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An Icy Art Installation Clear As Crystal
Yunziyi Lang
"Thinning Ice", an installation commissioned by Swarovski for its ninth year at Design Miami (December 3 – 7, 2014), links melting glaciers and climate change through a three-dimensional experience. Architect Jeanne Gang collaborated with James Balog, a National Geographic filmmaker/photographer, to create the installation, which includes a kind of glacier sculpture and a series of photographs, as well as video.
Swarovski Crystal's headquarters in Wattens, Austria. (Photo: HellasX/Wikimedia Commons)
The installation was inspired by Balog's photographs of the shrinking Stubai Glacier in the Austrian Alps, where Swarovski is headquartered, over a three-year period. The Stubai photographs are part of Balog's ongoing "Extreme Ice Survey," an innovative, long-term photography project founded in 2007. The project consists of 28 cameras at 13 glaciers in Greenland, Iceland, the Nepalese Himalayas, Alaska and the Rocky Mountains of the United States, which have been recording the rapidly depleting glaciers every thirty minutes over the past several years.
In an effort to bring Balog's photographs to life, Gang displayed a fluid-formed luminous block, which represents a melting glacier, in the center of the room. This structure, which resembles a kind of table, is pocked with asymmetric holes embedded with a diverse selection of Swarovski crystals, from unprocessed fragments and shards to finely finished pieces. The holes are meant to resemble cryoconite holes, tiny perforations found on glaciers that are created by wind-blown dust made of rock particles, soot and microbes.
Glacial Environment for Swarovski: At the Design Miami 2014, American artist Jeanne Gang des… http://t.co/9bo5gL3v9p #Mysecretshowroom
— My Secret Showroom (@Secret_showroom) December 14, 2014
The installation's floor is set with curving illuminated cracks, also filled with small bits of Swarovski crystal, which resemble the crevasses one might find in a receding glacier. Gang finished the installation room with an 11.5-foot tall and a 70-foot long media wall, which presented a running slideshow of epic photographs and video footage of the world's glaciers.
Details from the "Thinning Ice Installation" (Source: Super Architects/Facebook)
"'Thinning Ice' is a work which captures the haunting beauty of the Earth's threatened glaciers in a powerful, almost elegiac way," said Nadja Swarovski, a member of the Swarovski Executive Board, in a statement. The immersive nature of the work is meant to inspire visitors to contemplate the implications of and solutions to the melting of the world's glaciers.
Swarovski chose to showcase glaciers in Florida to highlight its commitment to sustainability. For 14 years, the company has funded its Swarovski Waterschool Program, which educates children around the world in the principles of sustainable water management. Swarovski also sources materials from suppliers that comply with the United Nations Global Compact's human rights and environmental standards.
GlacierHub has posted other stories recently about artists from the United States, Italy, and Peru whose work centers on glaciers.
Tags: alaska, Alps, austria, greenland, himalayas, ice, iceland, nepal, rocky mountains, swarovski
For An Alien World, Look No Further Than Iceland
Iceland's Svinafellsjokull Glacier played a prominent role in Christopher Nolan's Interstellar. (Photo credit: Melinda Sue Gordon – © 2014 Warner Bros. Entertainment, Inc. and Paramount Pictures Corporation. All Rights Reserved.)
After hundreds of years, the Svinafellsjokull Glacier is ready for its close-up. The Icelandic glacier has a starring role in Interstellar, the sci-fi movie about a team of astronauts lead by Matthew McConaughey that travel to a distant planet in search of a new home for the human race as the Earth becomes uninhabitable.
The glacier, and Vatnajökull National Park where it resides, are stand ins for the of icy, alien world the film is meant to depict. Little set dressing was required for the mid-September 2013 shoot, only a huge model of McConaughey's space ship was brought to the section of Iceland's largest glacier.
"How would you recreate the biggest glacier in Europe in a studio?" said actor David Gyasi, who plays one of the astronauts, in a promotional video for the movie. "You wouldn't."
The glacier is getting plenty of exposure worldwide thanks to the movie. Interstellar has taken in more than $200 million at the international box office since it opened last week.
The space epic isn't director Christopher Nolan's first time filming at the glacier. In 2005's Batman Begins, Nolan used Svinafellsjokull and other areas of Iceland as stand ins for the Tibetan Himalayas, a remote training ground for Bruce Wayne, where he learns how to fight prior to becoming Batman. Iceland is easier to access for film crews than the Himalayas and other mountain ranges, so the tiny North Atlantic country often plays many real and imagined locations.
Interstellar is hardly the first, or the last, movie to take advantage of Iceland's frozen landscapes. (Photo credit: Melinda Sue Gordon – © 2014 Warner Bros. Entertainment, Inc. and Paramount Pictures Corporation. All Rights Reserved.)
Iceland's unique and varied landscapes have also been featured prominently in TV and film before. The country stood in for another alien landscape in Prometheus, the frozen northern region Beyond the Wall in HBO's Game of Thrones, and the black sands of Iwo Jima in Flags of Our Fathers and Letters from Iwo Jima.
This year has been a big one for glaciers in the movies. GlacierHub previously wrote about Austria's Hintertux glacier appearing in Snowpiercer, a movie about the last of humanity zooming around a frozen Earth on a train. It's worth noting that both Snowpiercer and Interstellar feature humans searching for a way out of climate problems plaguing the planet. Perhaps the most feared future in science fiction isn't a world of warm temperatures and high seawater, but one too frozen for people to live.
Tags: austria, batman, batman begins, game of thrones, hintertux, iceland, interstellar, prometheus, snowpiercer
Glacier stories you may have missed this week – 9/29
Nepal tourism adapts to climate change
"Weather can ruin the vacation while climate can devastate a holiday destination. Climate change not only impacts on tourism directly by changes in temperature, extreme weather events and other climatic factors, but it will also transform the natural environment that attracts tourists. Despite the global nature of tourism industry and its economic contributions, scholars of climate change research have hardly acknowl- edged the threat of climate change to the tourism industry."
Read more about Nepal's tourism industry's efforts to deal with climate change in this study in the International Journal of Disciplinary Studies.
Pakistan needs more glacier data-sharing to mitigate disasters
"'Our elders used to say this glacier was very high, so high there was no one living here. This was a giant glacial lake,' Sajjad Ali said. Standing on a cliffside, he pointed down at the Hopar Glacier, more than a 1,000 metres below, its surface covered by massive boulders it had swept out of its way as it carved a valley through the Karakoram mountains."
Read more about in Pakistan's efforts to monitor glaciers in IRIN Asia.
Austrian and Swiss Alps look back at their history…way, way back
"The landscapes in mountain regions are often strongly influenced by the steep climatic gradients and by past variations in climatic conditions. Therefore, the study of geological landscape features such as moraines, landslides and rock glaciers with appropriate geochronological approaches allows insights into past variations in climate."
Read the full study in the July 8, 2014 issue of Quaternary Science Reviews.
Tags: adaptation strategy, Alps, austria, Climate Change, environment, monitoring, mountain, ourism, pakistan, switzerland
In state of the climate report, mountain glaciers get special attention
Gina Stovall
(Ruth Hartnup/Flickr)
The year 2013 hasn't been a good one for climate change (as you might've guessed) and mountain glaciers have been singled out, according to a new report released by the National Climatic Data Center.
The largest climate data archive in the world sits in North Carolina's Appalachian Mountains and contains 14 petabytes of information, enough to stream 23 million movies. Asheville, N.C. is home to the NCDC, a division within the National Oceanic and Atmospheric Administration – that provides climatological services and data worldwide. For the last 24 years, NCDC scientists have been producing an annual report on the state of the world's climate. These reports provide updates on global and regional climate and notable weather from the preceding year. Published by the American Meteorological Society in the Bulletin of the American Meteorological Society (BAMS), this report is a large international collaboration. The most recent report, covering the year 2013, involved over 400 scientists from 57 countries.
(Luca Carturan/University of Padua)
Among the 2013 report's distinguished highlights, along with carbon dioxide levels topping 400 parts per million, and the record-breaking super-typhoon Haiyan, is the news about mountain glaciers. The supplementary report begins by explain the importance of these glaciers:
"Around the globe, some 370 million people live in basins where rivers derive at least 10 percent of their seasonal discharge from glacier melt. Glacier melt provides drinking water for human populations, and irrigation water for crops. Dams on glacier-fed rivers are key sources of hydroelectric power in some parts of the world. The retreat of the majority of mountain glaciers worldwide is one of the clearest signs that climate is warming over the long term; some glaciers have already disappeared."
The report indicates that mountain glaciers lost more ice from melt than they gained from seasonal snow-fall for the 23rd year in a row. This pattern is expected to continue. Since 1980, glaciers have lost the equivalent of 50 feet (more than 15 meters) of water.
Five regions with long histories of data are used in the report as a barometer for the health of mountain glacier: Austria, Norway, New Zealand, Nepal, and the Northern Cascades of Washington State. The news – a pattern dominated by loss – is grim. Of the 96 glaciers evaluated in the Austrian Alps, 93 are retreating, two are stable, and just one is advancing. Norway is much the same: 26 of the 33 are retreating, another four are stable, and only three are advancing. Things are worse in North America (the 14 glaciers of the Northern Cascades in Washington State and Alaska are all significantly retreating) and in New Zealand, where all 50 are anticipated to have retreated by the end of the 2013 melt season. Only in Nepal, where the 3 glaciers monitored are near equilibrium, this near-balance reflects an unusually good year. In 2013, those glaciers received the largest amount of snow accumulation in the last seven years.
The plight of diminishing mountain glaciers has serious implications for the health, food, energy resources and livelihoods of the 370 million people who live close to them. There are also serious effects in adjacent lowlands. Just as steady upward trend of the Keeling Curve of carbon dioxide concentrations is closely watched, so should be its apparent reflection: the glacier mass balance curve, shown each year in the State of the Climate report for the world to see.
This year's' report and all previous reports are available for free download online.
Tags: alaska, austria, careser glacier, italy, national climatic data center, ncdc, nepal, new Zealand, noaa, northern cascades, state of the climate, washington
The glaciers win in "Snowpiercer", but at what cost?
Humanity struggles to stay warm in a train speeding around a frozen Earth in "Snowpiercer". (© 2013 – RADiUS/TWC)
Remember when Godzilla used to be scary?
Climate change horror seems to be the new go-to disaster for Hollywood films as of late. Unlike giant floods, tornados or even Godzilla, the world freezing over affects everyone at once. There might be an escape from a giant atomic lizard, but when the temperatures change, there's nothing we can do as a species but adapt.
That adaptation comes in the form of a speeding, circumnavigating train in the new movie Snowpiercer. The exposition in the opening minutes of the movie sets up the scenario: to counteract warming global temperatures, scientists in the present day developed a chemical that will cool the earth when released into the atmosphere. It worked a little too well.
What's left of humanity is stuffed into a train, divided so neatly into class sections it would make a political science sophomore blush. The poor are crammed into industrialized bunk beds in the tail section while the rich at the front of the train enjoy saunas, sushi and never-ending raves. After spending 17 years in the squalid back of the train eating gelatinous black protein blocks, Curtis, the film's lead (Captain America's Chris Evans), reluctantly leads an uprising to take over the engine.
What's interesting about Snowpiercer isn't so much the setting but that climate change horror seemed to be playing a larger role in movies right now. As New Yorker film critic David Denby wrote about the Snowpiercer, "The current designers of awe, in Hollywood and elsewhere, have gone back to the Apocalypse. They've created what might be called the Seven Horsemen of the Multiplex: aliens, pandemics, floods, ice, comets and other interplanetary flotsam, nuclear war, and zombies."
That fourth one, ice, popped up in last year's The Colony, which imagines humanity living underground after the world freezes over once climate-changing weather machines break down. In both films, the fear seems to come from geoenginnering gone wrong as much as it does from a permanent Ice Age. (In some sense, this is also what the mega-hit Frozen is about.)
On location at the Hintertux glacier in Austria. (from left) TJ Park (Producer), Sung Ho Nam (Production Manager), Dooho Choi (Co-Producer), Alex Hong (DoP), Thomas Fuchs (Cine Tirol), Bong Joon-Ho (Director), Robert Bernacchi (Co-Producer). (Cine Tirol Film Commission)
In an odd way, Snowpiercer highlights the seriousness of glacial retreat; only a cosmically huge event is capable of bringing them back. One scene in the movie features a shot of the Hintertux glacier in the Tyrolean Alps of Austria. Though the movie takes place in 2031, the glacier will almost certainly be visibly smaller by time that year actually rolls around.
Over Independence Day weekend, Snowpiercer only took in a little over a million dollars at the box office. In South Korea, where it was co-produced, the movie made nearly $60 million, setting a new record in that country. This was the first English-language production for Snowpiercer's director, Joon-ho Bong, whose monster movie The Host achieved popularity in the U.S. when it was released in 2006.
Whether the most expensive Korean movie ever made finds popularity here in America (which accounts for only 2 percent of worldwide box office receipts so far), remains to be seen. Audiences may instead choose to find comfort this summer in a much more comforting disaster from the east: Godzilla.
Tags: austria, Climate Change, europe, glacier, global warming, hintertux, korea, movie, snow piercer
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Policy & Economics
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After getting blown out Wednesday at Duke, things don't necessarily get much easier for IU when Morehead State comes to town Saturday.
The Eagles have just one loss – by one to a tough Illinois State team on the road – and are on a four-game win streak.
Tom Crean described them as a team that wouldn't shock anyone if they won their conference.
Morehead State does two things well that IU struggles with. The Eagles rank 16th in the country in turnovers forced (17.7), and 17th in the nation in offensive rebounding (15.7). They also have the best scoring defense in the country, allowing just 54.5 points per game.
IU will have its hands full on defense, as it will with most opponents this year. After playing a mix of zone and man-to-man defense against Duke, Crean says he isn't going to simplify the defense. He noted an example of nobody being in the corner and bumping out to nobody Wednesday.
He also said the Hoosiers didn't play the ball hard enough, and says it's easier said than done to keep opponents in front of the ball. Duke wanted to get to the free throw line, he added, and that trying to stop the dribble penetration often caused open shooters on the perimeter.
He said IU must be more aggressive early on. With freshman Thomas Bryant manning the post, Crean said it will be a while before the rim protection is where he wants it to be.
While Morehead State doesn't have the height to stay matched up with IU, Bryant and others will have to pay attention to DeJuan Marrero, a forward, who leads the Eagles in rebounds per game at 6.7.
After being asked a question about his best scorers being weaker defenders and how it differs from teams in the past, Crean gave a very basic answer that he would later repeat several times.
Maybe CTC is too intent on innovation, wants to be the new 'Chip Kelly' of basketball and can't quite get it done?
And actually any average college coach, including IU's!
Who is going to decide on "a really good coach"? Can you trust the same people who are empowering Crean?
I'm not sure he intends it as flattery towards me! LOL.
Personally I just don't think he is a quitter which is a quality I admire. But I don't see how he can continue to put his family through this. But at the same time the man needs to take care of his future too. If he doesn't give up the buyout he can use that as leverage for Glass to help him find a job elsewhere.
Money – I'll concede that money is of some importance in every decision, but it is a fairly minor factor in the current context of IU basketball. My humble guess is that adequate money would "show up" if it were directed toward the betterment of the program…and even more so if tied to a beloved, successful alum/legend. Regardless, if money was a deciding factor then the search for this role could be narrowed to those willing to take it on as an "honorary" position and not receive University compensation.
Confusing Responsibility – I didn't explain the role in detail in an effort to be succinct. The AD calls the shots and the coach runs the program…as is customary. The GM/mentor is an adjunct to the program who provides insight on a team-level and on an individual-level when asked. This role is active during the offseason and then fades into a "just for prestige" role during the season. They don't call plays or undermine anyone's authority. They do, however, give formal NBA-level feedback to recruits and current players. They speak at fundraisers and camps. They bolster in-state ties. They create a conduit for one last chance to bring RMK back into the fold…even if its just his blessing for a statue (but preferably a court naming or HoF induction). Obviously, it would have to be someone suited well for the role. The fact remains, it would provide an NBA voice and respect without bringing in an NBA or D-League coach (I firmly believe college basketball is a more strategic level and requires a better Xs and Os coach).
You likely still don't agree, but that may clear up my proposal.
Patience? That's all I got lol. But still, I'm thankful that he was willing to come in at a rough time when others wouldn't. He had a good thing going at Marquette. I don't know him so I'm just going to go off of what his former players have said and assume he is a good guy. I think he should leave, but I don't want to tar and feather the man.
Three. We hard after Zimmerman, Okonoboh, and Dwayne Morgan.
Great comment. AJ had more heart than most of these guys will know. That block on Boozer is a top 10 IU play for me. Was that the last time we beat Duke?
Then he doesn't know anything about poetry!
Exactly, I think he is overzealous about leaving his mark. Innovators usually master the "traditional" fundamentals first before they begin experimenting. But CTC is too stubborn in his delusions.
You don't win championships without truly great players. Knight could attest to that; three championships in 29 years. Unlike many, I don't believe our current roster is championship run caliber. As mentioned above, biggest glaring weakness is lack of front line size and depth. That said, we could be much more competitive if our defensive scheme as you suggest, leveraged our players. Knight's defensive approach (intelligent individual positioning with good weak-side awareness and help) was effective no matter the talent level. That's why his down years were much more acceptable than Crean's.
I wish that everything is great and was with IU basketball but it isn't. CTC is the coach and he will be for the entire season. Everyone on this board has a strong opinion and rightfully so. I hope that everything works well for the program and I wish that everyone would stop attacking CTC as a human being. He wants to win as everyone else wants and his family's income is dependent on that. He is being paid greatly and I am lost with words on the frustration of what is going on. Peace to everyone and I/team would get ripped in sports articles when we didn't win football games in the 80's even though we won the Holiday Bowl. Being ripped apart is a terrible aspect for anyone to handle. I hope for the best for Tom Cream and the program.
His brother-in-laws's accomplishment may have possibly motivated him toward an over-reaching goal. I agree CTC does seem to be sttubborn and maybe a little arrogant?
I was watching the Duke vs Buffalo game.. It's almost the half and Buffalo is playing them a lot tougher than IU did At least so far they're styin' in this game.. down by a few, but they're competing.
The GM can do nothing except advise the Coach and/or AD even given your clarified explanation. Why pay for NBA input by one person when you receive it now from 20 plus NBA executives for free?
Define what you mean by the term "empowering": 1) not breaking a valid contract; 2) hiring Crean- Glass was not at IU then; 3) extending Crean's contract after a great 5 year rebuilding program including a B1G Title and 2 straight Sweet Sixteens! You just have your own limited opinion. Most people believed that 1) not breaking a valid contract is good; 2) Crean was a good to very good choice at the time of his hiring; 3) the extension was deserved at the time. The AD picks the Coach. If he picks wrong, then the AD gets fired.
I'm listening to Tom Crean pregame with Fisher while driving. I don't think I've ever heard a guy speak so confidently while making no sense and with his seat on fire.
Do you live in Portland, Oregon?
Belly laughing. Also, put down your phone; dangerous while driving.
Not at all. I wasn't speaking as a coach but in the community.
He doesn't. He's just diggin' at me.
I consider the source and ignore it.


