surface acoustic waves (saw) propagate in opposite directions toward the particle suspension solution inside the microchannel. the constructive interference of the two saws results in the formation of a ssaw. leakage waves in the longitudinal mode are generated inside the channel, causing pressure fluctuations that act laterally on the particles. as a result, the suspended particles inside the channel will be forced toward either the pressure nodes or antinodes, depending on the density and compressibility of the particles and the medium. when the channel width covers only one pressure node (or antinode), the particles will be focused in that node.
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c9bb699b2348aa31ef0f8969e0264d05c1372719
fluorescence-activated cell sorters (facs) can sort cells by
fluorescence-activated cell sorters (facs) can sort cells by focusing a fluid stream containing the cells, detecting fluorescence from individual cells, and separating the cells of interest from other cells. they have high throughput but are expensive to purchase and maintain, and are bulky with a complex configuration. they also affect cell physiology with high shear pressure, impact forces and electromagnetic forces, which may result in cellular and genetic damage. acoustic forces are not dangerous to cells, and there has been progress integrating acoustic tweezers with optical/electrical modules for simultaneous cell analysis and sorting, in a smaller and less-expensive machine.
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7c88f75d06151f738ccacfb476cd7f1a9ffa1f97
the acoustic method might also be used to
the acoustic method might also be used to separate particles of different sizes. according to the equation of primary acoustic radiation force, larger particles experience larger forces than smaller particles. shi et al. reported using interdigital transducers (idts) to generate a standing surface acoustic wave (ssaw) field with pressure nodes in the middle of a microfluidic channel, separating microparticles with different diameters. when introducing a mixture of particles with different sizes from the edge of the channel, larger particles will migrate toward the middle more quickly and be collected at the center outlet. smaller particles will not be able to migrate to the center outlet before they are collected from the side outlets. this experimental setup has also been used to separate blood components, bacteria, and hydrogel particles.
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03093f71ba5c1036586d71f25853a28cfa4f0dcc
cells with different densities and compression strengths can
cells with different densities and compression strengths can theoretically be separated with acoustic force. it has been suggested that acoustic tweezers could be used to separate lipid particles from red blood cells. this is a problem during cardiac surgery supported by a heart-lung machine, for which current technologies are insufficient. according to the proposal, acoustic force applied to blood plasma passing through a channel will cause red blood cells to gather in the pressure node in the center and the lipid particles to gather in antinodes at the sides (see figure 4). at the end of the channel, the separated cells and particles exit through separate outlets.
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7e0cae4a16c1fb80a63cb71d2384e6315711ed04
for applications in a static flow, the fluid
for applications in a static flow, the fluid velocity comes from the acoustic streaming. the magnitude of acoustic streaming depends on the power and frequency of the input and the properties of the fluid media. for typical acoustic-based microdevices, the operating frequency may be from the khz to the mhz range. the vibration amplitude is in a range of 0.1 nm to 1 μm. assuming the fluid used is water, the estimated magnitude of acoustic streaming is in the range of 1 μm/s to 1 mm/s. thus, the acoustic streaming should be smaller than the main flow for most continuous flow applications. the drag force is mainly induced by the main flow in those applications.
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ca9c11cf8c9642a0be8ec5771e54b6c5a0af651d
as mentioned, acoustic streaming is driven by mass
as mentioned, acoustic streaming is driven by mass and force sources originating from the acoustic attenuation. however, these are not the only driven forces for acoustic streaming. the boundary vibration may also contribute, especially to "boundary driven streaming". for these cases, the boundary condition should also be processed by the perturbation approach and be imposed on the two order equations accordingly.
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376d23983a9d33b37869a453cfc1e244a1d5af78
in determining the acoustic streaming, the second-order equations
in determining the acoustic streaming, the second-order equations are thus most important. since navier-stokes equations can only be analytically solved for simple cases, numerical methods are typically used, with the finite element method (fem) the most common technique. it can be employed to simulate the acoustic streaming phenomena. figure 3 is one example of acoustic streaming around a solid circular pillar, which is calculated by fem.
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309720341d512315f05a247dac8eccf7fbb98b65
it is important to note that the time-averaging
it is important to note that the time-averaging of pure first-order terms lead to their cancellation, since they are by definition harmonic. this means that they are pure sine waves, and thus have a mean of 0, which leads to the cancellation of any term that contains them. second-order terms are, however, not harmonic, and do not get cancelled out by time-averaging. this is most important for understanding acoustic streaming: first-order terms, related to simple oscillatory motion, have much larger magnitudes than second-order terms, and thus are dominant in the oscillation time-scale. those first-order terms, however, being pure sines, in a quasi-steady state, repeat after each oscillation cycle, yielding no net fluid flow. second-order terms, instead, are not harmonic, and thus can have a cumulative effect which, despite being smaller, can add up over many oscillation cycles, leading to the development of the net steady-state flow we identify as acoustic streaming.
