text:
Talk:Mixing (mathematics)

Things to mention
Things that could be mentioned, beyond the basic definitions:
 * K. E. Petersen (1970) "A topologically strongly mixing symbolic minimal set" Trans. Amer. Math. Soc. 148 (1970), 603-612  We give here a "machinal" construction of a bilateral sequence with entries from 0, 1 whose orbit closure is topologically strongly mixing and minimal. We prove in addition that the flow we obtain has entropy zero, is uniquely ergodic, and fails to be measure-theoretically strongly mixing.

The above talks about blocks, and as far as I know, there are no Wikipedia articles on blocks (which are used all over the place in ergodic theory...) 67.198.37.16 (talk) 06:40, 5 November 2020 (UTC)

Mixing stronger than ergodicity
The text says " Mixing asks for this ergodic property to hold between any two sets A and B, and not just between some set A and X." It seems that the difference is not B vs X, but that mixing requires the non-empty intersection for all n,  whereas ergodicity only requires it for some  n (\forall vs \exist). I'm not confident enough of this to edit the text. Could someone more familiar with this please check? LachlanA (talk) 11:09, 22 December 2022 (UTC)

 * This part is false as written : if you take A, B to be the singleton sets on two points in distinct orbits (which will exist as soon as X is uncountable) it will never occur that $$A \cap T^{-n}B \not= \emptyset$$. I think that to define topological mixing you want A, B to be open.
 * On the other hand you certainly want "almost all n" and not "all n" in the definition : for a measurable transformation T of a standard Borel spaces, for an arbitrarily large N there will always exist nontrivial open sets A, B for which $$A\cap T^{-n}B$$ is empty for all $$0 \le n \le N$$.
 * This section "informal explanation" is a mess starting with the fourth paragraph. It should probably be pruned and the relevant information within incorporated in the rest of the article. jraimbau (talk) 13:26, 22 December 2022 (UTC)

Doesn't the total measure need to be = 1 ?
In the section Mixing in dynamical systems this passage appears:

"Let $$(X, \mathcal{A}, \mu, T)$$ be a measure-preserving dynamical system, with T being the time-evolution or shift operator. The system is said to be strong mixing if, for any $$A,B \in \mathcal{A}$$, one has

 * $$\lim_{n\to\infty} \mu \left (A \cap T^{-n}B \right ) = \mu(A)\mu(B).$$"

Isn't it necessary to assume this is a probability measure space, that is, that µ(X) = 1 ?

Because then the measure of set A or B is the fraction of the total measure of X that A or B possesses, and then µ(A)µ(B) makes sense as the limit when the dynamical system is strongly mixing.

Merge proposal
I propose merging Mixing (physics) and Mixing (mathematics). These articles are about exactly the same concept in dynamical systems, which happens to be important in both physics and math. Further, Mixing (physics) has been a stub since its creation in 2004, even linking to Mixing (mathematics) for "a more detailed explanation", and its content could be easily incorporated into Mixing (mathematics). I am not sure what article title they should be moved to. Mathwriter2718 (talk) 14:43, 7 July 2024 (UTC)

 * A few relevant pings: @Cosmia Nebula @Linas @Michael Hardy Mathwriter2718 (talk) 14:58, 7 July 2024 (UTC)
 * Ideas:
 * 1. Mixing (Dynamical Systems)
 * 2. Mixing (Mathematics)
 * 3. Mixing (ergodic)
 * 4. Ergodic theory of mixing pony in a strange land (talk) 18:25, 7 July 2024 (UTC)
 * How about Mixing (ergodic theory)? –LaundryPizza03 ( d c̄ ) 08:04, 8 July 2024 (UTC)

@User:Cosmia Nebula Mixing (Dynamical Systems) and Mixing (Mathematics) would violate WP:MOS because of the incorrect capitals. They should be Mixing (dynamical systems) and Mixing (mathematics). Michael Hardy (talk) 00:02, 9 July 2024 (UTC)

@User:Mathwriter2718 If you want this to get attention among the communities that can help, you should post to Wikipedia talk:WikiProject Mathematics and Wikipedia talk:WikiProject Physics. Michael Hardy (talk) 00:06, 9 July 2024 (UTC)

 * Without more content at mixing (physics), I'm inclined to think that the more developed article mixing (mathematics) is the primary one, although I could see scope for a separate article at some later time. Tito Omburo (talk) 01:35, 9 July 2024 (UTC)
 * Neither of these topics was the one that I first think of with respect to mixing, which can instead be found at Markov chain mixing time. Maybe whatever we do here, we at least need a hatnote? —David Eppstein (talk) 05:41, 9 July 2024 (UTC)
 * I think Mixing (physics) should be a redirect to Mixture which is much more detailed (but needs a little work and seems to have experienced an odd editing war of late). That page is general for chemistry/chemical engineering/materials science/physics/etc, we need to stop artificially creating field boxes. Hence Mixing (mathematics) needs to go beyond saying "in physics" and refer to Mixture. Some mention of Phase diagram and similar probably as well. There is also all the applied math/materials science on kinetics, for instance Cahn-Hilliard equation and Spinodal decomposition that at least is a "See also", perhaps more. Ldm1954 (talk) 07:12, 9 July 2024 (UTC)

title: Talk:Mixing (mathematics)


text: Category:Gifu geography stubs

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User:T-kita~enwiki

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http://t-kita.net

title: User:T-kita~enwiki


text: Template:Gunma-geo-stub

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Coffman Memorial Union

Coffman Memorial Union (abbreviated CMU, and commonly known as Coffman Union or simply Coffman) is a student union on the East Bank campus of the University of Minnesota in Minneapolis. Situated near the Mississippi River, Coffman anchors the south end of Northrop Mall, a grassy area at the center of campus that is bordered by the University's physics, mathematics, chemistry, and administration buildings, plus Walter Library and Northrop Auditorium. Coffman sits at the south end of the mall, across Washington Avenue, and opposite Northrop.

History
Coffman Memorial Union was built between 1939 and 1940 as a new "center of social life" for the University of Minnesota campus, a role that had previously been filled by Shevlin Hall and Nicholson Hall in the Old Campus Historic District, for the women's and men's student unions, respectively. Designed by architect Clarence H. Johnston Jr, the new building opened in September 1940 and was dedicated on October 25 of the same year. It was named in memory of Lotus D. Coffman, President of the University of Minnesota between 1920 and 1938, who first imagined the campus having one, united student union. Although the new building separated the men's and women's lounges, most of the other spaces inside were open to both, equally. It was built to accommodate 14,000 students.

By 1965, Coffman was the most used building on campus. The furniture began to show wear and tear, due to its excessive use over the years and 20,000 students utilizing Coffman on any given day. That same year, students began staging protests in the building in response to the United States' involvement in the Vietnam War. On May 4, 1970, the same day as the Kent State shootings, protesters started occupying Coffman 24 hours a day which lasted for a month. In May of 1972, the largest demonstrations at the university took place in response to President Richard Nixon's announcement that the United States would begin to blockade and mine North Vietnam's harbors. On May 10, over 6,000 protesters gathered at Coffman for a rally that included former United States Congressman Eugene McCarthy.

From 1974 to 1976, the building underwent a renovation that became widely criticized for its adverse effect on the building's exterior. Much of the original Streamline Moderne aspects were eliminated; a third of the back terrace was enclosed by angled glass; the main longue was reduced from two stories to one, in order to provide space for student organizations; the game and billiards lounge relocated to the basement, later becoming known as "Goldy's Gameroom", while a theater/lecture hall was built in its place; and the doors between the front pillars were replaced with large, deep-cut apron windows containing angular green-house styled roofs, requiring students to use the side doors to enter the building. Additionally, the color scheme was changed to bright magenta, blue, yellow, orange, purple, and green. The new angled glass extended floor space in the Main Lounge, which was renamed the Ski-U-Mah lounge, but was found to trap heat during the summer and not retain any during the winter. Minnesota Daily cartoonist Steve Sack referred to the building as the "Coffman Memorial Microwave Oven" and stated, "the windows of dear Coffman were designed most of all, to waste energy during the winter and deep-fry us spring and fall". While the renovation added 25,000 feet of space overall and raised the number of students it could accommodate to 42,000, its design made it harder for large groups to assemble in the building, as a direct response to the protests. The renovation was considered "an architectural crime" by critics led by University Librarian Herbert Scherer.

Throughout the 1980s, Coffman became well known as a place to watch television and catch up on the news. The building's tv brought students together during difficult times, such as during the Space Shuttle Challenger's launch and subsequent explosion. In the 1990s, several groups were given space within Coffman: the African, Asian-American, La Raza, Disabled Student, and Queer Students cultural centers.

In 1999, the building began preparing for a second significant renovation. In 2001, the Board of Regents approved the $71.5 million budget and construction began the following month, lasting until 2003. Almost all traces of the 1976 renovation were removed, and the building's exterior was restored to its original appearance. While the interior's old terrazzo floors and light fixtures were brought back, it was also modernized, such as with the addition of air conditioning. The lower floors were greatly expanded to include the main University of Minnesota Bookstore, food vendors, offices, lounges, and the glass "Cube" which sits adjacent to Washington Avenue. Additionally, a new 1,900-car parking garage opened behind the building, with 400 short term parking spaces. When the building reopened, the Al-Madinah and American Indian cultural centers were also given space inside. In 2013, the second floor was renovated. The new design features the cultural centers' spaces surrounding an open section in the middle. It also includes conference rooms and several more open areas for students to utilize. That same year, a large statue of the university's mascot, Goldy Gopher, was unveiled in front of Coffman, which has since become a popular spot for students to take pictures at.