Coat of dark and gray A most trendy colors of the period were sable and gray. They are universal and fit for anything. These coats look more elegant. They may be worn any day. This style is devoid of the frills, but a coat looks more chic. Delete the black color of his collections failed any style designer, so the elegancy and simplicity are yet in vogue. A lack of whiteness bloom in style collections, in principle, justified, since the fall color is too pretentious. Resembling articles: Summer orientation for business woman Summer vogue: Photo Gallery trendy sundresses-TWO: For the beautiful and slender Fashion of fashionable hats.


text:
Bob Marley – Get Up Stand Up
About Bob Marley:
Nesta Robert Marley OM (6 February 1945 – 11 May 1981) was a Jamaican singer-songwriter who achieved international fame through a series of crossover reggae albums. Starting out in 1963 with the group the Wailers, he forged a distinctive songwriting and vocal style that would later resonate with audiences worldwide. The Wailers would go on to release some of the earliest reggae records with producer Lee Scratch Perry. After the Wailers disbanded in 1974, Marley pursued a solo career which culminated in the release of the album Exodus in 1977 which established his worldwide reputation. He was a committed Rastafarian who infused his music with a profound sense of spirituality.
Bob Marley was born on the farm of his maternal grandfather in Nine Mile, Saint Ann Parish, Jamaica, to Norval Sinclair Marley and Cedella Booker. Norval Marley was a European-Jamaican of British/Syrian descent whose family came from England. Norval claimed to have been a captain in the Royal Marines though at the time of his marriage to Cedella Booker, an African-Jamaican then 18 years old, he was employed as a plantation overseer. His family named him Nesta Robert Marley though later a Jamaican passport official would reverse his first and middle names. Although Norval provided financial support for his wife and child he seldom saw them as he was often away. Bob Marley attended Stepney Primary and Junior High School which serves the catchment area of Saint Ann. In 1955, when he was 10 years old, his father died of a heart attack at the age of 70. Although Bob Marley recognised his mixed ancestry, throughout his life and because of his beliefs, he self-identified himself as a Jamaican of African descent, following the ideas of Pan-African leaders.
The Wailers' first major label album, Catch a Fire was released worldwide in April 1973, packaged like a rock record with a unique Zippo lighter lift-top. Initially selling 14,000 units, it didn't make Marley a star, but received a positive critical reception. It was followed later that year by Burnin', which included the standout songs "Get Up, Stand Up", and "I Shot the Sheriff", which appealed to the ear of Eric Clapton. Vincent Ford, a childhood friend from Jamaica, was given writing credit for "No Woman, No Cry" on the 1974 album Natty Dread, as well as the songs "Crazy Baldheads" (with Marley's wife Rita), "Positive Vibration" and "Roots Rock Reggae" from the 1976 album Rastaman Vibration, along with "Inna De Red" and "Jah Bless" with Marley's son, Stephen. "Three Little Birds" is a song by Bob Marley; The Wailers. It is the fourth track on side two of their 1977 album Exodus and was released as a single in 1980. The song reached the Top 20 in the UK, peaking at number 17. It is one of Bob Marley's most popular songs. The song has been covered by numerous other artists. One of the most notable covers was by British singer Connie Talbot, whose version reached number one on the Billboard Hot Singles Sales chart in 2008. "Don't Worry, Be Happy" is a song by musician Bobby McFerrin but is often erroneously attributed to Bob Marley.
Get Up, Stand Up, stand up for your right (3 times) Get Up, Stand Up, don't give up the fight Preacher man don't tell me heaven is under the earth I know you don't know what life is really worth Is not all that glitters in gold and Half the story has never been told So now you see the light, aay Stand up for your right. Come on Get Up, Stand Up, stand up for your right Get Up, Stand Up, don't give up the fight (Repeat) Most people think great God will come from the sky Take away ev'rything, and make ev'rybody feel high But if you know what life is worth You would look for yours on earth And now you see the light You stand up for your right, yeah! Get Up, Stand Up, stand up for your right Get Up, Stand Up, don't give up the fight Get Up, Stand Up. Life is your right So we can't give up the fight Stand up for your right, Lord, Lord Get Up, Stand Up. Keep on struggling on Don't give up the fight We're sick and tired of your ism and skism game Die and go to heaven in Jesus' name, Lord We know when we understand Almighty God is a living man You can fool some people sometimes But you can't fool all the people all the time So now we see the light We gonna stand up for our right So you'd better get up, stand up, stand up for your right Get Up, Stand Up, don't give up the fight Get Up, Stand Up, stand up for your right Get Up, Stand Up, don't give up the fight.