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5d928f0f4a2303945d85ca2edb08c0a0993297de
the second-order equations can be considered as governing
the second-order equations can be considered as governing equations used to describe the motion of fluid with mass source {\displaystyle } and force source {\displaystyle }. generally, the acoustic streaming is a steady mean flow, where the response time scale is much smaller than the one of the acoustic vibration. the time-average term v 2 ¯ {\displaystyle {\overline {{\textbf {v}}_{\textbf {2}}}}} is normally used to present the acoustic streaming. by using ∂ t ρ 2 ¯ = 0 {\displaystyle {\overline {\partial _{\mathit {t}}{\mathit {\rho }}_{2}}}=0}, the time-average second-order equations can be obtained:
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6386701c47d1a858ae791b674a514f036b0139a9
this is an acoustic wave equation with viscous
this is an acoustic wave equation with viscous attenuation. physically, p 1 {\displaystyle {\mathit {p}}_{1}} and v 1 {\displaystyle {\textbf {v}}_{\textbf {1}}} can be interpreted as the acoustic pressure and the velocity of the acoustic particle.
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402372c0a725511629ef23e83ecd6870ed068a81
1 c f 2 ∂ t 2 p
1 c f 2 ∂ t 2 p 1 = ∇ 2 p 1 {\displaystyle {1 \over {c_{f}^{2}}}\partial _{t}^{2}{p_{1}}={\nabla ^{2}}{p_{1}}}.
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a497912af01c29e2ad7883af77e32d98c430955b
the liquid is quiescent and homogeneous at its
the liquid is quiescent and homogeneous at its zero-order state. substituting the perturbation series into the mass conservation and navier-stokes equation and using the relation of p 1 = c f 2 ρ 1 {\displaystyle {p_{1}}=c_{f}^{2}{\rho _{1}}}, the first-order equations can be obtained by collecting terms in first-order,
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7ae220e20f16d7a5b8bc45c35df613cc5daeeec9
the perturbation series can be written as p
the perturbation series can be written as p = p 0 + p 1 + p 2 {\displaystyle p={p_{0}}+{p_{1}}+{p_{2}}}, v = 0 + v 1 + v 2 {\displaystyle {\textbf {v}}={\textbf {0}}+{\textbf {v}}_{\textbf {1}}+{\textbf {v}}_{\textbf {2}}}, ρ = ρ 0 + ρ 1 + ρ 2 {\displaystyle {\mathit {\rho }}={\mathit {\rho }}_{0}+{\mathit {\rho }}_{1}+{\mathit {\rho }}_{2}}, which are diminishing series with the higher-order terms much smaller than the lower-order ones.
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7b7ffdc880e74a138152ea78e9e585b47ef0e232
ρ = − ∇ p + μ ∇
ρ = − ∇ p + μ ∇ 2 v + β μ ∇ (∇ ⋅ v)) {\displaystyle {\mathit {\rho }}=-\nabla {\mathit {p}}+{\mathit {\mu }}\nabla ^{2}{\textbf {v}}+{\mathit {\beta }}{\mathit {\mu }}\nabla (\nabla \cdot {\textbf {v}}))}
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e98495302cebc63c30d3f2c80e591fac0e75efc3
∂ t ρ = − ∇ ⋅ (ρ
∂ t ρ = − ∇ ⋅ (ρ v) {\displaystyle \partial _{\mathit {t}}{\mathit {\rho }}=-\nabla \cdot ({\mathit {\rho }}{\textbf {v}})},
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32e41d88fe6ee020d6f7b576c4b1c8b6786bd698
acoustic streaming is a steady flow generated by
acoustic streaming is a steady flow generated by the nonlinear component of the oscillations in an acoustic field. depending on the mechanisms, the acoustic streaming can be categorized into two general types, eckart streaming and rayleigh streaming. eckart streaming is driven by a time-average momentum flux created when high-amplitude acoustic waves propagate and attenuate in a fluid. rayleigh streaming, also called "boundary driven streaming", is forced by reynolds stresses in the viscous boundary layer. both of the driven mechanisms come from a time-average nonlinear effect.
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3a1e1f475145c673eb90e54fb2c4b6ca529a226f
the influence of the secondary forces is usually
the influence of the secondary forces is usually very weak, and only has an effect when the distance between particles is very small. it becomes important in aggregation and sedimentation applications, where particles are initially gathered in nodes by the acoustic radiation force. as inter-particle distances become smaller, the secondary forces assist in further aggregation until the clusters become heavy enough for sedimentation to begin.
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f996fd6ff6969483fd6d7edffcc8663cbbed7a83
in addition to the scattering-related secondary acoustic forces,
in addition to the scattering-related secondary acoustic forces, the flow field resulting from the interactions of the various acoustic streaming fields, generated by the acoustic boundary layer of each particle (sometimes called microstreaming), can induce additional viscous shear forces on each of the particles' surfaces, which then results in an additional contribution to the secondary acoustic forces in its fully viscous formulations. the viscous effects on the secondary acoustic force can become significant when compared to the perfect fluid formulation exemplified above, and even dominant in certain limit cases, yielding both quantitatively and qualitatively different results than what is predicted by inviscid theory. the relevance of the viscous contributions varies greatly depending on the specific case being investigated, and thus important care needs to be taken in selecting an appropriate secondary acoustic force model for the given scenario.