On January 19, 2018, Coffman, along with the buildings lining Northrop Mall and a few in the surrounding area, was listed on the National Register of Historic Places as part of the Northrop Mall Historic District.

In 2019, after 16 months of study, a university task force recommended removing Lotus Coffman's name from the building due to his racist and anti-Semitic policies.

According to the December 2021 update to the Twin Cities Campus Plan, approved by the Board of Regents, Coffman is set to receive a third major renovation to meet the current needs of the student population. The building's overall architecture and integrity is to be untouched, while at the same time a more welcoming space for the many diverse uses the building has is meant to be created. Some recommended changes and additions include constructing an accessibility ramp on the building's east side in order to provide easier access from the front lawn to Delaware street, which runs behind the building; and connecting the bookstore directly to the transit stop on Washington Avenue, which also includes building a new transit lounge, waiting area, and amenity space.

Services and amenities
The building hosts a variety of services including the University of Minnesota Bookstore, Minnesota Marketplace Food Court, US Postal Service, IT Student Lab, administration services, and student group services. While the main lounge and theater are located on the main floor of the building, the lower level offers access to the bookstore, Great Hall, and several dining options. The basement features the Whole Music Club and an entertainment center called Goldy's Gameroom, featuring more food options, a bowling alley, foosball, and billiard tables. The building's upper floors are largely reserved for student and administration use, with student groups occupying much of the second floor. The fourth floor is home to the Campus Club, a member-based dining and event venue primarily used by faculty and alumni.

Organizations
The building is home to the University of Minnesota Student Unions & Activities office, the Minnesota Student Association (the undergraduate student government organization), and the Graduate and Professional Student Assembly (the graduate student government organization). Other student groups located within the building include:
 * Al-Madinah Cultural Center
 * American Indian Student Cultural Center
 * Asian-American Student Union
 * Black Student Union
 * Disabled Student Cultural Center
 * La Raza Student Cultural Center
 * Minnesota International Student Association
 * Queer Student Cultural Center

title: Coffman Memorial Union


text: Category:Gunma geography stubs

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User:Aenimated

aenimated enjoys cooking waffles and pancakes.

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User:Bigbluefish

Hello. For varied reasons, I may be able to provide specialised information connected with the following areas:
 * Formula One
 * Stratospheric Particle Injection for Climate Engineering
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 * Guildford
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text:
Talk:Martha

Nabatfan
Surely this ought to be "[

Nabatean"? [[User:Palmiro
]|Palmiro]] | Talk 13:45, 8 October 2005 (UTC)

Opera
'There is an by Friedrich von Flotow called "Martha". It has nothing to do with the biblical Martha, but'' maybe it should be mentioned in an disambiguation page. --85.180.124.61 09:19, 8 December 2005 (UTC)

Link
This link: dot com/customstimeafterpentecost5a.html Feast of Saint Martha was removed several times as apparent linkspam, one of over a hundred such links inserted into articles by the owner of the site. Please discuss why you think this link is more appropriate than,.

Attempted redirect to Martha of Bethany
For some reason, User:StAnselm insists on re-directing a generic name to one biblical figure. That makes no more sense than if some other user wanted to re-direct the page to Martha Washington. Every other common name, when typed into a wikipedia search bar, goes to a name page, and those pages often have lists of notable people who have that name. The name Martha is certainly no different. — Preceding unsigned comment added by ArchieOof (talk • contribs) 05:32, 10 March 2012 (UTC)

 * This is a little disingenuous; you are currently involved in an edit war with StAnselm on very subject, having made an un-warranted page move here.
 * I suggest you read, with profit, WP guidelines on consensus and the importance of working in a collaborative manner. Moonraker12 (talk) 18:10, 10 March 2012 (UTC)

Just in case anyone feels the need to suggest it, it might be helpful to give my reasons why I oppose a move to Martha of Bethany: I hope this helps. StAnselm (talk) 03:17, 11 March 2012 (UTC)
 * 1) Although her sister is known as Mary of Bethany to distinguish her from other Marys, this person is most commonly known as "Martha" - WP:COMMONNAME
 * 2) The article gets 300 hits per day, while the disambiguation page gets 20, which suggests that most people typing in "Martha" are looking for this person - WP:PRIMARYTOPIC
 * 3) The phrase "to be a Martha" is well attested.
 * 4) Many other biblical characters have articles named with just their mononym: Sarah, Rebecca, Dorcas, Abigail, Deborah, Esther, Isaac, Jacob, Joshua, Rachel, Leah and David.
 * 5) Very few of the people at Martha (disambiguation) are referred to by the single name "Martha".

I agree, edit war or not, linking to the Biblical Martha makes no sense, it's not referring to the Biblical Martha (I'm pretty sure).

Move?
Page to be returned to Martha: reversion of unwarranted page move. Existing redirect page moved to Martha/redirects per suggestion. Moonraker12 (talk) 17:31, 10 March 2012 (UTC)

Martha of Bethany → Martha –
 * Move made without consensus, and this is probably the primary topic. StAnselm (talk) 22:47, 9 March 2012 (UTC)
 * Or Martha (name) to Martha (and the existing Martha to Martha/redirects to get that load of old redirects out from under the incoming page Martha (name) to avoid WP:Parallel histories between deleted and undeleted histories at the same page name)? Anthony Appleyard (talk) 06:32, 10 March 2012 (UTCm

 * Support, per A Dictionary of the Bible and Columbia, both of whom give the subject as simply "Martha". We've got the subject's brother at Lazarus of Bethany, although I never heard him called him anything other than "Lazarus." Kauffner (talk) 11:25, 10 March 2012 (UTC)
 * Support - simply to get back to status quo with least disruption ...but Anthony Appleyard has a good point when looking at Paul, Matthew etc. Might be better to move there after. (Incidentally the reason for Lazarus of Bethany is probably due to the Lazarus in the parable). In ictu oculi (talk) 14:32, 10 March 2012 (UTC)
 * Support This is most likely to be what people searching for the plain name are after, with the opera as runner-up. Imo, disam pages, like Peter, with a tiny random selection of people called Peter etc, are a waste of time, and we should use the formula at John or Paul, which excludes them. Pages like Paul used to go to the most famous figure not long ago & perhaps should again. Johnbod (talk) 15:11, 10 March 2012 (UTC)

I've taken a liberty and closed this RM, and have returned the page to its previous title, which had been stable up until two days ago. There was no discussion of the move, which was made by a previously uninvolved editor, and was completely out-of-process. If anyone feels the new title was inappropriate, they should open a Request move and give a reason, not move it unilaterally. The editor making the original move has been informed. Moonraker12 (talk) 17:31, 10 March 2012 (UTC)

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Martha Anderson w5
Oletha53 2600:387:C:6A12:0:0:0:2 (talk) 19:03, 12 July 2022 (UTC)

title: Talk:Martha


text: Template:Hiroshima-geo-stub

title: Template:Hiroshima-geo-stub


text:
WOJO

WOJO (105.1 FM) is a radio station broadcasting a Regional Mexican format. Licensed to Evanston, Illinois, United States, the station serves the Chicago area. The station is currently owned by TelevisaUnivision, via its division Uforia Audio Network through licensee Tichenor License Corporation.

WOJO's studios are located at 541 N. Fairbanks Ct, Suite 1100, Chicago, and its transmitter is located atop the John Hancock Center.

WEAW
The station began broadcasting in February 1947, and held the call sign WEAW. The station was owned by North Shore Broadcasting, and its call sign stood for its president Edward A. Wheeler.

The station broadcast at 104.3 MHz briefly in 1947, before moving to 96.7 MHz later that year. The station's transmitter was located in Evanston and it had an ERP of 665 watts. In 1948, the station's frequency was changed to 105.1 MHz and its ERP was increased to 36,000 watts at a HAAT of 240 feet. The call sign officially became WEAW-FM in 1953 when a companion AM station was launched. In 1961, the station's ERP was increased to 180,000 watts. In 1970, the station's transmitter was moved to the top of the new John Hancock Center in Chicago, with its ERP reduced to 6,000 watts.

Among the music heard on WEAW was light music, easy listening, classical music, and show tunes. The station also carried programs from local schools, community organizations, and Northwestern University. The station also broadcast background music to stores and other businesses, with ads removed for subscribers. By 1964, all of its subscription services had been moved to subcarriers.

From 1947 through the 1960s, WEAW broadcast Northwestern Wildcats football games. It was also the flagship station of the Chicago White Sox radio network in 1971 and 1972.

WOJO
By late 1972, most of the station's programming was in Spanish, and in December 1972, its callsign was changed to WOJO.

In 1986, WOJO was sold to Tichenor Media for $1.4 million. In 1997, Tichenor Media merged with Heftel Broadcasting to form the Hispanic Broadcasting Corporation, which merged with Univision Communications in 2004.

title: WOJO


text: Category:Hiroshima geography stubs

title: Category:Hiroshima geography stubs


text:
1999 Rugby Borough Council election

Elections to Rugby Borough Council were held on 6 May 1999. One third of the council seats were up for election. The council stayed under no overall control. The number of councillors for each party after the election were Labour 22, Conservative 11, Liberal Democrat 7, Residents 4 and Independent 4.

Election result

 * }

title: 1999 Rugby Borough Council election


text: User talk:87.242.159.52

title: User talk:87.242.159.52


text: Template:Hyogo-geo-stub

title: Template:Hyogo-geo-stub


text:
Morton's fork coup

Morton's fork is a coup in contract bridge that forces an opponent to choose between
 * 1) letting declarer establish extra tricks in the suit led; or
 * 2) losing the opportunity to win any trick in the suit led.

It takes its name from the expression Morton's fork.

Basic
After winning the Q lead with the A, lead a low heart to the Queen. Then lead a low diamond.