redpajama_set_name: RedPajamaCommonCrawl


"It didn't make sense for us to deny our restaurant owners the opportunity to realize what I think will be a real benefit over the summer," Seils said, adding that he's heard from several restaurant owners enthusiastic to take advantage of the new law.
Orange County Commissioner Penny Rich, who also works in the food industry, told the board how rolling back the start time for alcohol sales could help restaurant workers as well as owners.
Carrboro's town ordinance now permits the sale of malt beverages, wine, fortified wine and mixed drinks starting at 10 a.m. Sundays, the earliest time allowed under the new state law. Mayor Lydia Lavelle noted that with the change, North Carolina becomes one of 47 states that allow Sunday sales before noon.
(Not) everybody is as appreciative of the opportunity to start brunch a little earlier.
Though no one spoke against the brunch bill at the special meeting, Alderwoman Bethany Chaney read into the public record the text of a tweet she received critical of the new rules.
Chaney urged supporters of the Brunch Bill to be respectful in their celebrations and remember that some don't see it as a positive change.
"It struck me that this is a reminder that not everybody is as appreciative of the opportunity to start brunch a little earlier, and there are plenty of people out there that have been hurt by alcohol either directly or indirectly," Chaney said.
Local governments must decide to opt in to the new law. Hillsborough will consider it at a public hearing on July 20. Chapel Hill may wait until regular meetings resume in September.
Rich said Orange County officials are looking to see what businesses, if any, might be affected in the unincorporated areas of the county before deciding if a special meeting is warranted before the fall.


Microsoft stifles innovation. They can't help it. They had a walled garden of corporate customers for so long they have no idea how to compete, and no clue as to how they've damaged the realm of personal computing.


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Canales provides update of Hanna damages
Nueces County Judge Barbara Canales detailed the damage Hurricane Hanna caused at Bob Hall Pier.
CORPUS CHRISTI, Texas — Nueces County Judge Barbara Canales detailed the damage Hurricane Hanna caused at Bob Hall Pier.
Canales said the pier's parking lot was destroyed, the t-head structure at the end of the pier was broken off, railings and power lines and light poles were damaged or destroyed.
There is also a concern about hidden damage, Canales said.
"The structural integrity at this moment is in question and we're going to have to have a thorough engineering analysis in order to answer whether or not this pier has good structure still," Canales said.
For the time being, .the pier and the beach nearby are not allowing visitors because of safety concerns.
There is also a lot of trash and debris that still needs to be cleared out.


Neptune Aviation is the most reliable and innovative aerial firefighting company in the nation. As the primary provider of large airtanker services to the United States Forest Service for more than 25 years, Neptune Aviation has proven to be an invaluable partner. Neptune Aviation employs a proficient cadre of A&P mechanics, FAA certificated repairmen and pilots who meticulously maintain and operate a fleet of 9 BAe 146 firefighting aircraft. Unwavering in our commitment to recurrent training and quality assurance, and adhering to the most stringent safety standards in the industry, Neptune Aviation is proud to serve our nation's ground wildfire crews as the undisputed leader in the aerial firefighting industry.


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\section{Introduction}
Systems of interacting fermions are in superfluid phases at low enough temperatures. Thus the core and inner crust
regions of neutron stars consist mainly of superfluid neutrons. The neutron superfluid in the core,
carrying the bulk of the mass and moment of inertia of the star, is the most important agent in the star's rotational dynamics.
The observed timing properties, the period and spindown rate of the outer crust, are determined by the external
magnetospheric torques as well as the internal torques reflecting angular momentum exchange with the core and inner crust.
The neutron superfluid is coupled to the crust through the interactions of its quantized vortex lines with the charged components,
the protons and the electrons, which are tightly coupled to each other by electromagnetic forces and to the crust through electron viscosity.

The protons in the neutron star core are likely to be in a Type II superconducting phase with
a uniform density array of quantized flux lines carrying the magnetic flux through the core in a state of minimum free energy.
Although it makes up only a few percent of the neutron star's mass and moment of inertia, the
proton superconductor plays a crucial role in the rotational dynamics of the neutron star by defining the physical properties and
interactions of neutron vortex lines. A primary effect of the coexistence of two interacting superfluids, the neutron superfluid
and the proton superconductor is that the two superfluid currents drag each other such that the neutron superfluid
circulation around a quantized neutron vortex line drags a proton supercurrent circulating the vortex line. The induced ``spontaneous''
magnetization of the vortex lines make them scatter any relative electron and proton current strongly.
This effect leads to very short coupling times between the superfluid core and the observed outer crust of a neutron star
(Alpar, Langer \& Sauls 1984).

Observational clues and constraints on the dynamical properties of neutron star cores come from
the study of pulsar timing, pulsar glitches in particular. Glitches are observed sudden increases in the rotation frequency.
There is also a jump in the magnitude of the angular frequency derivative, the spindown rate of the pulsar.
There are no signs of change in the {\em external} magnetospheric torque, as would be reflected as changes in the electromagnetic
signature of the pulsar concurrent with the glitch. This in turn is assumed to indicate that the spin-up of the crust is due to an
exchange of angular momentum {\em within} the star. The timescales found in the relaxation of the system after a glitch extend to the
order of days and months, timescales too long for normal fluid viscosity Ekman processes. This is the argument,
based on observations, for the presence of superfluid components in neutron stars. Fractional changes in the spindown rate at glitches
and during postglitch relaxation indicate that the superfluid component involved contains about a few percent of the star's moment of inertia.
This correlates very well with the inertia of the neutron superfluid in the crustal region. The dynamical properties of the inner crust
superfluid, modeled in detail, explain the observed postglitch relaxation times (Alpar et al. 1993). The implication is that superfluids in
the neutron star's bulk, the core, must be already coupled rigidly to the observed outer crust on timescales shorter than the glitch
rise times, which have been resolved down to about 30 seconds in the Vela pulsar (Dodson, Lewis \& McCulloch 2007).
Calculations of the dynamical coupling times between
a neutron superfluid in the core and the crust and charged components of the star, based on the scattering of charges against
spontaneously magnetized neutron vortex lines, indeed yield such short relaxation
times (Alpar, Langer \& Sauls 1984, Alpar \& Sauls 1988, Andersson, Sidery \& Comer 2006, Sidery 2009).

The vortex lines in the core superfluid should also be interacting with the flux lines carried by the proton superconductor.
Since vortex lines are aligned with the rotation axis and flux lines along the magnetic axis of the neutron star, it is
unavoidable that vortex line motions, in particular motions radially outward from the rotation axis that should take place if the
core neutron superfluid is to spin down, will encounter flux lines. Vortex line flux line junctions are energetically favorable,
as the condensation energy cost of the normal matter phase in the central regions of both types of lines will be reduced by utilizing
the overlap volume at a junction. This potential pinning of vortex lines to flux lines, and modes of vortex line motion against
flux line pinning must clearly play a role in determining the rotational dynamics of the neutron star core, as was first pointed out
by Sauls (1989) as a possible agent for pulsar glitches. The vortex line flux line interaction was also proposed as an agent for
correlated spindown and magnetic field decay on evolutionary timescales for neutron stars in binaries, evolving towards the low
mass X-ray binary and subsequent millisecond pulsar configuration (Srinivasan et al 1990).

When investigating the internal dynamics of neutron stars the various interactions of the two superfluid constituents may be
of comparable importance. In this paper we investigate the dynamics of the neutron superfluid in the star's core by taking into
account, for the first time, the vortex line-flux line interaction together with the previously investigated effect of scattering
of charged particles against the spontaneously magnetized vortex lines.
We treat the neutron star core as a two component system, with superfluid neutrons as one component and
the charged particles, electrons and superconducting protons that are electromagnetically
rigidly coupled together as the second component.
If the charged fluid is treated in similar fashion as the normal component in a terrestrial superfluid,
then comparisons can be made to the dynamics of vortex lines in superfluid Helium.
In contrast to Helium the second component in the neutron star contains magnetic flux tubes.
The interactions between the neutron vortices and the magnetic flux tubes will complicate the dynamics.

There will be several possible scenarios.
The first is that the energy needed for a neutron vortex to overcome the favourable conditions at a junction and pass through a flux line
will be so large that a vortex line effectively never passes through a flux line.
When the neutron vortices' motion is thus locked to another component of the star vortices are said to be pinned.
Because we are considering pinning on flux {\em lines} - prohibition of motion through flux lines - there is still freedom to move
in the direction parallel to the magnetic flux lines.
This is different from the situation often considered in the inner crust superfluid where the neutron vortices pin to the crustal lattice.
In this case the vortices are pinned to specific fixed nuclei and so the vortex has no freedom to move in any direction unless it unpins.
At the other extreme the energy barrier of the obstruction could be so low that the neutron vortices simply pass through the
flux tubes with no hindrance. In between these two cases is that in which the vortices may gain enough energy to pass through via thermal fluctuations,
supporting some average rate of vortex motion in the direction perpendicular to the flux lines.
Thermally activated vortex motion in the presence of pinning barriers
is known as vortex creep (Alpar et al 1984a).

In Section 2 we review the dynamics in the presence of drag forces on neutron vortices alone, setting up the
description of vortex motion in response to local forces as well as the ensuing macroscopic dynamics. In Section 3,
we investigate the case of magnetic flux lines acting as absolute barriers to obstruct vortex motion.
The case of vortex creep across the flux lines is treated in Section 4. In both cases, vortex motion in the
direction parallel to the flux lines is governed by the damping force due to the scattering of charged
particles against the vortices. We consider the creep of vortex lines through a toroidal distribution of
flux lines in Section 5.

We use a simple model in which the superfluid constituents in the star, as well as the normal electron fluid rotate rigidly,
and the rotation axes of all the constituents and the external torques on the star are aligned. The magnetic flux lines
corotate with the charged component (the electrons + the superconducting protons).
The present paper addresses the dynamics of spindown (or spinup) of the neutron star under external torques, leaving the case of
precession to a subsequent paper.

\section{Dynamics with only Drag Forces on Neutron Vortex Lines}

\subsection{Local forces}
Before considering the global dynamical picture one needs to calculate the motion of a single neutron vortex under various forces.
The equation of motion for a vortex line under a force {\bf F} per unit length is the Magnus equation
\begin{equation}
\label{eq:MagnusForce}
    {\bf F} = \rho_{n} {\bf \kappa} \times \left( {\bf v}_{n} - {\bf v}_{L} \right).
\end{equation}
The kinematic right hand side of this equation is sometimes called the ``Magnus force''. Here $\rho_{n}$ is the mass
density of the superfluid neutrons, ${\bf \kappa}$ is the vorticity vector directed along the vortex line, parallel to the rotation
axis, with magnitude $\kappa = h/2m_n$ , the quantum of vorticity in terms of the Planck constant and the bare neutron mass.
${\bf v}_{n}$ and ${\bf v}_{L}$ are the velocities of the neutron superfluid and the vortex line respectively.