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521d17bdff9fee27435a4174dca77b1daf66da90
the sign of the force represents its direction:
the sign of the force represents its direction: a negative sign for an attractive force, and a positive sign for a repulsive force. the left side of the equation depends on the acoustic particle velocity amplitude v i n (x) {\displaystyle {\mathit {v}}_{\mathit {in}}({\mathit {x}})} and the right side depends on the acoustic pressure amplitude p i n (x) {\displaystyle {\mathit {p}}_{\mathit {in}}({\mathit {x}})}. the velocity-dependent term is repulsive when particles are aligned with wave propagation (Θ=0°), and negative when perpendicular to wave propagation (Θ=90°). the pressure-dependent term is unaffected by the particle orientation and is always attractive. in the case of a positive contrast factor, the velocity-dependent term diminishes as particles are driven to the velocity node (pressure antinode), as in the case of air bubbles and lipid vesicles. in a similar way, the pressure-dependent term diminishes as particles are driven towards the pressure node (velocity antinode), as are most solid particles in aqueous solutions.
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b626a56bfe32045dfae58af6fdc2dd4c1f0fc083
when multiple particles in a suspension are exposed
when multiple particles in a suspension are exposed to a standing wave field, they will not only experience acoustic radiation force, but also secondary acoustic forces caused by waves scattered by other particles. the inter-particle forces are sometimes called bjerknes forces. a simplified equation for the inter-particle forces of identical particles is:
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774a34827249f55764ce2c6c173520630ee4004f
the term sin (2 k x) {\displaystyle \sin({\mathit
the term sin (2 k x) {\displaystyle \sin({\mathit {2kx}})} shows that the radiation force period is one-half of the pressure period. also, the contrast factor can be positive or negative depending on the properties of particles and fluid. for positive value of Φ {\displaystyle \phi }, the radiation force points from the pressure antinodes to the pressure nodes, as shown in figure 2, and the particles will be pushed to the pressure nodes.
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f1baae30a54f6378ce48f34405c7481791789f03
e a c = p 0 2 4
e a c = p 0 2 4 ρ f c f 2 {\displaystyle {e_{ac}}={{p_{0}^{2}} \over {4{\rho _{f}}c_{f}^{2}}}}, Φ = f 1 + 3 2 f 2 = 5 ρ p − 2 ρ f 2 ρ p + ρ f − ρ f c f 2 ρ p c p 2 {\displaystyle \phi ={f_{1}}+{3 \over 2}{f_{2}}={{5{\rho _{p}}-2{\rho _{f}}} \over {2{\rho _{p}}+{\rho _{f}}}}-{{{\rho _{f}}c_{f}^{2}} \over {{\rho _{p}}c_{p}^{2}}}},
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905d740be810fa4386adacb0af5d3f35b9c5df8e
f x r a d = − ∂
f x r a d = − ∂ x u = v 0 k e a c sin (2 k x) Φ {\displaystyle {f_{x}}^{rad}=-{\partial _{x}}u={v_{0}}k{e_{ac}}\sin(2kx)\phi },
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8b7f3edc9f13f1e80907ba07a036c045f53ef368
u = v 0 p 0 2 4
u = v 0 p 0 2 4 ρ f c f 2 {\displaystyle u={v_{0}}{{p_{0}^{2}} \over {4{\rho _{f}}c_{f}^{2}}}},
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c8e45bd942f9f4192e64457c658e52ae4032b99e
v i n 2 ¯ = p 0
v i n 2 ¯ = p 0 2 2 ρ f 2 c f 2 sin 2 (k x) {\displaystyle {\overline {v_{in}^{2}}}={{p_{0}^{2}} \over {2\rho _{f}^{2}c_{f}^{2}}}{\sin ^{2}}(kx)},
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9f4e7dcd47bb7e278931252cf85ca5706ed8799e
p i n 2 ¯ = 1 2
p i n 2 ¯ = 1 2 p 0 2 cos 2 (k x) {\displaystyle {\overline {p_{in}^{2}}}={1 \over 2}p_{0}^{2}{\cos ^{2}}(kx)},
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03d0763539ab23dbc7238579115ecfc3c2003b9e
v in (x, t) = − p 0
v in (x, t) = − p 0 ρ f c f sin (k x) cos (ω t)) e x {\displaystyle {\textbf {v}}_{\textbf {in}}(x,t)={\frac {-p_{0}}{\rho _{f}c_{f}}}\sin(kx)\cos(\omega t)){\textbf {e}}_{\textbf {x}}},
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