 * If West takes his ace, South takes the remaining four diamond tricks. South makes 3NT with 2 spade, 3 heart and 4 diamond tricks.
 * If West ducks, South wins with the K and leads clubs knocking out the ace. South makes 3NT with 2 spade, 3 heart, 1 diamond and 3 club tricks.

More complex
South receives the lead of the J against his contract of 6. It appears that South has both a heart and a club loser. Although South can establish another winner in diamonds, just one discard on a diamond honor does not help. There are two ways that the contract can be made. South might manage to avoid any heart loser, or South might take two heart tricks, in which case South could discard one club on the K and another club on a diamond honor.

Judging from the opening lead that East holds the A, South plays the 9 from dummy at the first trick, ruffs in hand, and draws trumps. Hoping that West holds the A, South leads the 7, executing Morton's Fork:

 * If West takes the A, declarer can win any return, unblock hearts, take a ruffing finesse against the ace of diamonds, then discard two clubs on dummy's winning diamond and K. In this case South loses only a heart.
 * If West ducks South's lead of the 7, declarer wins dummy's K, takes a ruffing finesse against the ace of diamonds, and throws the Q on the established diamond winner. In this case South loses only a club.

Note that declarer must be careful not to play a high diamond on the opening lead, as East could then withhold the ace. That would force the declarer to choose a discard prematurely. South must get a discard on a diamond honor eventually, but not before West has been forced to decide whether to take the A or duck it. Only then will South know whether to discard a heart or a club on the diamond winner.

Example defense
Robert Gray gives this spectacular example of an impossible defense to Morton's Fork. West leads the 2 against South's six club contract. South wins and initiates the coup by leading the 8.

If West takes the A, he might as well continue with the 3. South wins and leads a heart, covered and ruffed. A third club to South's hand, and another heart, again covered and ruffed. A diamond to South's hand, and a third heart covered and ruffed. The K is cashed, and then another diamond to South's hand allows dummy's last two losing diamonds to be discarded on the Q and the established heart.

If West ducks the A at the second trick, South sets up a heart via ruffing finesses as before, discarding dummy's losing spade on the established heart. Now a third diamond from South either wins or establishes dummy's 10, and South has twelve tricks: one spade, one heart, three diamonds and seven clubs.

Gray points out that to defeat the contract, West must lead the 2 at trick one. (He goes on, "And I hope that is not too obvious.") Against the opening lead of the 2, South must discard from dummy before West has been forced to play to South's spade lead. If South discards dummy's spade at trick one, West's A will later take dummy's K, and South must lose a spade and a diamond. If South discards a diamond from dummy, West ducks South's spade lead, saving his A for the Q, and again South must lose a spade and a diamond.

Gray speculates on a name for West's opening lead coup: "This play of giving declarer a trick early ... is probably worth a name. The Anti-Morton Coup or the Down With Morton Coup spring to mind, but these names seem rather unfriendly. Let us settle for the Morton Coup Defense."

title: Morton's fork coup


text:
Brooke Vincent

Brooke Levi Vincent (born 4 June 1992) is an English actress, known for her portrayal of Sophie Webster in the ITV soap-opera Coronation Street, which she played from 2004 to 2019.

Early life
Vincent was born in Audenshaw, Greater Manchester, England to Nicola Anderton, a crime scene officer for Greater Manchester Police, and Anthony Vincent, a tour guide in Tenerife. Her parents separated when she was two; she was raised by her mother and her stepfather, John McDermott. Vincent has a paternal older half-brother, Zak, and a younger maternal half-sister, Maisie. Vincent is the cousin of Ellie Leach, a fellow Coronation Street actress, who plays Faye Windass; Vincent was said to be "overjoyed" by Leach's casting in the soap.

Vincent attended Fairfield High School for Girls in Droylsden and The Manchester College, where she gained a National Diploma in Acting.

Career
Vincent's first television appearance was as a guest character, Casey Emma Glass, in the TV series The League of Gentlemen. Shortly after landing the role of Sophie in Coronation Street, she appeared on Children in Need. In 2018, Vincent competed in the tenth series of Dancing on Ice and finished in second place, alongside professional partner Matej Silecky.

Coronation Street
Vincent joined the long-running British soap-opera Coronation Street in April 2004 as the third actress to play Sophie Webster, replacing Emma Woodward, who had decided to leave the soap at the end of 2003. Vincent's first appearance was shown on 12 May.

In an interview on 7 September 2010 with Vincent and Sacha Parkinson, both actresses discussed their roles in the lesbian storyline, whereby their relationship transformed from best friends to girlfriends with the realisation of their sexuality. This storyline on started on 11 April 2010. At the Stonewall Awards ceremony on 5 November 2010, Coronation Street won the new Broadcast of the Year award, in recognition of its gay storylines. Vincent was nominated for Best Dramatic Performance from a Young Actor or Actress for her portrayal of Sophie at The British Soap Awards in 2008. At the 2008 Inside Soap Awards, Vincent was nominated in the category Best Young Actor. In October 2019, Vincent took maternity leave from the show.

Other ventures
In 2018, Vincent launched her own stationery brand, Oh So B. From 5 June 2023, she stood in for Gemma Atkinson on Hits Radio alongside Mike Toolan whilst Atkinson was on maternity leave. Vincent's first three stationery planners were named after her half-sister and her cousins.

Personal life
Vincent has been in a relationship with footballer Kean Bryan since 2016, and the couple have two sons.

In 2018, Vincent revealed that she had stopped smoking after ten years. In April 2019, Vincent announced that she was pregnant with her first child. On 23 October 2019, Vincent gave birth to a baby boy named Mexx S J Bryan. In November 2020, Vincent announced she was pregnant with her second child. On 4 May 2021, she gave birth to her second son, named Monroe S J Bryan.

title: Brooke Vincent


text: Category:Dutch cardinals

title: Category:Dutch cardinals


text:
El Presidente (band)

El Presidente (also written El Pres!dente) was a pop rock band from Glasgow, Scotland. Formed in 2002 by Gun member Dante Gizzi, the band gained major exposure with slots at T in the Park 2005, V Festival 2005 and again at T in the Park in 2006. The band have also supported Oasis, Duran Duran, Simple Minds and Kasabian on major tours of the UK.

History
Whilst touring in France with Gun, Gizzi came up with the name El Presidente and after Gun split, began working on his own songs. In 2002 he made a few demos, along with brother Jools, on a small sampler and Billy Sloan aired them on his Sunday night Radio Clyde show.

After a couple of gigs at King Tuts in Glasgow as a solo artist with studio recorded backing tracks, Gizzi got a band together. The original line-up included brother Jools (previously also with Gun) on guitar and current drummer Dawn Zhu on drums. On signing up with One Records a subsidiary of GR management in Glasgow (also the Gun management team) a couple of the original members decided they did not want to tour with the band. Gizzi then recruited Laura Marks, Thomas McNeice and Johnny McGlynn. Shortly after the band signed a deal with Sony BMG. The band's first release was a limited edition (1000 copies), red 10" vinyl released on 31 January 2005 which was promoted by the band's first video, which was produced by Jonas Odell and cost over £25,000. On 17 January they embarked on their first UK tour, supported by Stagger Lee. In February they shot their next video for the single "100 MPH". The accompanying video featured the band playing the song in different size boxes, reminiscent of a giant Rubik's Cube.

In April they supported Kasabian on another UK tour, then Oasis in May, on their only Scottish date. "100 MPH" was released on 2 May on a two-track CD, a DVD single and limited yellow vinyl. It reached #37 in the UK Singles Chart. To promote it, the band made their début on the BBC Television music programme Top of the Pops; plus on GMTV and CD:UK. In June, the band played two back to back sell out nights at King Tuts, and on 24 June 2005, were meant to play at the Glastonbury Festival, but their stage flooded and the band's set was cancelled.

On 25 July 2005, the band released "Without You". To promote it, they performed on GMTV, Top Of The Pops and TRL (on MTV). They did a session on BBC Radio 2 (in which they performed "Without You" and a cover of Prince's "Raspberry Beret"). There was a number of articles in The Sun and other national newspapers and the song was playlisted on BBC Radio 1, BBC Radio 2 and Xfm. The single reached number 30 in the UK chart. In July and August 2005 the band played some festivals, and a sell-out gig at The Liquid Rooms in Edinburgh. In September their next single was announced, which was to be a re-release of "Rocket". The video was an edited down version of the older video, but the single was re-recorded with the current line-up. They appeared on TRL again, but only for an interview, and they did numerous radio sessions on XFM and BBC Radio 2, The video was also playlisted on MTV Hits and Brand Spanking New. The single reached number 48.

On 24 October 2005, the band's début album was released with nine drum tracks recorded by original GUN drummer Alan Thornton and backing vocals on Turn This Thing Around. It reached number 57 in the UK Albums Chart. The band embarked on a full UK tour in September and October, and in early September supported Jamiroquai. In November they also took part in the charity recording of "Ever Fallen in Love (With Someone You Shouldn't've)" (originally by the Buzzcocks) as a tribute to the late John Peel. On 17 December the band played a Christmas show at the Barrowlands. Then on New Year's Eve 2005, they played at the annual Hogmanay celebration in the Royal Gardens in Scotland.

On 6 February 2006 the band released their fourth and final single from their début album, which was a re-recorded version of "Turn This Thing Around". The video to the song was shot in November in Japan. The story line to video was the lead singer, Gizzi had lost his memory, and must find the band on time to get to the show. The single did better than "Rocket", and went to number 39.

In July 2006 they performed at T In The Park on the main stage. They premièred one new song "Late Night Binges". On 21 July 2006, the band attended the Northsound 1 Awards, nominated for Best Live Act.