The physical drag force on unit length of vortex line, arising from the scattering of charged particles against the magnetization
of the neutron vortex lines has the form:
\begin{equation}
    {\bf F} = C \left( {\bf v}_{c} - {\bf v}_{L} \right) = \rho_{c} n_{v}^{-1}(\tau_v)^{-1}\left( {\bf v}_{c} - {\bf v}_{L} \right).
    \label{eq:notes011}
\end{equation}
The drag coefficient $C$ is expressed in terms of $\rho_{c}$, the mass density of the charged component,
$n_{v} = 2\Omega_n / \kappa$, the number of
vortex lines per unit area in the neutron superfluid rotating at the (uniform) rate $\Omega_n$,
and $\tau_v$ a relaxation time describing the vortex line-charged component interaction.
The velocity of the charged component is denoted by ${\bf v}_{c}$ .

Substituting this drag force in the Magnus Equation, we obtain:
\begin{equation}
\label{eq:forceBalance1}
   C \left( {\bf v}_{c} - {\bf v}_{L} \right) =
   \rho_{n} {\bf \kappa} \times \left( {\bf v}_{n} - {\bf v}_{L} \right).
\end{equation}
Eliminating ${\bf v}_L$ we obtain the force in terms of the velocity lag $({\bf v}_n - {\bf v}_c)$:
\begin{align}
  {\bf F} & = \rho_{n} \kappa \beta' \hat{{\bf \kappa}} \times ({\bf v}_{n} - {\bf v}_{c})
  + \rho_{n} \kappa \beta \hat{{\bf \kappa}} \times \hat{{\bf \kappa}} \times ({\bf v}_{n} - {\bf v}_{c}) \nonumber \\
\label{eq:MutualFriction}
            & = \rho_{n} \kappa \beta' \hat{{\bf \kappa}} \times ({\bf v}_{n} - {\bf v}_{c})
  - \rho_{n} \kappa \beta ({\bf v}_{n} - {\bf v}_{c})
\end{align}
where the last equation holds when, as in the present model, $({\bf v}_{n} - {\bf v}_{c})$ is perpendicular to $\kappa$.
The coefficients $\beta$ and $\beta'$ are introduced to make contact with the conventional notation, employed in work on
superfluid helium (ref.), to describe the strength of the dissipative (antiparallel to ${\bf v}_n$) and inertial
(along $\pm \hat{\kappa} \times \hat{v}_n $) parts of the force per unit length of a vortex line. In terms of $C$ and $\rho_{n} \kappa$
these coefficients are
\begin{equation}
  \beta = \frac{C/\rho_{n} \kappa}{1 + \left( C/ \rho_{n} \kappa \right)^{2}} \qquad \qquad \beta'
  = \frac{ \left( C/ \rho_{n} \kappa \right)^{2}}{1 + \left( C/ \rho_{n} \kappa \right)^{2}}.
\end{equation}
\\
Superfluids with $C_{strong}/\rho_{n} \kappa >> 1,\; \beta << 1,\; \beta' \cong 1$ are said to be in the ``strong coupling'' regime, while
$C_{weak}/\rho_{n} \kappa << 1,\; \beta' \cong \beta^2 << 1$ are in the weak coupling regime.

In cylindrical coordinates with ${\bf \kappa}$ and the angular velocities of the neutron superfluid
as well as the proton-electron component along the z-axis, the superfluid velocity is $v_{n,\phi}= r \Omega_n$, in the azimuthal direction.
We denote the radial and azimuthal components of the vortex line velocity ${\bf v}_{L}$ with $v_r$ and
$v_{\phi}$ respectively. All vortex lines at a given radius will have the same velocity ${\bf v}_{L}$, which
does not depend on $\phi$. Eliminating $v_{\phi}$ in the radial and axial components
of Eq.(\ref{eq:forceBalance1}), we obtain:
\begin{equation}
\label{eq:lineVelFree1}
v_r = \left[ \frac{\rho_n}{\rho_c} 2\Omega_n \tau_v + \frac{\rho_c}{\rho_n}\frac{1}{2\Omega_n \tau_v} \right]^{-1}
(\Omega_n - \Omega_c) r = \left[ \frac{\rho_n \kappa}{C} + \frac{C}{\rho_n \kappa} \right]^{-1}
(\Omega_n - \Omega_c) r = \frac{\rho_c}{\rho_n} \frac {\beta^2}{\beta'} \frac{1}{2\Omega_n \tau_v} (\Omega_n - \Omega_c) r .
\end{equation}

In this paper we shall use the results of Alpar, Langer \& Sauls (1984) who calculated the microscopic
coupling time $\tau_v$ for the scattering of electrons (and the protons which
are tightly coupled to the electrons by electromagnetic interactions) by neutron vortex lines.
The scattering is due to the very strong localized magnetic field structure carried by the neutron vortex lines.
This ``spontaneous magnetization'' arises from proton supercurrents circulating the vortex line, dragged along with
the usual neutron supercurrent circulation.
This mechanism, a two-superfluid effect, gives an extremely short coupling time
\begin{equation}
  \tau_v \cong 6.2 P (\rho_{c,14})^{-1/6} \left( \frac{m_p}{\delta m_p} \right)^2 \left( 1- \frac{\delta m_p}{m_p}\right)^{1/2}
  \cong (10-200) P
\label{eq:tauvortP}
\end{equation}
where $P$ is the neutron star's rotation period, $\rho_{c,14}$ is $\rho_{c}$ in units of $10^{14}$ gm cm$^{-3}$,
$m_p$ and $\delta m_p$ are respectively the proton mass in vacuum and
its deviation from the vacuum value in the neutron star medium,
with the effective proton mass given by ${m_p}^{*} = m_p - \delta m_p$ (Alpar, Langer \& Sauls 1984, Alpar \& Sauls 1988).
The prefactor (10-200) describes the variation of $\tau_v$ with density, proton
fraction and proton effective mass throughout the neutron star core, with shorter coupling times at higher densities.
The proton effective mass is not known very accurately, theoretical calculations giving
${m_p}^{*}/m_p \sim 0.5-0.9$. We have used the results of (Chamel \& Haensel 2006, Baldo \& Ducoin 2009)
at nuclear matter density
$\rho_{nuc} \cong 2.8 \times 10^{14}$ gm cm$^{-3}$ and at $3 \rho_{nuc}$.
The range (10-200) P also reflects the variations in the calculated parameters as reported in these two papers.
Eq. (\ref{eq:tauvortP}) gives
\begin{equation}
  \frac{C}{\rho_n \kappa} = \frac{\rho_c}{\rho_n}\frac{1}{2\Omega_n \tau_v} \sim \frac{\rho_c}{\rho_n}\frac{1}{4\pi (10-200)}
  \sim O(4 \times 10^{-4} - 2 \times 10^{-5})
\label{eq:weakcoupling}
\end{equation}
since the charged component makes up only a
small fraction of the density in the neutron star core, $\rho_c / \rho_n \approx 5 \times 10^{-2}$.
Thus the charge scattering by spontaneous magnetization of the neutron vortex lines leads to short coupling times,
which are nevertheless in the weak coupling regime in the sense of Eq. (\ref{eq:weakcoupling}).
The coefficient in Eq. (\ref{eq:lineVelFree1}) simplifies to
\begin{equation}
\label{eq:lineVelFree2}
  v_r = \frac{\rho_c}{\rho_n}\frac{1}{2\Omega_n \tau_v} (\Omega_n - \Omega_c) r
  = \frac{C}{\rho_n \kappa} (\Omega_n - \Omega_c) r.
\end{equation}

The neutron star core superfluids would be in the strong coupling regime
if much stronger coupling mechanisms existed between the charges and the neutron
vortex lines (Sedrakian \& Sedrakian 1995). Strong coupling would keep the neutron vortex lines almost in corotation
with the
charged component and flux lines. The presence of flux lines therefore should not alter the dynamical
coupling times significantly. The dynamical coupling times obtained from the particular range of
drag coefficients $C_{strong} = \eta$ of Sedrakian \& Sedrakian (1995) are much longer than the observed glitch rise times.
We will derive general expressions for dynamical coupling times
in terms of the parameters $\beta$ and $\beta'$ which can be used for both weak and strong coupling. The model of
Alpar, Langer \& Sauls (1984), which is in the weak coupling regime, will be used for the applications throughout the paper.

\subsection{Macroscopic Dynamics}

We are now ready to introduce equations for $\Omega_n$ and $\Omega_c$, the two macrosopic dynamical variables of the rotational dynamics.
The superfluid is able to spin up or spin down only by radial motion of the vortex lines,
\begin{equation}
\label{eq:spinDownSimple}
\dot{\Omega}_{n} = - \frac {n_v \kappa v_r}{r} = - \frac {2\Omega_{n} v_r}{r}.
\end{equation}
This equation, appropriate for axial symmetry about the rotation axis,
follows from the fact that a superfluid's vorticity resides in quantized vortex lines, whose number density is conserved:
\begin{equation}
\label{eq:vortexcurrent}
\dot{\Omega}_{n} = - \Omega_{n} \nabla \cdot {\bf v}_{L}
\end{equation}
When integrated over a cylindrical volume $\pi r^{2}$ times a unit length, Gauss' Theorem leads to
\begin{equation}
\label{eq:spinDownSimpleInt}
\dot{\Omega}_{n} = - \frac{\Omega_{n}}{\pi r^{2}} \oint v_{r} d l
\end{equation}
where the line integral is on a circle of radius $r$ around the equator of the star in the $x$-$y$ plane
with the $z$-axis parallel to the axis of rotation.
Eq. (\ref{eq:spinDownSimple}) follows with $d l= r d \phi$ and axial symmetry.

The last equality holds in the case of uniform rotation. Substituting the model result in Eq. (\ref{eq:lineVelFree2}) for $v_r$ gives
\begin{align}
\label{eq:nSpindownFree}
\dot{\Omega}_{n} & = - \frac{\rho_c}{\rho_n} \frac{\beta^2}{\beta'} \frac{1}{\tau_v}(\Omega_n - \Omega_c) \nonumber \\
                 & \equiv - \frac{\omega}{\tau_n}
\end{align}
where
\begin{equation}
\tau_n = \frac{\rho_n}{\rho_c}\frac{\beta'}{\beta^2}{\tau_v}
= \left[ \frac{\rho_n \kappa}{C} + \frac{C}{\rho_n \kappa} \right]\frac{P}{4\pi}
\end{equation}
and $\omega \equiv \Omega_n - \Omega_c$ denotes the lag between the rotation rates of the two components.
This is complemented by the angular momentum evolution of a two-component star under an external torque $N_{ext}$,
\begin{equation}
\label{eq:totalSpindown}
  I_n \dot{\Omega}_{n} + I_c \dot{\Omega}_{c} = N_{ext} \equiv I \dot{\Omega}_{\infty}
\end{equation}
where $I = I_n + I_c$ is the total moment of inertia and $\dot{\Omega}_{\infty} = N_{ext}/I$ denotes the steady
state spin down
(or spin up) rate reached asymptotically - hence the suffix ${\infty}$ - when both components are spinning down (or up)
at the same rate.
In the present linear drag force model, Eq.(\ref{eq:notes011}), initial conditions away from the steady state
actually relax
exponentially to the steady state. Eq.(\ref{eq:totalSpindown}) can be written, at each radius $r$ in
an axisymmetric model, as
\begin{equation}
\label{eq:totalAngMomR}
  \rho_n \dot{\Omega}_{n} + \rho_c \dot{\Omega}_{c} = \rho \dot{\Omega}_{\infty}
\end{equation}
where $\rho = \rho_n + \rho_c$ is the total density. In the neutron star core matter is mostly neutrons, with $\rho_c/\rho$
of the order of a few per cent.
From Eqns. (\ref{eq:nSpindownFree}) \& (\ref{eq:totalAngMomR}) we obtain the solution for the lag in rotation rate between
the two components
\begin{equation}
\label{eq:lagSolSimp}
  \omega(t) \equiv \Omega_n(t) - \Omega_c(t) = [\omega(0) - \omega_{\infty}] \exp (- \;t/\tau) + \omega_{\infty}
\end{equation}
where the dynamical relaxation time $\tau$ is
\begin{equation}
\label{eq:scaleTauNTau}
  \tau = \frac{\rho_c}{\rho}\tau_n = \frac{\rho_c}{\rho}\left[ \frac{\rho_n \kappa}{C} + \frac{C}{\rho_n \kappa} \right]\frac{P}{4\pi}
= \frac{\rho_n}{\rho}\frac{\beta'}{\beta^2} \tau_v \cong \tau_v,
\end{equation}
and the steady state lag is given by
\begin{equation}
\label{eq:scaleTauNLag}
  \omega_{\infty} = |\dot{\Omega}_{\infty}|\tau_n = |\dot{\Omega}_{\infty}|\tau_v \frac{\rho_n}{\rho_c}.
\end{equation}

The solutions for $\Omega_n(t)$ and $\Omega_c(t)$ for any initial conditions can be obtained from the solution
for the lag, Eq.(\ref{eq:lagSolSimp}),
and the integration of Eq.(\ref{eq:totalAngMomR}). These solutions are also characterized by
exponential relaxation with the dynamical relaxation time $\tau$.
We note that the result of Alpar \& Sauls (1988) for the dynamical relaxation time, $\tau = \rho_n\;/\;\rho_c \tau_v$, was an artefact of
keeping $\Omega_c$ constant (Andersson, Sidery \& Comer 2006).

The physics of any particular model of superfluid - normal matter coupling is described
by an equation like Eq.(\ref{eq:spinDownSimpleInt}).
When the dependence on the lag $\omega$ is linear the coupling is described by $\tau_n$. The dynamical relaxation time
$\tau$ and the steady state lag $\omega_{\infty}$ scale with $\tau_n$, as given in
Eqs. (\ref{eq:scaleTauNTau}) and (\ref{eq:scaleTauNLag}).
These generic relations hold in two-component models with different physics, as long as
the coupling is linear like in Eq.(\ref{eq:nSpindownFree}) and angular momentum evolution is given by Eq.(\ref{eq:totalSpindown}).

\section{Dynamics with Vortex Line - Flux Line Pinning and Drag Forces}

\subsection{Local forces}

Let us now introduce flux lines. The proton flux lines act as barriers offering obstruction to neutron vortex motion
in the direction perpendicular to the flux lines.
\begin{figure}
    \label{fig:vortexLine}
    \centering
      \includegraphics[width=8cm]{vortexLine2.jpg}
    \caption{A sketch of the neutron star core. In the frame fixed with the charged fluid the magnetic vortices are stationary and
    parallel to the $x$-axis. The neutron vortices can move in the $x$ direction, encountering only the drag force.}
\end{figure}
To impose this we introduce a cartesian coordinate system in which the $z$-axis is parallel to the axis of rotation
(See Figure (\ref{fig:vortexLine})).
We fix the $x$-axis in the direction of the proton vortices (projected on the $x$-$y$ plane) and so the coordinates will
rotate with the proton fluid.
The neutron vortices can move in the $x$ direction, moving parallel to the flux lines, but are obstructed
in the $y$ direction,
perpendicular to the flux lines.

To include the obstruction by the flux lines we use a directionally dependent drag coefficient
and rewrite the balance of forces as
\begin{equation}
\label{eq:notes012}
    {\bf F} = C_{x}\left( v_{x,c} - v_{x,L} \right)\hat{{\bf x}} +  C_{y}\left( v_{y,c} - v_{y,L} \right)\hat{{\bf y}} =
    \rho_{n} {\bf \kappa} \times \left( {\bf v}_{n} - {\bf v}_{L} \right)
\end{equation}
Noting that this still holds in a rotating frame we can set $v_{x,c} = v_{y,c} = 0$ by using the coordinate system
fixed to the proton flux lines, proton superconductor and electrons (the charged, $c$, component).
The $x$ and $y$ components of this equation are
\begin{align}
  C_{x} v_{x,L} &= \rho_{n} \kappa \left( v_{y,n} - v_{y,L} \right)
  \label{eq:notes013}\\
  C_{y} v_{y,L} &= - \rho_{n} \kappa \left( v_{x,n} - v_{x,L} \right).
  \label{eq:notes014}
\end{align}
The case of absolute pinning in the $y$ direction corresponds to the limit $C_{y} \to \infty$ .
Equation (\ref{eq:notes014}) shows that for a reasonable solution we must have $v_{y,L} = 0$.
To put it more carefully, the physical force in the $y$ direction is not necessarily a linear drag force,
it is some probably highly nonlinear force that imposes $v_{y,L} = 0$, so that Eq. (\ref{eq:notes014}) becomes
\begin{equation}
  F_{y} = \rho_{n} \kappa \left( v_{x,n} - v_{x,L} \right).
\label{eq:carenotes014}
\end{equation}
As the vortices are not constrained by the flux lines in the $x$ direction $C_{x}$ is simply the
electron scattering drag coefficient $C$.
Substituting this into Eq.(\ref{eq:notes013}) gives us the force on unit length of vortex line as
\begin{equation}
F_{x} =  - C v_{x,L} = - \rho_{n} \kappa v_{y,n}
    \label{eq:notes015}
\end{equation}
In the $y$ direction we have,
\begin{equation}
  \label{eq:notes0161}
  F_{y} = \rho_{n} \kappa v_{x,n} -  \frac{\rho_{n}^{2}\kappa^{2}}{C} v_{y,n}
  = \rho_{n} \kappa v_{x,n} - \rho_{n} \kappa \frac{\beta}{\beta'} v_{y,n}.
\end{equation}
In the inertial frame where ${\bf v}_{c} \neq 0$ the force per unit length is:
\begin{align}
{\bf F}_{n} & = \rho_{n} {\bf \kappa} \times ({\bf v}_{n} - {\bf v}_{c})
- \frac{\rho_{n}^{2}\kappa^{2}}{C} ({\bf v}_n \cdot \hat{{\bf y}}) \hat{{\bf y}} \nonumber \\
            & = \rho_{n} {\bf \kappa} \times ({\bf v}_{n} - {\bf v}_{c})
            - \rho_{n} \kappa \frac{\beta}{\beta'}({\bf v}_n \cdot \hat{{\bf y}}) \hat{{\bf y}}
\end{align}
which clearly does not have the symmetries of Eq.(\ref{eq:MutualFriction}).

Assuming an array of vortices of constant density $n_{v}$ and expressing the velocities in terms of the angular velocity lag
$\omega$, we find the force density on the neutron superfluid to be
\begin{align}
  F_{x,n} &= - \rho_{n} (\kappa n_{v})\; \omega x \\
  F_{y,n} &= - \rho_{n} (\kappa n_{v})\; \omega y - \frac{\beta}{\beta'} \rho_{n} (\kappa n_{v})\; \omega x.
\end{align}

We should also note that the form of the force in (\ref{eq:notes015}) and (\ref{eq:notes0161}) in the limit of  strong damping by
electron scattering ($C \to \infty$) is the same as in the case with no magnetic flux lines.
In this strong coupling limit the vortices are locked into the charged component (proton superconductor plus normal electrons)
whether the magnetic flux lines are present or not and so the vortex dynamics are not modified by the flux lines.

\subsection{Macroscopic Dynamics}

Up to this point we have derived the macroscopic dynamics from considerations of vortex currents, as in Eq.(\ref{eq:spinDownSimpleInt}).
The dynamics of our two component system can also be formulated in terms of torques.
In this section, for illustrative purposes, we shall present both derivations.

The equations of motion in a frame rotating with the proton fluid will be given by
\begin{equation}
  \label{eq:EqnMotLX}
  I_{X} \dot{\bf \Omega}_{X} + I_{X} {\bf \Omega}_{c} \times {\bf \Omega}_{X} = \int_{Star}  {\bf r}\times {\bf F}_{X} d V
\end{equation}
where $X$ denotes either of $n$ and $c$.

For the neutron fluid component we find
\begin{equation}
  I_{n} \dot{\bf \Omega}_{n} + I_{n} {\bf \Omega}_{c} \times {\bf \Omega}_{n}
  = - 2 \rho_{n} \Omega_{n} \omega \int_{Star}\left\{ x {\bf r} \times \hat{{\bf x}}
  + {\bf r} \times \hat{{\bf y}} \left( y + \frac{\beta}{\beta'} x \right) \right\} dV
\end{equation}
Most of the integral vanishes by symmetry so we are left with
\begin{equation}
  I_{n} \dot{\bf \Omega}_{n} = - 2 \rho_{n} \Omega_{n} \omega \int_{Star} \frac{\beta}{\beta'} x^{2} \hat{{\bf z}}\; dV
\end{equation}
For a spherical star of constant density
\begin{equation}
  \rho_{n} \int_{Star} x^{2} dV = \frac{1}{5} \rho_{n} V R^{2} = \frac{I_{n}}{2}
\end{equation}
where $I_{n}$ is the total moment of inertia of the neutron fluid.
Taking the angular velocity vectors initially in the $\hat{{\bf z}}$ direction,
only the magnitudes of $\Omega_{X}$ will change, according to
\begin{align}
\label{eq:obsSpinDownN}
  I_{n} \dot{\Omega}_{n} &=  - I_{n} \Omega_{n} \omega \frac{\beta}{\beta'}  \\
\label{eq:obsSpinDownP}
  I_{c} \dot{\Omega}_{c} &= I_{n}\Omega_{n} \omega \frac{\beta}{\beta'}.
\end{align}

Alternatively, Equation (\ref{eq:obsSpinDownN}) can be derived using Eq.(\ref{eq:spinDownSimpleInt}),
the relation between spindown rate and vortex current.
In the present case
\begin{equation}
v_r = v_{x,L} \cos(\phi)= \frac{\rho_{n} \kappa}{C} v_{y,n} \cos(\phi) = \frac{\rho_{n} \kappa}{C} r \omega \cos^2(\phi),
\end{equation}
where we have used Eq.(\ref{eq:notes015}), and substituted $v_{y,n} = r \omega \cos(\phi)$.
The integration of radially outward vortex current leads to Eq. (\ref{eq:obsSpinDownN}), in the form
\begin{equation}
\dot{\Omega}_{n} = - \frac{\beta}{\beta'} \Omega_{n} \omega
= - \frac{\rho_{n}\kappa}{C}\Omega_{n}\omega \equiv - \frac{\omega}{\tau_{n,pin}}
\end{equation}
with
\begin{equation}
\tau_{n,pin} = \frac{C}{\rho_{n}\kappa\Omega_{n}} .
\end{equation}
In the presence of an external torque $N_{ext}$ aligned with the angular velocity vectors, Eq. (\ref{eq:obsSpinDownP}) becomes
\begin{equation}
\label{eq:totalSpinDown}
  I_{c} \dot{\Omega}_{c} =  - I_{n}\dot{\Omega}_{n} + N_{ext},
\end{equation}
so that the equation for the lag is
\begin{equation}
    \label{eq:something01}
  \dot{\omega} = - \Omega_{n} \omega \frac{\beta}{\beta'} \frac{I}{I_{c}} - \frac{N_{ext}}{I_{c}}.
\end{equation}
Observed rotation rates of neutron stars have variations of at most a fraction $\Delta\Omega_{c} / \Omega_{c} \sim 10^{-6}$
even in the largest glitches. The lag $\omega$ must therefore be small compared to $\Omega_{c}$ and $\Omega_{n}$, and
(\ref{eq:something01}) can be solved with $\Omega_{n}$ set to a constant representative value $\Omega_{0}$. The solution is
\begin{equation}
\label{eq:omegaObsSol}
  \omega (t) = (\omega(0)- \omega_{\infty}) \exp\left(\;- \frac{t}{\tau_{pin}} \right) + \omega_{\infty}
\end{equation}
which is just Eq.(\ref{eq:lagSolSimp}) with the relaxation time $\tau_{pin}$ appropriate for the present situation.
The dynamical timescale $\tau_{pin}$ over which the two fluids couple is related to the timescale $\tau_{n,pin}$,
with the generic relation
\begin{equation}
\tau_{pin} = \frac{\rho_{c}}{\rho}\tau_{n,pin}
\end{equation}
leading to
\begin{equation}
\tau_{pin} = \frac{\rho_{c}}{\rho \Omega_{0}} \frac{\beta'}{\beta} =
\frac{\rho_{c}}{\rho \Omega_{0}} \frac{C}{\rho_{n} \kappa}
\end{equation}
and $\omega_{\infty} = |\dot{\Omega}_{\infty}|\tau_{n,pin}$.
The solutions for $\Omega_{n}(t)$ and $\Omega_{c}(t)$ are obtained from Eqs. (\ref{eq:totalSpinDown}) and (\ref{eq:omegaObsSol}).
Thus the introduction of flux line - vortex line pinning as an absolute barrier to vortex motion in one direction
reduces the coupling time by a factor
\begin{equation}
    \frac{\tau_{pin}}{\tau} = \frac{\tau_{n,pin}}{\tau_{n}}
    = 2 \beta' \cong 2 \left( \frac{C}{\rho_{n}\kappa} \right)^2 \sim O(3.2 \times 10^{-7} - 8 \times 10^{-10}).
\label{eq:reducedCouplingTime}
\end{equation}