On their French November 2006 tour, another new song, "Reach Out" was played. Recording on their second album started in October. Johnny McElhone (Texas' bassist) also worked with the band on their second album, although just what his contribution will be is yet to be announced.

They played RockNess on 9 June 2007 and Saturday of the 2007 Glastonbury Festival.

Prior to the band's tour of France in November 2006, it was reported on the band's MySpace page by Marks that 'some recording was finished' in Glasgow. A further internet blog from the band came in January 2007 stating that recording was ongoing, and a new single and album would follow in the summer of 2007. No new information followed, and, due to Marks' current TV presenting role and Gizzi's work with Gun in 2008, it is uncertain where the band's future lies. The band's website, has since been re-directed to an unregistered domain and it is unknown whether the website itself still exists.

Studio albums

 * El Presidente (24 October 2005); #57 (UK); #10 (Jpn); #59 (Fra); Worldwide Sales: estimated 10,000
 * El Presidente (8 February 2006); #1 (Jpn); Japanese Sales: estimated 10,000

title: El Presidente (band)


text:
Sir William Gage, 7th Baronet

Sir William Gage (1695 – 23 April 1744) of Firle Place was a British landowner and politician who sat in the House of Commons from 1727 to 1744. He was an early patron of cricket, in association with his friend Charles Lennox, 2nd Duke of Richmond.

Early life
Gage was born in Firle, East Sussex, the third son of Sir John Gage, 4th Baronet, and his first wife Mary Stanley, daughter of Sir William Stanley, 1st Baronet, of Hooton, Cheshire. He succeeded his brother to the Baronetcy in October 1713.

Parliamentary career
The Gage family were Roman Catholic recusants but Sir William chose to conform to the established Church so that he could become an MP in 1722. His seat was the former constituency of Seaford and where he remained until his death in 1744.

Cricket career
Sir William was a keen cricketer and patron who led and backed teams. One of his teams has been credited with the earliest known innings victory. He was a close friend of Charles Lennox, 2nd Duke of Richmond and it seems they had organised a number of cricket matches before 1725 when their involvement first becomes clear through a surviving letter that Gage wrote to Richmond in humorous terms about cricket:

My Lord Duke, I received this moment your Grace's letter and am extremely happy your Grace intends us ye honour of making one a Tuesday, and will without fail bring a gentleman with me to play against you, One that has played very seldom for these several years. I am in great affliction with being shamefully beaten Yesterday, the first match I played this year. However I will muster up all my courage against Tuesday's engagement. I will trouble your Grace with nothing more than that I wish you Success in everything except ye Cricket Match and that I am etc. etc. W. Gage Firle July ye 16th 1725

Sir William's name appears in connection with a number of matches over the next few years. A game against Edwin Stead's XI on 28 August 1729 is regarded as the earliest innings victory on record. A contemporary report states that Sussex "got (within three) in one hand, as the former did in two hands, so the Kentish men threw it up". Sir William was greatly assisted by the outstanding play of Thomas Waymark "who turned the scale of victory".

In August 1733, Sir William's team challenged one backed by Frederick, Prince of Wales at Moulsey Hurst for "a wager of 100 guineas". Sir William was officially Lord Gage by then. The result of the match is unknown but it featured "11 of the best players in the county on each side". In September 1734, his Sussex team played a Kent team led by Lord John Philip Sackville in the earliest match recorded at Sevenoaks Vine. This was won by Kent. Apart from one minor fixture a few years later, that is the last record of Sir William in a cricketing context.

Death and legacy
Gage was unmarried and died without issue aged 49 on 23 April 1744. He was succeeded in the Baronetcy by his cousin Thomas Gage who, in 1754, was raised to the Peerage of Ireland as Viscount Gage.

Gage did much to develop Firle Place, including the external cladding of the building in the Georgian style, using Caen Stone.

title: Sir William Gage, 7th Baronet


text:
Talk:Double layer

Untitled
Art, I restored "Quasi-neutrality" and "Particle flux" items, together with some reference. Perhaps I have misunderstood them?

I'm still not sure whether a Debye Sheath is synonymous with a Double Layer (is a Debye Sheath the name of one half of a double layer?). In which case, perhaps ion fluxes across Debye Sheaths and Double layers are different. --Iantresman 13:49, 8 October 2005 (UTC)

 * I see everything as a Debye sheath because that's my specialty. (If your only tool is a hammer, everything starts looking like a nail.) I hope I can get a better grip on it with the help of your references. I'll continue to rephrase you if I don't understand your physics. Maybe between the two of us we'll get it right in the end. --Art Carlson 17:58, 8 October 2005 (UTC)

 * Many thanks, appreciated. --Iantresman 18:12, 8 October 2005 (UTC)

Double Layer formation text
I'm trying to describe how a double layer may form without resorting to maths. I am proposing the diagrams, right, and the text below. Since I am no expert, and my understanding may be incorrect, and would welcome criticisms before adding it to the main page. --Iantresman 19:36, 18 October 2005 (UTC)

Proposed text

[Proposed text subsequently moved into body of article]

 * This explanation is about as good as any I could come up with. (I hope it's also right.) I think this mechanism can only explain weak double layers. Something additional, perhaps a net current, is needed to explain strong double layers. --Art Carlson 16:13, 19 October 2005 (UTC)

Synchrotron Radiation?
Hello Art, hello Lantresman,

in the first paragraph of the article it is mentioned that sychrotron radiation can be produced in double layers. This sounds a little strange to me. Should'nt it be called Bremsstrahlung in this case? Isn't sychchrotron radiation only that radiation which is produced by particles on a curved path, e.g. a circular path produced by a magnetic field? Im sure that in some cases sychrotron radiation is produces in double layers but the sentence implies that ist is produced by the strong electric field or the acceleration.

Best regards,

Klaus

 * I don't quite understand this either, since Ian Tresman continually emphasizes that the currents are field-aligned (Birkeland currents). If that is strictly true, then there will be no synchrotron radiation. But I'm pretty sure Bremsstrahlung will not be important here either. --Art Carlson 15:34, 28 October 2005 (UTC)

 * I may have misunderstood, but my understanding is that the double layers cause the electrons to be accelerated to relativistic velocities in a magnetic field where they spiral and emit sychrontron radiation. A Birkeland current is merely a stack of double layers, and double layers may occur in a Bennet pinch (z-pinch), so it may all depend on your perspective. However, for some details on what produces what, see Anthony Peratt's paper "Evolution of the plasma universe. I - Double radio galaxies, quasars, and extragalactic jets" [PDF] where he explains the details. Any suggestions are welcome. (Ian Tresman) --Iantresman 15:49, 28 October 2005 (UTC)

 * A Birkeland current doesn't have to have "a stack of double layers", or even a single one, does it?
 * Where do the double layers occur in a Z-pinch? Perpendicular to the axis?
 * It's not enough to accelerate charged particles in a magnetic field. If the velocity is parallel to the field, there will be no synchrotron radiation. How do the particles get from being parallel to being perpendicular (or at least oblique)?
 * --Art Carlson 17:26, 28 October 2005 (UTC)

 * I think I have this understood. Birkeland currents may supply electrons and ions to a double layer where they are accelerated to relativistic velocities. Alfvén writes: "Although the electrons are primarily accelerated in the direction of the magnetic field, they will be scattered by magnetic inhomogeneities and spiral in such a way that they emit synchrotron radiation." Peratt says that a Bennett pinch may be produced, which will also result in synchrotron radiation.

 * What do you mean "a Bennett pinch may be produced"? Isn't a current always subject to the pinch effect? Why do you say that a pinch "may produce synchrotron radiation"? Simply because a current (whether pinched or not) produces a magnetic field, and a finite pressure plasma in a field always produces some radiation? --Art Carlson 19:28, 31 October 2005 (UTC)

 * All I can do is refer you to the article by Anthony Peratt, above, who explains this in more detail. --Iantresman 09:47, 8 November 2005 (UTC)

 * Sorry, but I was not able to find the places in Peratt's article where he addresses these questions. Can you help me? --Art Carlson 15:37, 8 November 2005 (UTC)

 * Does my understanding makes sense:
 * On p. 643, the section on V. Synchrotron Radiation from Bennett-pinched Filaments, is relevant. ie. Bennett-pinches produce synchrotron radiation.
 * On p. 642, the section on IV. Biot-Savart Forces between filaments, first paragraph, Peratt writes: ".. a galactic filament can be expected to retain its columnar filamental form provided the Bennett-pinch condition is satisfied .. ", indicates that a Bennett pinch may occur in a filament if certain current conditions are met.
 * A filament is a Birkeland current (see Fig 2, 641). So if synchrotron radiation is produced from a Bennett pinch, then it is also coming from within a Birkeland current.
 * On p. 641 Section C. The Formation of Double Layers within Birkeland currents, Peratt writes that "Moreover, Birkeland currents and double layers appear to be associated phenomena..", and on p. 639 I. Introduction point (1) Electric double layers, which did not attract much attention a decade ago, are now known to accelerate charged particles to kilovolt energies in the terrestrial magnetosphere [4]—[7]. They may also exist elsewhere and accelerate particles to even higher energies.
 * From which I infer that double layers accelerate electrons in Birkeland currents which may then pinch and produce synchrotron radition. I say "may" because it depends on the characteristics of the plasma.
 * If you have access to Alfvén's Cosmic Plasma, he mentions synchrotron radiation in a section on p.36 Section II.7 Field-aligned currents in 'cables', where he writes: "In the same way as two high power transmission cables connect a generator and a 'consumer', a pair of plasma cables may connect a generator and a 'consumer'. The generator often consists of a plasma moving with a velocity component perpendicular to the magnetic field B and hence generating an e.m.f. where the integral is taken between the ends of the two cables. The consumer may be a double layer accelerating charged particles which later produce light or synchrotron radiation." (my emphasis).
 * --Iantresman 20:23, 8 November 2005 (UTC)

Changes for Wiki Double Layers
I have only quickly read through the page as it is now, and I think it needs major reconstruction. Here is some of the comments I have so far.