\section{vortex creep}

\subsection{Vortex Creep in the Axially Symmetric Case}

At finite temperature vortex lines can pass (creep) through flux tubes via thermal fluctuations.
We shall model the resulting vortex creep velocity in the $y$ direction by generalizing the model developed for the neutron star crust
superfluid where vortices creep against an isotropic distribution of point pinning centres (Alpar et al 1984a).

We first review this familiar model to set the stage for anisotropic creep against flux lines.
For a vortex line to unpin there is an energy barrier of size $E_{p}$ to overcome.
The rate of spindown of a superfluid is determined by the vortex velocity in the radially outward direction from the rotation axis,
as we saw in Eq. (\ref{eq:spinDownSimple}). The creep velocity in the radial direction is
\begin{equation}
    v_{r} = v_{0} \left[ \exp\left(\;-\frac{E_{p-out}}{kT}\right) - \exp\left(\;-\frac{E_{p-in}}{kT}\right) \right]
\end{equation}
where $v_{0}$ is the average trial velocity against pinning potentials, $E_{p-out}$ and $E_{p-in}$ are
the pinning energy barriers for radially outward and inward motion, respectively.
If there is no lag between the two fluid constituents, $\omega = 0$, then there is no difference in pinning energy barriers
for vortices creeping outwards or inwards; $E_{p-out} = E_{p-in}$ and so $v_{r} = 0$. When the star is spinning down,
driven by an external torque,
the crust and charged constituent is rotating faster than the neutron superfluid ($\omega > 0$).
Vortex motion in the outwards direction will reduce this lag and so is energetically favourable.

A pinned vortex line is dragged along with the crust and charged fluid. A velocity difference will be set up between
the line and the neutron superfluid. According to the Magnus equation, Eq.(\ref{eq:MagnusForce}), a radially inward force must be applied
on the vortex line by the pinning centres. The pinning energy barrier in the outward direction is reduced by an amount
$\Delta E$ proportional to the lag $\omega$, while the barrier to motions in the radially inward direction is enhanced by the same amount.
The pinning barrier $E_{p}$ can sustain a maximum lag $\omega_{crit}$; there is not enough pinning force to keep vortices
pinned at higher lags:
\begin{equation}
\label{eq:pinEnergCrit}
    E_{p} = b \xi F_{critical} = b \xi \rho_{n} \kappa \omega_{crit} r
\end{equation}
where $b$ is the distance between pinning sites and $\xi$, the coherence length, is the radius of the vortex core,
the distance scale over which the pinning force acts. The second equation relates the critical pinning force per
unit length of vortex line to the critical lag through the Magnus equation. At the actual lag $\omega < \omega_{crit}$
the correction $\Delta E$ to the pinning energy $E_{p}$ is
\begin{equation}
    \Delta E = b \xi F = b \xi \rho_{n} \kappa \omega r.
\end{equation}
The energy barrier in the outwards direction is given by
\begin{align}
    E_{p-out} &= E_{p} - \Delta E \\
              &= E_{p} \left( 1 - \frac{\omega}{\omega_{crit}}\right).
\end{align}
Vortex motion in the radially inwards direction faces an energy barrier enhanced by $\Delta E$, so that
\begin{equation}
    E_{p-in} = E_{p} \left( 1 + \frac{\omega}{\omega_{crit}}\right).
\end{equation}
This finally gives the radial creep velocity
\begin{equation}
\label{eqn:creepVelBasic}
  v_{r} = 2 v_{0} \exp \left( -\frac{E_{p}}{kT} \right) \sinh \left( \frac{E_{p}}{kT} \frac{\omega}{\omega_{crit}} \right) .
\end{equation}
Substituting the radial creep velocity in the equation for superfluid spindown, Eq.(\ref{eq:spinDownSimple}) completes the creep model
for the case of an isotropic distribution of point pinning centres.
There will be no creep in the azimuthal direction.

\subsection{Vortex Creep Across Flux Lines}

In the presence of flux lines, vortex motion in the $y$ direction will be determined by creep through the flux lines.
We model vortex motion in the $y$ direction in terms of creep alone, $v_{L,y} = v_{creep}(\omega)$,
ignoring the effects of drag forces. This approach is appropriate in the case of weak coupling drag forces, and is justified
for the drag forces given in Eqs.(\ref{eq:tauvortP}) and (\ref{eq:weakcoupling}). Strictly speaking,
a vortex line moving in the $y$ direction experiences drag forces between encounters with flux lines. For weak enough drag,
the governing rate (bottleneck) for motion in the $y$ direction is given by the very slow rate of creep across the flux lines,
so that the effect of weak coupling drag forces can be neglected. Strong coupling, with drag and creep having comparable effects
on the motion of vortex lines in the $y$ direction requires a more complicated treatment which will not be adressed in this paper.

To find the appropriate expression for $v_{creep}$ we must recalculate $E_{p-out}$ and $E_{p-in}$ or
rather in this case the effective pinning energies of the positive and negative directions along $y$ ($E_{p+}$ and $E_{p-}$ respectively).
Again any bias must be due to vortex motion in the radially outward  or inward direction. This is taken into account
by introducing a factor $\hat{\bf r} \cdot \hat{\bf y}=\sin (\phi)$:
\begin{align}
    E_{p+} &= E_{p} \left[ 1 - \frac{\omega}{\omega_{crit}} \sin (\phi) \right] \nonumber \\
    E_{p-} &= E_{p} \left[ 1 + \frac{\omega}{\omega_{crit}} \sin (\phi) \right].
\end{align}
The vortex lines' velocity in the $y$ direction, due to vortex creep is thus
\begin{equation}
\label{eqn:creepVelFluxlines}
v_{L,y} =  v_{creep}(\omega \sin(\phi)) =
2 v_{0} \exp \left( -\frac{E_{p}}{kT} \right) \sinh \left( \frac{E_{p}}{kT} \frac{\omega \sin(\phi)}{\omega_{crit}} \right) .
\end{equation}

In the $x$ direction, vortices move parallel to the flux lines, at velocity $v_{L,x}$
encountering only the drag force due to scattering of charged particles off the magnetized vortex core.
The components of the Magnus equation Eq.(1) with anisotropy in the rotating frame of the charged component $c$,
analogous to Eqs.(\ref{eq:notes013}) and (\ref{eq:carenotes014}), are
\begin{align}
  C v_{L,x} &= \rho_{n} \kappa \left( v_{n,y} - v_{creep} \right) = \rho_{n} \kappa \left( \omega r \cos (\phi) - v_{creep} \right)
  \label{eq:pincreep1}\\
  F_{y}(\omega) &=  \rho_{n} \kappa \left( v_{n,x} - v_{L,x} \right) = \rho_{n} \kappa \left( - \omega r \sin (\phi) - v_{L,x} \right).
  \label{eq:pincreep2}
\end{align}
Since the vortex line velocity in the $y$ direction can, in principle,
be a nonlinear function of $\omega$, the physical force per unit length $F_{y, creep}$ representing the
interaction of the creeping vortex with the flux lines can also be a nonlinear function of $\omega$.

With these two different vortex line velocities in the $x$ and $y$ directions, the equation of superfluid spindown,
Eq. (\ref{eq:spinDownSimpleInt}) becomes
\begin{equation}
\dot{\Omega}_{n} = - \frac{\Omega_{n}}{\pi r^{2}} \oint \left[ v_{L,x} \cos (\phi)  + v_{L,y} \sin (\phi) \right] r d \phi.
\end{equation}
Substitution from Eqns. (\ref{eqn:creepVelFluxlines}) and (\ref{eq:pincreep1}) leads to
\begin{equation}
\dot{\Omega}_{n} = - \frac{\Omega_{n}}{\pi r^{2}}
\oint \left[\frac{\rho_{n} \kappa}{C} \left( \omega r cos^2 (\phi) - v_{creep}(\omega \sin (\phi)) \cos (\phi) \right)
+ v_{creep}(\omega \sin (\phi)) \sin (\phi) \right] r d \phi.
\end{equation}
The second term clearly integrates to zero. Evaluating the integral in the first term, our equation of motion is now given by
\begin{equation}
  \dot{\Omega}_{n} = - \frac{\rho_{n} \kappa}{C} \Omega_{n} \omega - \frac{2 \Omega_{n} v_{0}}{\pi r}\exp \left( -\frac{E_{p}}{kT} \right)
  \oint \sinh \left[ \frac{E_{p}}{k T} \frac{\omega}{\omega_{crit}} \sin (\phi) \right] \sin (\phi) d \phi
    \label{eq:VelVortexPolar}
\end{equation}