1st Paragraph A double layer … in a plasma. You have to be more specific here what kind of double layers you want to discuss. There are the DLs in current carrying plasmas and there are the DLs at the boundary of two different plasmas, these are not the same. The first one gets created, e.g. when the current gets too strong and the flow velocity of the current carriers is higher then the thermal velocity of the plasma, or when there is too little density and the current carriers have to be accelerated to maintain the current (this last one is comparable to the faster flow of a fluid through a narrowing of the flow channel).

Large potential drops and layer separation. The layer separation has nothing to do with the acceleration of the particles. The final increase in energy of the electrons and ions is given by the voltage drop ΔV and not by the length L between the pos en neg layer. Which in inhomogeneous … radiation. There is no need for inhomogeneous magnetic fields, let alone some obscure term like Bennett pinch. Charged particles in ANY magnetic field will “twirl” around the magnetic field lines and emit synchrotron of cyclotron radiation. There is no need to make this so highly complicated. Double layers may self … into contact. Here we have the dichotomy. How do you mean self generate (there has to be a cause that they get generated, I guess you mean here the DLs in a current carrying plasma). Then you also, like I said above, say that there are two kinds of DL, the second of which, does not carry any net current.

Classification, 1st item Time-dependent: You mix up here the time-dependent and time-independent terms. A time-Independent DL is an idealized form, where as real DLs are time-DEPENDENT. Particle acceleration: The same as I said above, with respect to the magnetic field presence and synchrotron radiation. Formation: Rather than a magnetic field one. The original term is electrostatic double layers, why would anyone expect that the formation would be an magnetic field phenomenon? Energy supply: I am not sure if you can write here that voltage drop and total current are directly proportional. It tends to be highly dependent on the properties of the plasma that the DL is embedded in. Magnetized plasmas: Most of the plasmas in space are magnetized (if not all) why would you want to make a comment on having the magnetic field keep the plasma from the walls? That is a very special case in the laboratory. Furthermore, that seems to suggest an initial thought that all DLs are produced by boundary effects, which is not the case. Oblique DLs: A smooth bore magnetron. I think at least you mean Bohr. If there is truly a connection between an oblique DL and a Bohr magnetron I do not think so. AFAIK a Bohr magnetron has something to do with the electron circling around a proton in a hydrogen atom. It sets a value for a basic magnetic unit. The DL may also drift: but this is not only the case for oblique DLs.

Simulation: I think if you wanted to keep the page without math but then come with a BGK approach, that is making rather strange choices. Also, I think that only the magneto-acoustic DLs are described like that.

DL formation needs to be totally rewritten, as it only discusses the boundary double layer, which does not carry any current. The current carrying double layers, which are e.g. in the Earth’s magnetosphere form in a different way. These are also the DLs that you are so interested in, the ones that accelerate particles and can create beams etc. Almost per definition, the boundary DLs are marginally strong DLs always on the order of the thermal energy of the hot plasma.

I do not understand the strange boxes in the page, but I don't care :-)

 * Have at it! I think Ian and I may be slightly out of our depth on this subject, so we welcome more expert knowledge. I hope to learn something from you. --Art Carlson 17:47, 20 November 2005 (UTC)

 * I've made some tweaks to the double layers page based in your comments. --Iantresman 12:18, 24 November 2005 (UTC)

New version of the paper
Okay, I send this to Ian, but I thought it might be good to have it also here. I have edited the whole text, and taken out stuff and put some in. (Unashamedly I just copied a part of my PhD thesis into the page). The marked-up word document can be found through the following link: ftp://ftp.iwf.oeaw.ac.at/pub/volwerk/ the file is called wiki double layer.doc

-Martin

Electrostatic double layers are small-scale, high-intensity electric fields in a current carrying plasma or at the boundary of two plasmas with different characteristics, e.g. temperature, density or composition. It consists of two oppositely charged parallel layers, resulting in a voltage drop and associated electric field across the layer, which accelerates the plasma's electrons (positive ions) entering the double layer at the low (high) potential side, and decelerates them when entering from the high (low) potential side.

Double layers may be found anywhere that plasmas are found, from discharge tubes to space plasmas to the Birkeland currents supplying the Earth's aurora. And although plasmas are highly electrically conductive, a property that tends to charge neutrality, double layers may form when two plasma regions with different properties come into contact, or when an electric current flows through a plasma.

Other names for a double layer are: electrostatic double layer, electric double layer, plasma double layers, electrostatic shock, and space charge layer. In laser physics, it is sometimes called ambipolar electric field [5].In electrochemistry, however, a double layer is a thin charged structure formed on the interface between electrode and a solution of electrolyte.

Contents [hide]
 * 1) Double layer features
 * 2) Typical double layers
 * 3) Double Layer formation
 * Boundary double layer formation

 * 1) History of double layers
 * 2) Some math
 * 3) External links
 * 4) References

[edit]

Double layer features

Is figure caption. Hall effect thruster. The electric field in a double layer is so effective at accelerating ions, that electric fields are used in ion drives

 * Classification: Double layers may be classified in the following ways:

 * Weak and strong double layers. The strength of a double layer is expressed as the ratio of the potential drop in comparison with the plasma’s equivalent thermal potential, or in comparison with the rest mass energy of the electrons. A double layer is said to be strong if the potential drop across the layer is greater than the equivalent thermal potential of the plasma’s components. This means that for strong double layers there are four different components to the plasma: 1. the electrons entering at the low potential side of the double layer which are accelerated; 2. the ions entering at the high potential side of the double layer which are accelerated; 3. the electrons entering at the high potential side of the double layer which are decelerated and successively refelected; and 4. the ions which enter the double layer at the low potential side of the double layer which are decelerated and reflected.Note that in the case of a weak double layer, the electrons and ions entering from the “wrong” side are decelerated by the electric field, however they will not be reflected, as the potential drop is not strong enough.

 * Relativistic and non-relativistic double layers. A double layer is said to be relativistic if the potential drop over the layer is so large that the total gain in energy of the particles is larger than the rest mass energy of the electron. The charge distribution in a relativistic double layer is such that the charge density is located at two very thin layers, and inside the double layer the density is constant at and very low compared to the rest of the plasma.In this respect, the double layer is similar to the charge distribution in a capacitor. As a special case of a relativistic double layer one can consider the vacuum gap at the magnetic polar cap of a pulsar.

 * Current carrying and current-free double layers. Depending under which circumstances the double layer is formed, it can either sustain a current or be current free. The first variation appears in a current carrying plasma where it may be generated by instabilities in the current or by random variations of the plasma density. (see formation below).

 * When a double layer is formed on the boundary of two plasmas with different characteristics, then it set up an electric field in order to maintain a balance between the penetration of particles from one plasma to another. In this case, there is a double layer electric field on the boundary, but no current flows.

 * Quasi-neutrality: The production of a double layer requires regions with a significant excess of positive or negative charge, that is, where quasi-neutrality is violated.(Block, 1978, p.60; Hasan et al., 1978, p.92) Since quasi-neutrality can only be violated on scales of the order of the Debye length, the thickness of a double layer is of the order of several tens of Debye lengths, a few centimeters in the ionosphere, a few tens of meter in the interplanetary medium, and tens of kilometers in the intergalactic medium.

 * Formation: As already stated above there are two different kinds of double layers, which are formed differently.
 * Current carrying double layers are formed in plasmas carrying a current. Various instabilities can be responsible for the formation: e.g. the Buneman instability which is dependent on the streaming velocity of the electrons. When the streaming velocity (basically the current density divided by the electron density) exceeds the electron thermal velocity of the plasma, an instability may arise. If the current is maintained, the instability may develop into the non-linear regime, and double layers may be formed.
 * Another mechanism which will work to create a double layer is when the current has to pass through a region of decreased density. In order to keep the current in the system continuous, the electrons have to be accelerated, in order to obtain the same current density with less charge carriers. This situation can be shown to be self-increasing, because of the electric field that is created more charge carriers are exported out of the density dip, until no more can be moved out. Then there is the situation of a double-double layer, of which one side will most likely be convected away by the plasma, leaving a regular double layer.

 * Current-free double layers, are at the boundary of two different plasmas. This needs some careful consideration. Two plasmas border each other, where on plasma has a higher temperature than the other (the same analysis can be done for different densities). A higher temperature means that the electrons and ions in the one plasma will have a greate thermal velocity. Now, for simplicity, we will consider a cold plasma (i.e. all particles in one plasma have the same thermal velocity) and use the ions as a neutralizing background (i.e. the ions do not move). As there is no solid wall between the two plasmas, the flux of electrons from the hot plasma to the cold plasma will be greater than the flux of the electrons from the cold plasma to the hot plasma. This leads to a charge imbalance, in the cold plasma many more electrons enter then exit. Thus, the cold will be negatively charged, whereas the hot plasma will be positively charged. Naturally, this cannot continue ad infinitum, as the electric field that will be build up through the charge build up in the two plasmas will start to decelerate the electrons coming from the hot plasma and accelerate the electrons coming from the cold plasma. In the end, the electric field will reach such a value as to stop the charge build up in the two plasmas, i.e. the fluxes of electrons in either direction will be equal. This balanced state will remain as long as the two plasmas do not mix and the temperatures are maintained. With equal fluxes of electrons, there is no net charge flowing over the double layer. The strength of the double layer is logically given by the difference in thermal potential of the two plasmas.

Particle acceleration: The potential drop across the double layer will accelerate electrons and positive ions in opposite directions. The magnitude of the potential drop determines the acceleration of the charged particles. In strong double layers, this will result in beams or jets of charged particles.

Our Moon in x-rays. Even the dark side of the Moon produces some x-rays. In the shadows, the Moon charges negatively in the interplanetary medium. The prediction of a lunar double layer [1] was confirmed in 2003 [2] PDF
 * Particle populations: As described in the formation of double layers, there are four populations of charge particles inside a double layer (1) Free electrons that are accelerated across the double layer (2) Free positive ions that are accelerated in the opposite direction across the double layer (3) Reflected electrons that approach the double layer, but are reflected back and counter stream away (4) Reflected positive ions that approach the double layer, but are reflected back and counter stream away.

 * Particle flux: For non-relativistic current carrying double layers the the electrons carry the main part of the current. The ratio of the electron and the ion current is given by the square root of the mass ratio of the ions and the electrons. This is the so called Langmuir condition. Simply said, this is a result of the small mass of the electrons, which are accelerated to higher velocities. and quasi-neutrality inside the double layer. (Block, 1978, p.65)

For relativistic double layers the current ratio is 1, i.e. equal amounts of current are carried by the electrons and the ions.

 * Energy supply: The voltage drop across a double layer is proportional to the total current. In this respect, Hannes Alfvén considered the double layer to be a load in part of an electric circuit. Anthony Peratt wrote: "Since the Double Layer acts as a load, there has to be an external source maintaining the potential difference and driving the current. In the laboratory this source is usually an electrical power supply, whereas in space it may be the magnetic energy stored in an extended current system, which responds to a change in current with an inductive voltage." (Peratt, 1991)

 * Stability: Double layers are usually noisy producing oscillations across a wide frequency band. They may also become unstable and explode resulting in a voltage drop that increases by several orders of magnitude, a phenomenon that was first discovered in mercury rectifiers used in high-power direct-current transmission lines. The double layer may also drift, usually in the direction of the emitted electron beam, and in this respect is a natural analogue of the smooth bore magnetron.(reference here to bore magnetron)

 * Magnetised plasmas: Double layers can both form in unmagnetised and magnetised plasmas. Cellular nature: While double layers are relatively thin, they will spread over the entire surface of a laboratory container. Likewise where adjacent plasma regions have different properties, double layers will form and tend to cellularise the different regions.

 * Energy transfer: Double layers fascilitate the transfer of electrical energy into kinetic energy, dW/dt=I.ΔV where I is the electric current dissipating energy into a double layer with a voltage drop of ΔV. Alfvén points out that the current may well consist exclusively of low-energy particles[12]. Torvén et al. also report that plasma may spontaneously transfer magnetically stored energy into kinetic energy by electric double layers [13]

[edit]
 * Oblique double layer: An oblique double layer has its electric field not parallel to the background magnetic field (i.e. it is not field-aligned). Simulation: Double layers may be modelled with particle-in-cell (PIC) computer simulations. To simplify calculations, they are sometimes treated as one-dimension or two-dimensional structures. However, current filaments require that they are treated as three-dimensional objects.

[edit]
 * Typical double layers
 * Location	Typical
 * Voltage drop	Source
 * onosphere	102- 104V	Satellite
 * Solar	109- 1011V	Estimated [14]
 * Galactic filament	1017V	Estimated (Peratt, 1991)

Double Layer formation Double layer formation. Hotter electrons moving into a cooler plasma region (Diagram 1, top) cause a charge imbalance, resulting in a double layer that is able to stop the total charge flux over the boundary between the two plasmas (Diagram 2, bottom).

Although the basic structure of all double layers is the same, a variety of different mechanisms have been proposed for their formation, depending on the environment of the plasma (eg. double layers in the laboratory, ionosphere, space plasmas, fusions plasma, etc). For example:
 * 1982: Disruption of a neutral current sheet [15]
 * 1983: Injection of non-neutral electron current into a cold plasma [16]
 * 1985: Increasing the current density in a plasma [17]
 * 1986: In the accretion column of a neutron star [18]
 * 1986: By pinches in cosmic plasma regions [19]
 * 1988: By an electrical discharge [20]
 * 1988: Current-driven instabilities (strong double layers) [21]
 * 1988: Spacecraft-ejected electron beams [22]
 * 1989: From shock waves in a plasma [23]
 * 2000: Laser radiation [24]
 * 2002: When magnetic field-aligned currents encounter density cavities [25]
 * 2003: By the incidence of plasma on the dark side of the Moon's surface [26]

[edit]

History of double layers A cluster of double layers forming in an Alfvén wave, about a sixth of the distance from the left. Click for more details

The research of these objects is a relatively young phenomenon. Although it was already known in the 1920s that a plasma has a limited capacity for current maintenance (Langmuir ,1929). He characterized double layers in the laboratory and called these structures double-sheaths. It was not until the 1950s that a thorough study of double layers  started in the laboratory (e.g. Schönhuber, 1958). At the moment many groups are working on this topic theoretically, experimentally and numerically.

It was first proposed by Hannes Alfvén (the developer of magnetohydrodynamics) that the creation of the polar lights or Aurora Borealis is created by accelerated electrons in the magnetosphere of the Earth. He supposed that the electrons were accelerated electrostatically by an electric field localized in a small volume bounded by wo charged regions. This so-called double layer would accelerate electrons Earthwards. Many experiments with rockets and satellites have been performed to investigate the magnetosphere and acceleration regions. The first indication for the existence of electric field aligned along the magnetic field (or double layers) in the magnetosphere was by a rocket experiment by McIlwain (1960). Later, in 1977, Forrest Mozer reported that satellites had detected the signature of double layers (which he called electrostatic shocks) in the magnetosphere [28].

The most definite proof of these structures was obtained by the Viking satellite (Boström 1991), which measures the differential potential structures in the magnetosphere with probes mounted on 40 m long booms. These probes can measure the local particle density and the potential difference between two points 80m apart. Asymmetric potential structures with respect to 0 V were measured, which means that the structure has a net potential and can be regarded as a double layer. The particle densities measured in such structures can be a los as 33% of the background density. The structures usually have an extent of 100 m (a few tens of Debye lengths). The filling factor of the lower magnetosphere with such solitary structures is about 10%. If one out of 5 such structures has a net potential drop of 1 V then the total potential drop over a region of 5000 km would be more than the 1 kV which is needed for the electrons to create the aurora. Magnetospheric double layers typically have a strength eφDL/kBTe≈0.1 (where the electron temperature is assumed to lie in the range 2 eV ≤ kBTe ≤ 20 eV) and are therefore weak.

In the laboratory double layers can be created in different devices. The are investigated in double plasma machines, triple plasma machines and Q-machines. The stationary potential structures which can be measured in these machines agree very well with what one would expect theoretically. An example of a laboratory double layer can be seen in figure …, taken from Torvén and Linberg (1980), where we can see how well-defined and confined the potential drop of a double layer in a double plasma machine is.

On of the interesting things of the experiment by Torvén and Lindberf (1980) is that onot only did the measure the potential structure in the double plasma machine but they also found high-frequency fluctuating electric fields at the high-potential side of the double laye (also shown in figure …). These fluctuations are probably due to a beam-plasma interaction outside the double layer which excites plasma turbulence. Their observations are consistent with experiments on electromagnetic radiation emitted by double layers in a double plasma machine by Volwerk (1993), who, however, also observed radiation from the double layer itself. The power of these fluctuations has a maximum around the plasma frequency of the ambient plasma.

A recent development in double layer experiments is the investigation of so-called stairstep double layers. It has been observed that a potential drop in a plasma column can be split up into different parts. Transitions from a single double layer into two, three or more-step double layers are strongly sensitive to the boundary conditions of the plasma (Hershkowitz, 1992). These experiments can give us information about the formation of the magnetospheric double layers and their possible role in creating the aurora.

Some scientists have subsequently suggested a role of double layers in solar flares Refs: 1 2 3 [edit]

Some mathematics.

External links

[edit]
 * A double layer review (1978), L.P. Block
 * Electrostatic double layers and a plasma evacuation process (1981), Raadu, M. A.; Carlqvist, P.
 * On the physics of relativistic double layers (1982), Per Carlqvist
 * On the role of double layers in astrophysical plasmas (1985), Smith, R. A.
 * Dynamical aspects of electrostatic double layers (1988) M. A. Raadu, & J. J. Rasmussen
 * Filamentary Double Layers (PDF, 1993), W.L. Theisen, R.T.Carpenter, R.L.Merlino
 * Energy release in double layers (1985), Raadu, M. A.
 * Parallel electric fields accelerating ions and electrons in the same direction (1988), Hultqvist, Bengt; Lundin, Rickard
 * Parallel electric fields in the upward current region of the aurora: Numerical solutions (2002, PDF), R.W. Ergun, et al.

References
 * Alfvén, H., On the theory of magnetic storms and aurorae, Tellus, 10, 104,. 1958.
 * Peratt, A., Physics of the Plasma Universe, 1991

Comments

 * Thanks for that, sorry I haven't gotten around to look at the details yet. Rather than replace the whole thing in one go, I wonder whether it would be better to go through the existing article a paragraph or section at a time, so we can clarify points? I've added some formatting to your draft above, just to make it easier to read through.

 * If we start with the introduction, the only query I have is regarding the description of "small-scale"; do you mean they are small as in thin relative to their length, or small-scale, and limited in size? It's just that I thought there is no actual size/scale limitation? --Iantresman 12:09, 21 February 2006 (UTC)

 * Small-scale here means "naturally" in the direction of the electric field. Martin

Question
Can we please start a discussion of the corrections I have proposed to the page. The whole text is shown above. There a things that are just plain incorrect in the wiki page about double layers.