Both of these terms have the same sign, and so taking the first term alone will give us an upper limit on the lag $\omega$.
Taking the Vela pulsar as an example, we have $\dot{\Omega} \approx - 10^{-10}$ rad s$^{-2}$,
$\Omega \approx 70$ rad s$^{-1}$. The range of values of $C/(\rho_n \kappa)$ quoted in Eq.(\ref{eq:weakcoupling})
imply that the lag will be less than $\sim 6 \times 10^{-16}$ rad s$^{-1}$.
This bound implies that the creep term is also linear in the lag $\omega$ since the argument of sinh is very small,
as can be seen using Eq. (\ref{eq:pinEnergCrit}), with a temperature $T = 10^8 K$ and typical parameter values for the
neutron star core.
Eq.(\ref{eq:VelVortexPolar}) becomes
\begin{equation}
  \label{eq:creepTime}
\dot{\Omega}_{n} = - \frac{\rho_{n} \kappa}{C} \Omega_{0} \omega
- \frac{2 \Omega_{0} v_{0}}{ R} \exp \left( - \frac{E_{p}}{kT} \right) \frac{E_{p}}{k T} \frac{\omega}{\omega_{crit}}
\end{equation}
where we have substituted a constant fiducial value $\Omega_{0}$ for the slowly varying $\Omega_{n}$, and taken $R = 10^6$ cm
to represent the radius $r$.
Introducing a relaxation time
\begin{equation}
\label{eq:creepTime1}
\tau_{n,creep} \equiv \frac{R}{2 \Omega_{n} v_{0}} \exp \left( \frac{E_{p}}{kT} \right) \frac{k T \omega_{crit}}{E_{p}}
\end{equation}
and an effective relaxation time
\begin{equation}
\frac{1}{\tau_{n,eff}} \equiv \frac{1}{\tau_{n,pin}} + \frac{1}{\tau_{n,creep}}
\end{equation}
Eq. (\ref{eq:creepTime}) can be written as
\begin{equation}
  \label{eq:effTime}
\dot{\Omega}_{n} = - \frac{\omega}{\tau_{n,eff}}.
\end{equation}
As in the earlier sections, treating this coupling together with the angular momentum evolution, Eq.(\ref{eq:totalSpinDown}), leads to
solutions of the form given in Eq. (\ref{eq:omegaObsSol}) with the dynamical relaxation time
\begin{equation}
  \label{eq:effTime2}
{\tau_{eff}} = \frac{\rho_{c}}{\rho}{\tau_{n,eff}} = \frac{\tau_{pin}\tau_{creep}}{\tau_{pin} + \tau_{creep}}
\end{equation}
where the dynamical relaxation time for creep (in the $y$ direction) is
\begin{equation}
  \label{eq:creepTime2}
{\tau_{creep}} = \frac{\rho_{c}}{\rho}{\tau_{n,creep}}.
\end{equation}
The effective relaxation time is the shorter of $\tau_{pin}$ and $\tau_{creep}$. The ratio of these relaxation times is
\begin{equation}
\frac{\tau_{creep}}{\tau_{pin}}
= \frac{ R}{2 \Omega_{n} v_{0}} \exp \left( \frac{E_{p}}{kT} \right) \frac{k T \omega_{crit}}{E_{p}} \frac{\rho_{n}\kappa\Omega_{n}}{C}.
\end{equation}
We take $T = 10^8 K, kT \approx 10^{-2}$ MeV, a typical density
$\rho = 3 \times 10^{14}$ g cm$^{-3}$, $v_{0} = 10^7$ cm s$^{-1}$, $R = 10^6$ cm,
the coherence length $\xi = 10^{-11}$ cm and the distance between pinning junctions (flux line spacing)
$b \cong 5 \times 10^{-10} (B_{12})^{-1/2}$, where $B_{12}$ denotes the magnetic field in the neutron star core in units of $10^{12}$ G.
We find that $\tau_{creep}$ is the longer timescale unless $E_{p}/kT < 9$. With estimates of the pinning
energy $E_p \sim 0.1 - 1$ MeV (Ruderman, Zhu \& Chen 1998, Srinivasan et al 1990) and $kT \approx 10^{-2}$ MeV, the creep rate is likely to be negligible,
and the core superfluid remains in the very tight coupling with the charged component imposed by the presence of the flux lines.
This result depends only logarithmically on the parameter values we have used.

If the pinning energy is closer to the thermal energy ($E_{p}/ k T < 5 $) then
the creep process determines the relaxation of the core, $\tau_{eff} \cong \tau_{creep}$, somewhat alleviating the almost rigid coupling
to the charged component inferred in Eq.(\ref{eq:reducedCouplingTime}).

\section{toroidal field}

Recent stability simulations of the type of magnetic fields expected in neutron stars (Braithwaite 2008)
suggest the presence of a large toroidal contribution to the internal magnetic field.
In this case the flux lines prevent radially outwards motion of the superfluid vortices in all directions, so that any
spin down of the superfluid must be due to creep. Because of azimuthal symmetry, the macroscopic dynamics will in fact be the
same as in the creep model for
the crust superfluid. If toroidal flux lines coexist with the uniform array of flux lines aligned in the $x$ direction,
reconnection will lead to a toroidal field;
in any case there is no ``easy'' direction with vortices moving outwards against drag forces only.
We therefore assume that the toroidal field is confined to an
equatorial belt surrounding but not overlapping with the core region with poloidal field lines
(here poloidal means a uniform parallel array of flux lines).  The dominant physical process
constraining the radial vortex current is creep against the torroidal flux lines.
The radially outward vortex current will have its dynamics
characterized by the {\em local} values of the lag $\omega$. In the region of toroidal flux lines the lag $\omega$
may have quite different values from the rest of the core.

The equation of motion is
\begin{equation}
\dot{\Omega}_{n} = - \frac{4 \Omega_{0}v_{0}}{R} \exp \left( -\frac{E_{p}}{k T} \right)
\sinh \left( \frac{E_{p}}{k T}\frac{\omega}{\omega_{crit}}\right).
\label{eq:creeptoroidal}
\end{equation}
Vortex creep can operate in the linear or nonlinear regimes (Alpar, Cheng \& Pines 89), depending on a comparison of the
spin down rate determined by the external torque and the efficiency of thermal creep, as reflected in the magnitude
of the sinh function
\begin{equation}
\sinh \left( \frac{E_{p}}{k T}\frac{\omega}{\omega_{crit}} \right) = \frac{4 \Omega_{0}v_{0}}{|\dot{\Omega}_{n}| R}
\exp \left( \frac{E_{p}}{k T} \right)
= \frac{8 \tau_{spindown} v_{0}}{R} \exp \left( \frac{E_{p}}{k T} \right)
\label{eq:sinh}
\end{equation}
where $\tau_{spindown} \equiv \Omega_{0}/2|\dot{\Omega}|$ is the characteristic spindown age of the pulsar.
For the Vela pulsar parameters, the estimate of the sinh is less than 1 if $E_{p}/k T < 31$, or $E_{p} < 0.3$ MeV,
if $T = 10^{8} \; {}^o$K.
In this case Eq.(\ref{eq:creeptoroidal}) is
linearized to give
\begin{equation}
\dot{\Omega}_{n} = - \frac{4 \Omega_{0}v_{0}}{R} \exp \left( -\frac{E_{p}}{k T} \right)
\frac{E_{p}}{k T}\frac{\omega}{\omega_{crit}} \equiv - \frac{2 \omega}{\tau_{n,creep}}
\equiv - \frac{ \omega}{\tau_{n,tor}}.
\label{eq:lincreeptoroidal}
\end{equation}
Thus, in the linear regime creep across toroidal flux lines the relaxation times $\tau_{n,tor}$ and $\tau_{tor}$
are half the corresponding relaxation times $\tau_{n,creep}$ and $\tau_{creep}$ for creep
across flux lines aligned in the $x$ direction.
This is easy to understand since creep operates in the $r$ direction, that is, both $x$ and $y$ motions are allowed,
while in the
latter case creep takes place only in the $y$ direction. The relaxation time of the toroidal region
has a sensitive dependence on $E_p/(kT)$ :
\begin{equation}
\tau_{tor} = \frac{\rho_c}{\rho}\tau_{n,tor}
= \frac{\rho_c}{\rho} \frac{ R}{4 \Omega_{n} v_{0}} \exp \left( \frac{E_{p}}{kT} \right)
\frac{k T \omega_{crit}}{E_{p}} \sim 10^{-8} T_8 \exp \left( \frac{E_{p}}{kT} \right) \textrm{s}
\end{equation}
Thus $\tau_{tor}\sim 3 \times 10^5 s $ for $E_{p}/k T = 31$, the limiting value for linear creep.
If $E_{p}/k T$ is somewhat smaller, the dynamical relaxation time is reduced exponentially;
for example $\tau_{tor} \sim < 2\times 10^{-4} $ s for $E_{p}/k T = 10$.

\section{conclusions}

If flux lines of the proton superconductor are not taken into account, the dynamical relaxation time for the core superfluid is
\begin{equation}
  \tau = \frac{\rho_c}{\rho}\tau_n = \frac{\rho_n}{\rho}\tau_v \cong \tau_v \cong (10-200) P.
\end{equation}
as given in Eqs. (\ref{eq:tauvortP}) and (\ref{eq:scaleTauNTau}), employing the results of (Alpar, Langer \& Sauls 1984).
The range of uncertainty corresponds to the uncertainty in the representative values of the effective proton mass in
the neutron star core.

We have found that the inclusion of the proton flux lines strengthens the coupling between
the neutron superfluid in the core and the charged component of the star, leading to substantially shorter dynamical coupling times.
When flux lines are included as absolute barriers in a poloidal like configuration,
the neutron superfluid spins down by the outward motion of the vortex lines in the ``easy" direction,
parallel to the flux lines, checked only by drag forces.
The dynamical coupling time is reduced by the factor $2 \beta' \cong 2 [C/(\rho_n \kappa)]^2$,
where $C$ is the coefficient of the drag force and $\rho_n \kappa$ is the Magnus inertial coefficient, yielding
\begin{equation}
    \frac{\tau_{pin}}{\tau} \sim 3.2 \times 10^{-7} - 8 \times 10^{-10}.
\end{equation}
Absolute pinning to poloidal flux lines forces the neutron superfluid into effective corotation with
the charged component and outer crust of the neutron star. Allowing vortex creep across the flux lines does not
effect this conclusion. For relevant neutron star core temperatures and
pinning energy estimates for flux line - vortex line junctions, the timescale for creep across the flux lines is typically
much longer than the timescale $\tau_{pin}$ of dynamical coupling achieved by vortex motion parallel
to the flux lines alone, so that the effective dynamical relaxation time with creep present is
not changed, $\tau_{eff} \cong \tau_{pin}$. Thus the presence of flux lines reduces dynamical coupling times
drastically and clamps the neutron star
core superfluid to the crust and charged component.

The likely toroidal arrangement of flux lines circumscribing the core superfluid does not allow any anisotropy
in vortex flow. All vortices have to creep
across the toroidal flux lines if they are to move out radially. If $E_{p}/k T$ is small enough
($E_{p}/k T < 31$ for Vela pulsar parameters, with a similar critical value for other pulsars) creep is
linear, the dynamical relaxation time is simply the creep relaxation time
$\tau_{tor} \sim 10^{-8} T_8 \exp \left( \frac{E_{p}}{kT} \right)$ s.
The toroidal region may well contain values of the pinning energy with $E_{p}/k T$ large enough for
the nonlinear creep regime. In the nonlinear regime, corresponding, for the Vela pulsar parameters, to $E_{p}/k T > 31$, or $E_{p} > 0.3$ MeV, if $T = 10^{8}$K,
The sinh function is approximated with $\sinh(x) = 1/2 \exp(x)$.
The resulting highly nonlinear dynamical model has been successfully
applied to the dynamics of the inner crust superfluid, and invoked to explain basic features of postglitch and interglitch
response in pulsars (Alpar et al 1984b). With its location at the boundary between the neutron star core and superfluid inner crust,
the region with toroidal flux lines could have a moment of inertia fraction $I_p/I \sim O(10^{-2})$, comparable to the
fractional moment of inertia of the superfluid inner crust. The steady state lag $\omega_{\infty} \cong \omega_{crit}$ and
the relaxation times for nonlinear creep in the toroidal region may also be similar to the lag and relaxation times of the inner
crust superfluid. The toroidal region will then have postglitch response signatures similar to those of the inner crust superfluid, and
will be responsible for some of the nonlinear response previously attributed to the inner crust superfluid. This makes
it impossible to draw unambiguous lower limits on the moment of inertia fraction of the inner crust superfluid to use
for constraints on the neutron star structure and equation of state.