 * Sorry for the delay. Shall we do this one section at a time? Do you want introduce your proposed changes into the introductory section, with clarification on "small scale" as mentioned above. --Iantresman 10:49, 13 March 2006 (UTC)

 * We can do it one section at a time, yes. I can live with the addition about the small scale, although I do think that also in e.g. a solar prominence or flare, the DL will not have an extent to cover the whole cross section of the magnetic tube, as I do believe in current filimentation. But that gets into too much detail and I think we should skip that for the moment. Tusenfem

 * Sounds good. So do you want to go ahead and make your changes to the introduction. --Iantresman 11:39, 14 March 2006 (UTC)

Changes to introductory changes
Thanks for the change to the introduction. I'm going to make some minor changes, for example, move the "small scale" characteristic to a little later in the paragraph where it can be explained in a single sentence, otherwise we're using a term which many people will not understand, and will not find out about until they have read further on.

Somewhere, can we reinstate the sentence "The physics of double layers are also utilised to produce ion thrusters, such as the Helicon Double Layer Thruster "? Or perhaps we could add this to the appropriate image caption?

I'd also like to add "charge separation region" somewhere in the introduction since I feel this is counter-intuitiuve to most people's understanding of a "neutral plasma". --Iantresman 10:28, 15 March 2006 (UTC)

 * I have made a small change in the changes you made. The thickness of a DL is approximately 10 debye lengths and not smaller than 1.

 * The ion thruster text could be moved down, somewhere, as an application.

 * Charge separation can be put in somewhere in the introduction, I will check

 * put in the charge separation in the introduction

 * took another look at the ion thruster and I have strong doubts that that could be considered a double layer. Yes, there is an electric field and a plasma and acceleration, but also a perpendicular magnetic field to achieve the Hall effect.

 * The thruster seems to be described as having a double layer, perhaps it has certain characteristics of a double layer, but I guess you'd need to contact their technical people for clarification.
 * And how about making changes to the next two sub-sections, "Classification" and "Quasi-neutrality" --Iantresman 11:12, 23 March 2006 (UTC)

 * MMM I did not check the ESA site, it truly seems to be a double layer in a strongly diverging magnetic field. So we could keep that. But I do think it would be better to have a separate section on applications, so I will move it to the "table of contents"

 * I will start changing the next sections. --Tusenfem 12:48, 23 March 2006 (UTC)Tusenfem

Changes Classification and Quasi-Neutrality
I have made the changes in these sections and I added also the formation section as it seemed to be the logical location. --Tusenfem 13:28, 29 March 2006 (UTC)

Changes to the last part as proposed above
Okay, as there were no comments on the last I continued editing the page. I have now changed it untill the list of characteristic double layers. I still have trouble with the bore magnetron, but added a link in which it is dicsussed. There is no wiki page that discusses it, it only gets mentioned on one page. For the next part, naturally the formation will be deleted, as that has been already discussed above. And the history needs to be replaced. Maybe also some figures need to be moved. --Tusenfem 19:05, 2 April 2006 (UTC)

On and On and On
Okay, I edited on, changed the history of the DLs and I have started the mathematical part of the page. More will follow. I need to find the figure I need in the history part, which shows the potential structure in the DL. I don't have it on this laptop. Cheers --Tusenfem 11:58, 9 April 2006 (UTC)

thesis on double layers
hi all, I have just finished writing up my PhD thesis on simulation of double layers. In particular, I work in the group that has invented the Helicon Double Layer Thruster (based on current-free double layers). I don't have much time at the moment to put into the DL wikipedia page, however, once my thesis is accepted, I am happy to send it to you guys - you may interested in the intro. I have noticed a few things that are stated in the article and that are not really true. Cheers, Albert Meige

 * Sounds great. I think there is also a Wiki page devoted to the Helicon Double Layer Thruster --Iantresman 08:37, 19 April 2006 (UTC)

 * Hey Albert! Nice to hear about another person who wrote his thesis on DLs. I would love to read it. My topic was "strong double layers in astrophysical plasmas". Good luck and cheers, Martin. --Tusenfem 20:10, 19 April 2006 (UTC)

Mathematical description section needs rethink
As it currently stands, the mathemetical description section is rather weak. I don't think it is very illuminating at all. I think either we go with a summary of the BGK description of time-independent electrostatic phase space structures (which is general enough to treat all the thermal effects and current-free double layers), or we decide not to do any maths at all. --Dashpool 08:23, 7 May 2006 (UTC)

 * I have not been working on it for a while, I was planning to add a lot more math in the section. I will see if I have some time soon, to type out all the stuff that I had planned to include onto the page.--193.170.90.98 13:35, 10 May 2006 (UTC)

 * I wonder whether it is more useful to the reader to describe more, rather than include the maths that few can understand. For example, in the maths section, it is written that:
 * "Double layers cannot be described in magnetohydrodynamics (MHD) and therefore we will often have to use the particle distribution function "
 * For me, this begs the questions:
 * Why would we consider MHD in the first place?
 * Why can double layers not be described with MHD?
 * What is a particle distribution function, and why is it better suited to double layers?
 * Is the maths used in the simulation of double layers, the same as that in distribution function?
 * --Iantresman 16:11, 10 May 2006 (UTC)

 * It is still useful to include maths which only people with a strong physics/maths background can understand: wikipedia is (believe it or not) often used as a starting point by physics graduate students and academics. It is possible for wikipedia to offer both a overview of the qualitative physics and a deeper and more mathematical approach to this topic. In response to Iantresman's questions:
 * MHD is often the first model chosen to try to describe any plasma, because even though it is rather simple, it captures many important aspects of plasma behaviour (conservation of energy/mass/momentum, bulk flow, plasma motion locked to field lines).
 * In MHD, there can be no potential drops along the field line because $$\mathbf{E} + \mathbf{V} \times \mathbf{B} = 0$$, so by definition no double layers. A sharp potential drop across the field is a contact or tangent discontinuity, rather than a double layer.
 * Ever hear of resistive MHD? --Art Carlson 12:10, 11 May 2006 (UTC)
 * Sure, resistive MHD (or other generalised MHD models) allows an electric field along the field line. However, no charge separation can be generated by assumption (maybe this is a better argument for Ideal MHD too), and therefore still no double layers. RMHD and other fluid models generally predict smooth potential gradients, rather than sharp layers, which are really kinetic in origin. Probably it is the incompatibility of double layers with fluid models in general which should be emphasised.. --Dashpool 16:54, 11 May 2006 (UTC)
 * Two-fluid MHD is enough to get you charge separation. But you seem to be saying that the velocity distribution of a single species necessarily deviates far from a thermal distribution near a double layer. --Art Carlson 19:10, 11 May 2006 (UTC)
 * (see correction at end) Actually, two-fluid MHD should be enough to describe the double layer of the first type considered in the mathematical analysis section: a single zero-temperature electron beam and a single zero-temperature ion beam (can relax temperature condition somewhat). But that's usually an unstable situation (nonrelativistic case, strongly Buneman unstable), which will rapidly evolve into a very non-thermal plasma, which no fluid theory could describe accurately. The timescale for the non-relativistic Buneman instability is faster than the timescale for ions to pass through the double layer. Maybe there is some special limit (relativistic?) where a (complicated) fluid model can describe the formation or evolution of a double layer.. but certainly in general fluid theory isn't adequate.--Dashpool 10:33, 13 May 2006 (UTC)
 * Correction: the analysis section assumed (but did not explicitly state) zero velocity trapped components outside the double layer: see discussion below. So I think the answer is what Art Carlson said just above: the velocity distribution is necessarily non-Maxwellian. --Dashpool 15:32, 15 May 2006 (UTC)
 * Two fluid theory just has two fluids at different temperature. that will not let you describe double layers very well, because there are more populations, thermal at both sides, accelerated ions and electrons, reflected ions and electrons, so you would need at least a six-fluid model (or maybe five if you consider both thermal plasmas equal). --Tusenfem 19:23, 11 May 2006 (UTC) Then again, you will have problem, I think describing the accelarated particles inside the DL.
 * Once you have a bunch of beams you are almost inevitably going to get instabilities (which need a kinetic description). In any case, you would be getting pretty far from what most people would call a fluid model.--Dashpool 10:33, 13 May 2006 (UTC)
 * See Distribution function. The point is that, unlike a conventional gas, many plasmas are collisionless, and particles can stream freely through a region. The consequence is that we cannot always think of the plasma properties at a certain location being described by the temperature, density and bulk flow (as in fluid theories like MHD). Instead, there may be a whole bunch of interpenetrating beams, streaming in different directions at different speeds: this is always the case for strong double layers.
 * Yes. The simulations describe the evolution of the distribution function.
 * --Dashpool 07:41, 11 May 2006 (UTC)
 * I will see if I have time this weekend to write up (or copy from what I have already once written) the math that I wanted to include on this page.
 * I for one, would like to find much more math on the physics pages of wiki.
 * Okay, 'till sunday then! --Tusenfem 12:33, 11 May 2006 (UTC)
 * Okay, I had some time free yesterday and today, so I wrote some more on the math of DL characteristics. It is not complete, naturally, nothing yet said about relativistic DLs, and non-current carrying DLs. But at least it is a start. I have all the equations also in relativistic form in my thesis, but doing it non-relativistically was already enough work :-) --Tusenfem 12:00, 12 May 2006 (UTC)
 * Now that I think about it a little more, I remember that a double layer cannot be constructed from two zero-temperature distributions alone: there need to be two values of the potential where the net charge is zero. But the analysis seems to imply the opposite. Perhaps the problem is that the plasma configuration needs to be more carefully described?--Dashpool 13:07, 14 May 2006 (UTC)

 * Well, the starting point is that we have a plasma with a current. How the DL is formed, is debatable, but a density dip could do the trick. So basically we have a zero-temperature plasma at both sides and an electron and ion current flowing. The analysis that I wrote down, is just the regular starting analysis that you will find in most overviews. I read through it, and I guess for an "encyclopedia" there needs to be more explanation.--Tusenfem 20:28, 14 May 2006 (UTC)

 * Perhaps you could point us to a book or journal article where this analysis might be found? I think you have missed an important point. I am fairly sure that you need to include some trapped particles from the start of the analysis, and include them in the Poisson equation. Otherwise, it is not going to be possible to satisfy quasineutrality far from the double layer. --Dashpool 07:06, 15 May 2006 (UTC)

 * Is a current a requirement? See:
 * Current-free double-layer formation in a high-density helicon discharge (2002) Christine Charles and Rod Boswell
 * --Iantresman 21:36, 14 May 2006 (UTC)

 * Look at the reference, on the page, the Raadu monograph, section 2 Steady state double layers. Or look in my paper on "Strong double layers, existence criteria and annihilation: an application to solar flares" ApJ Suppl. Series, 90, 589-593, 1994. (If you have no access I can send you a pdf)
 * In all there is a small localized electric field, on the order of 10 deBye lengths, so if you take a volume around the DL, you will find that the net charge in the volume (the positive and negative layer) equals to zero. So far away from the double layer, you have a quasi-neutral, current carrying plasma, where there is a potential difference of phi_DL beteen the "upstream" and "downstream" side. But that is easily explained, as there has to be a driver for the current, i.e. there is a potential difference over the plasma column, which is located in the DL.
 * A current is a requirement, because I clearly state that I am discussing the characteristics of a current carrying double layer.
 * --Tusenfem 08:20, 15 May 2006 (UTC)

 * OK, in the ApJ paper, it is stated nicely: 'at the boundaries of the Double layer there are cold (T=0) reflected particles species to maintain charge neutrality in the ambient plasma'. But the analysis as presented shows no trapped particles..--Dashpool 09:53, 15 May 2006 (UTC)

 * Yep, you are right, I did write that in the paper. Now, I am wondering why I did not write that in the introduction of my thesis. But if there is a population of cold (T=0) "reflected" particles, that means that they do not penetrate into the DL, only then T != 0 do they have energy enough to penetrate and be reflected.
 * On the whole, say take a flux tube with a DL in the middle, there is charge neutrality as the charge in the positive and negative layer is equal. However, we have different electron and ion currents, and their charge needs to be neutralized.--Tusenfem 10:18, 15 May 2006 (UTC)

 * I am attempting a bit of a rewrite to clarify this point, and neaten things up a little. On another point, I'm not sure the density cavity excavation analysis is a good idea here. It is qualitatively right, but only really valid for strongly collisional plasmas (where double layers won't occur anyway). It is (mathematically) better to use collisionless linear stability theory. Since we have already alluded to this mechanism earlier in the article, maybe we should leave it out of the mathematical analysis section? As another point, it is easy to construct a current free double layer from a (stationary) current-carrying one by symmetrizing the distribution.--Dashpool 15:32, 15 May 2006 (UTC)

Langmuir probes
I'd like to tap the expertise which is obviously present here. Whether it will ultimately benefit the article I can't say yet.

I worked many years with Langmuir probes in strong magnetic fields. The usual picture is an electrode that draws current from a plasma, and the current flows mostly along the magnetic flux tube intersecting the electrode. There are many things that are still not understood. Above all, the ratio of the electron saturation current to the ion saturation current is usually several times less than the value expected (roughly the square root of the mass ratio). In extreme cases the electron saturation current is even smaller than the ion saturation current! Another problem is that the current apparently does not (always) follow the flux tube. In extreme cases it seems to flow across the field (in the direct of E, not the direction of EXB) as easily as along it. Over the years I considered many theories, but I never thought much about double layers. Double layers are simply not well-known in the fusion research community.

That leads me to my first question. Is there a reason to expect that double-layers are not important in fusion plasmas? Is it possible they are important but have been overlooked? Where would double layer effects most likely be manifest in a tokamak? That brings us to the second question. Is there any obvious or at least plausible way that a double layer somewhere in the current tube can explain the strange features of Langmuir probes?

If I were still active in the field I would dig into the literature and figure it out myself. As it is, I am now working in astrophysics and must treat the question more or less as a hobby. But if you can throw me a chunk of meat, I might still take up the chase.

Thanks. --Art Carlson 10:31, 15 May 2006 (UTC)

 * Is there an analogy between these probe-plasma interactions and density cavities in the Aurora? --Dashpool 16:27, 18 May 2006 (UTC)

Proposed change to intro.
Trying to clean up a little. I think sheaths are conceptually related to double layers but not quite the same thing.

Proposed text:

An electrostatic double layer is a thin layer in a plasma which supports a sharp drop in electrical potential. The thickness of a double layer is of the order of ten Debye lengths. There is an electric field perpendicular to the layer, which is produced by two oppositely charged sheets of plasma, one on each side of the layer. The electric field accelerates the plasma's electrons (positive ions) entering the double layer at the low (high) potential side, and decelerates them when entering from the high (low) potential side. In general, double layers separate regions of plasma with quite different characteristics. Double layers are found in a wide variety of plasmas, from discharge tubes to space plasmas to the Birkeland currents supplying the Earth's aurora, and are especially common in current-carrying plasmas.

Other names for a double layer are: electrostatic double layer, electric double layer, plasma double layers, electrostatic shock, space charge layer. In laser physics, a double layer is sometimes called an ambipolar electric field .Double layers are conceptually related to the concept of a 'sheath' (see Debye sheath).

--Dashpool 16:27, 18 May 2006 (UTC)

 * Plasma, as a subject, I find quite difficult to grasp because of its technical terminology. In the introduction, I would say that the phases "drop in electrical potential" and "the order of ten Debye lengths" is meaningless to most people, which means that we loose most readers in the first couple of sentences. If was being very pedantic, I would also say that "thin layer" is misleading, because thin is a relative term, and several debye lengths in intergalactic space could imply a double layer that is tens of thousands of kilometers thick. I would suggests something that begins:
 * A double layer may occur in a plasma, and consists of two parallel, but not flat, layers of opposite electrical charge. This results in a sharp potential drop that accelerate ions entering the layer in opposite direction, sometimes up to velocities approaching the speed of light. The thickness of a double layer is very thin compared to its areas, of the order of ten Debye lengths, a characteristic that changes between different kinds of plasma (milimetres to thousands of kilometers)...
 * --Iantresman 17:37, 18 May 2006 (UTC)

 * I would say the terminology is complex because plasmas are difficult to understand, rather than the other way around, but we may as well keep it as simple as possible. Maybe a drop in voltage would be more familiar terminology?
 * Suggested:
 * A double layer is a structure in a plasma and consists of two parallel layers with opposite electrical charge. The sheets of charge cause a strong electric field and a correspondingly sharp change in voltage (electrical potential) across the layer. Ions and electrons which enter the layer are accelerated, decellerated, or reflected by the electric field. In general, double layers (which may be curved rather than flat) separate regions of plasma with quite different characteristics. Double layers are found in a wide variety of plasmas, from discharge tubes to space plasmas to the Birkeland currents supplying the Earth's aurora, and are especially common in current-carrying plasmas. Compared to the size of the plasmas which contain them, double layers are very thin (typically ten Debye lengths), with widths ranging from a few millimeters for laboratory plasmas to thousands of kilometres for astrophysical plasmas.
 * --Dashpool 08:18, 19 May 2006 (UTC)

 * Looks better to me. Be good to get another opinion or two from some of the other editors first, before committing the change. --Iantresman 10:03, 19 May 2006 (UTC)

 * looks pretty good to me. It is a good thing going through the whole page and sprucing it up. Maybe, between brackets we can give a few examples of what the different characteristics are between the plasmas separated by DLs. In mind come: electric potential (for current carrying DLs)), density, temperature, plasma make-up (different mixes of species).
 * One spelling comment decelarated with only 1 l. --Tusenfem 21:51, 19 May 2006 (UTC)

Bohr Magnetron
I have changed the text regarding the Bohr Magnetron (h e / 2 pi m), which is not a unit of energy, to which it was changed, it is a unit of magnetic moment. First when multiplied by the magnetic induction B it becomes an energy. --Tusenfem 22:03, 19 May 2006 (UTC)

Biophysics
I disagree with the biophysics part about cellular structure, Ian. I hope you understand that the cells in biophysics are totally different from the cells that Alfven was talking about. Biological cells have membranes that are corpuscular, whereas plasma cells do not.--Tusenfem 19:33, 26 May 2006 (UTC)

 * Indeed, I agree they are difference, but there is at least one peer-reviewed paper using electric double layers to help explain cellular double layers... so I figured that Alfvén and Langmuir's comments were relevant. Perhaps you could take a look at the refernces by Mituo Uehara and Jennifer Gimmell, and explain the analogy better? --Iantresman 19:47, 26 May 2006 (UTC)

title: Talk:Double layer


text:
East Antrim Hockey Club

East Antrim Hockey Club was a men's field hockey club based in Newtownabbey, County Antrim, Northern Ireland, 7 miles north of Belfast. It was affiliated to the Ulster Branch of the Irish Hockey Association and was one of the oldest clubs in Irish hockey. The club's motto was Non Sibi Cunctus. It folded circa 2005.

title: East Antrim Hockey Club