Nonlinear creep implies a much larger value of the steady state lag $\omega_{\infty}$ in the toroidal region
than the typical lags in the linear regime, which we found to be extremely small in the neutron star core with
its poloidal (uniform) array of flux lines.
This change in $\omega$ means a sharp increase in $\Omega_n$, and therefore a large density of neutron vortex lines in the boundary
between the core superfluid and the toroidal region. This may well be an axially symmetric vortex reservoir to provide the source
of glitches when vortex lines are unpinned catastrophically. Thus the toroidal region could become an alternative,
or a complement to the inner crust superfluid as a source of glitches as well as being a prominent agent of postglitch relaxation.

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text:
The Party for Renewal and Redemption () is a political party in Togo.
At the last presidential of 24 April 2005, its candidate Nicolas Lawson won 1.04% of the vote.

The party participated in the October 2007 parliamentary election, but did not win any seats in the National Assembly.

References

Political parties in Togo

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text: Rails.application.config.session_store :cookie_store, key: '_bbb_session'

redpajama_set_name: RedPajamaGithub


Now, remove the old 2000 V secondary, being careful not to damage the primary. Battery boxes must be of the vented type to allow for the escape of gases. Some areas to avoid mounting the inverter are under-the-hood, on the floor over the exhaust system, or in sealed areas where moisture could condense. Induction motors will run only with special tricks, reduced or not at all. I even use 5v 2A charger as input and I been able to light up a 13watt cfl. Larger transformers and more powerful transistors can be substituted for T1, Q1 and Q2 for more power.
Now, detach the previous 2000 V secondary, being careful not to break the primary. This makes unnecessary losses and is to be avoided. The most proficient inverter is the pure sine wave which produces an alternating current like to the in wave form. Openings at the bottom of the compartment will let in replacement fresh air. So-called rail-to-rail opamps handle signals very close to the supply voltage limits.
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Better use a compressed air tacker. So it can work through this. Tags: xantrex inverter charger wiring diagram xantrex inverter circuit diagram xantrex inverter wiring diagram. Run both charging cables directly to the alternator. I have an inverter that plugs into an automobile cigarette lighter. The inverter design circuit adopts voltage three phase bridge inverter circuit, its schematic diagram shown in figure 3.
We are beginning with the assumption that the main three system components - inverter, battery, and alternator - have all been chosen. Now protect the windings using tape. I was looking for short circuit protection circuit. But it takes two times the current at 12V to generate 240V as it does 120V. If no then suggest other circuit for suitable for my aim. These old microwave transformers are charged at about 1kilo watts and are ideal.
Also the output voltage was observed to be 89 volts … Please reply and point out the possible errors. When trying to source the variable resistor trimmer or potentiometer one of the specifications is the wattage rating. These devices are capable in running more sensitive devices that a modified sine wave may possibly lead to damage to such as: laser printers, laptop computers, power equipment, digital clocks and medical gear. Do not use the vehicle chassis as a conductor. Theoretically we do not need the snubber.
This is fed into the capacitor through the snubber diode. Pure sine wave inverters, alternatively, generate a sine wave output identical to the power coming out of an electrical outlet. The circuit should not be too difficult to adapt to other mains voltages or frequencies, for example 110 V, 115 V or 127 V, 60 Hz. But now going by the problem with the said inverters, I need to build one that in components can bé adjusted to get the required output wattage anytime myself. But practically we need it anyhow.
I want to connect battery supply from my scooti. Does the load effect the frequiency while in use? What do I really mean? Remove the transformer from the bigger microwave and the bigger transformer being alert not to touch the huge voltage capacitor that might still be charged. This circuit can be tricky to get going. Inverter Schematics The power part… …is simple. These kinds of inverters are considerably cheaper than pure sine wave inverters and therefore are attractive options. At low loads, this makes a rough and non-rectangular voltage shape, both bad for the load and the iron losses in the transformer.
So use a step-down tansformer 12V,1. The same is also available at the bottom of this article too! The name inverter implies first changes alternating current to direct current to charge the battery then, it inverts direct current to alternating current for powering the electric devices There are different types of Inverters are available in the market. Thats all there is to it. Later, I will then add a small solar panel. If u want to connect a charging circuit u can make it of your own. Circuit explanation: circuit diagram of 100 watt dc to ac inverter has been given below. Note that the inverter cannot share an area where combustible fuel vapors exist because switching components could cause ignition.


Fantagio Entertainment had recently announced the debut of their second actor group! They have finally revealed the official members for SURPRISE U.
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Meanwhile, the members have been greeting the fans through their short film project, 'Mini Film Project: Beginning' on Naver's V Live. They show just how great they are at acting! The group will start their debut promotions with a showcase on July 5th. Are you excited for SURPRISE U debut? Let us know in the comments below!
New Girl Group Favorite Begins Teasing For Their Debut!


Kimberly is a 22-year veteran of the aviation industry. She has worked as a customer service representative, flight attendant, and pilot with United Airlines, Fedex Corporation, Northwest Airlines (nee Delta), ExpressJet Airlines and JetBlue Airways respectively. She has also worked in the corporate aviation as a charter pilot. She received a BS in Business Administration from Florida A&M University and an MA in Training & Development from Roosevelt University before completing pilot training at Western Michigan University. She is from and currently resides in Chicago, IL, where in her spare time, she works as a Program Director for the AeroStars Exploration Apprenticeship Program which teaches inner-city high school students about aviation and STEM-related curriculum. Kim also travels around the US speaking to students of all ages about aviation as well as teaching aviation at summer camps. She is a member of the Organization of Black Aerospace Professionals, Women in Aviation, Inc and AOPA.


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State of the States for 2 February: The war on democracy in Virginia, Cuomo's war chest, and Idaho's 'Kansas-style' tax cut
USAPP Managing Editor, Chris Gilson, looks at the week in US state blogging.
In New Hampshire this week, NH Labor News reports that the state Senate has voted to kill a bill which would ban bump stocks in the state, similar to those used in last year's mass shooting in Las Vegas.
Heading south, RIPR says that Rhode Island Governor has kept up her large financial advantage in the state's gubernatorial contest, with over $3.3 million on hand, compared to the $240,000 raised by her closest competitor. Raimondo is also currently enjoying a 40 percent approval rating.
Continuing on to New York, State of Politics writes this week that Deputy State Senate Majority Leader, John DeFrancisco has stated that he will run for the GOP's gubernatorial nomination to take on incumbent Democratic Governor, Andrew Cuomo this fall. The race won't be easy – Cuomo reportedly has a $30 million war chest and is relatively popular.
Save Jersey comments Monday that the announcement by GOP Congressmen, Rodney Frelinghuysen that he will not be seeking another term has already set off a frenzied behind the scenes contest for his replacement. The 11th Congressional district leans Republican, so a busy primary field is to be expected. Staying in the Garden State, Observer has the news that Governor Phil Murphy is beginning his term with a 35 percent approval rating, which is lower than that of his last two predecessors at the same point in their terms.
Down in Pennsylvania, Raging Chicken Press says that Rick Saccone – who is contesting the special election for the state's 18th Congressional district – has done everything he can to suck up to Donald Trump and would be the state's own version of the volatile president.
Blue Virginia writes Friday that there seems to be a "war" on Democracy in the state's General Assembly by Republicans, after the state House Finance Committee moved forward a bill which would reinstate the expired coal tax credit after voting down similar credits for solar power and electric vehicles. They comment that some of the Republican legislators involved have received tens of thousands of dollars from coal and coal related companies.
NC Capitol Connection reports this week that the state's Supreme Court has thrown out a law which would create a bipartisan board over elections and ethics, citing that it is unconstitutional. The ruling will put power back in the Governor's hands to determine the size and structure of state administrative bodies. Staying in North Carolina, Wataugawatch says that state Republicans currently have no announced candidates for 46 state House seats. State Democrats are doing a little better, only lacking 42.
Heading south to the Peach State, GeorgiaPol has the news that under Governor Nathan Deal, the African-American prison rate dropped by 30 percent.
On Monday, Florida Politics looks at three scenarios facing state Democrats in two upcoming special elections this year. They say that the most likely outcome is a win and a loss for the party.
Yellowhammer gives an update in what's been going on in the state legislature. Bills making their way through the process include one which would authorize county commissioners to hold voter referendums to approve gas tax increases to fund road projects, a law to extend the state's Stand Your Ground law to churches, and one which would criminalize voyeurism.
In Texas, Juanita Jean lets us know that despite his December guarantee that he would, Congressman Blake Farenthold has not yet repaid $84,000 of taxpayer dollars he used to pay off a woman he sexually harassed.
On Thursday, Michigan's eclecta blog reports that gubernatorial candidate, Abdul El-Sayed, has gone negative in his campaign, calling his rival and fellow Democrat, Gretchen Whitmer a "sub-standard candidate" and comparing her to Donald Trump-style Birthers.
Moving on to Illinois, Capitol Fax rounds up coverage of Governor Bruce Rauner's State of the State including comments that he was vague in his proposals for achieving economic development in the state as well as in his plans to roll back income taxes.
Right Wisconsin takes a look at state conservatives' spring legislative agenda; they argue that they should be looking at measures to reduce red tape in occupational licensing, ending the practice of civil asset forfeiture, and allowing terminal patients the 'Right to Try'. Staying in the Badger State, The Political Environment comments that Governor Scott Walker has moved from "divide-and-conquer" to "unify-and-collect" tactics, after a number of big-dollar campaign contributions.
In North Dakota this week, Say Anything blog writes that state Democrats are continuing to struggle with candidate recruitment, with low attendance levels for conventions covering several legislative districts.
Dakota Free Press talks poop on Friday, or more precisely, Republican state legislators' obsession with it, in the context of two new bathroom bills which have been floated. These measures would require warning labels on multi-person or unisex restrooms and for public school districts to have a policy regarding the use of bathrooms and lover rooms by the transgendered.
West and Pacific
On Wednesday, The Montana Post reckons that Congressman Greg Gianforte is now trolling voters as he has been selected as a speaker at an upcoming communications workshop for the National Republican Congressional Committee, despite generally eschewing public town hall meetings.
Moving on to Idaho, The Spokesman Review reports that state House Democrats have decried a proposal to cut $202 million in state taxes as "reckless", and have argued that it could make the state more like Kansas, which saw its revenues shrink and major budget cuts made following similar tax decreases.
In the Golden State this week, Fox & Hounds says that despite what some in the media have been claiming, US Senator, Dianne Feinstein has no Democratic primary challenger. In fact, there is no primary at all. CALMatters talks the state's gubernatorial election on Wednesday, commenting that in a recent candidates' event, four Democrats who are running to replace Governor Jerry Brown struggled to disagree on anything much at all.
Over in Alaska, The Mudflats says that state Senator Senator David Wilson from Wasilla has given an "epic non-apology" of a press conference following accusations of inappropriate conduct towards a high-level staffer.
Heading out to Hawaii, Honolulu Civil Beat writes that the state's Attorney General, Doug Chin, will be stepping down to serve as Lieutenant Governor after the state's Senate President and House Speaker both declined to take the position.
Featured image credit: J. Stephen Conn (Flickr, CC-BY-NC-2.0)
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February 2nd, 2018|State of the States|0 Comments


Downpour Theatre Company presents Shakespeare's The Comedy of Errors, one of his shortest yet wittiest plays.
Downpour Theatre Company is no stranger to open air theatre, having been named in honour of a particularly damp final performance of their debut production, A Midsummer Night's Dream back in 2016.
Click the button below to buy tickets for The Comedy of Errors. Being outdoors, please bring your own seating (blankets, camping chairs, etc) and dress for the weather!


We spent four amazing days by Lake Como last week, visiting our very good friends Mireille & Gaudenz and their two boys. They have a beautiful house there overlooking the lake and they took us to all their favourite places in the region. Amazing food, wine and scenery, one of our best holidays ever!